All of this sheds light on something we intuitively know: as we move the mic further from the sound source we get more reverberation (aka room sound). What really happens, as confirmed by the previous graph, is that as we move further from the sound source the reverberation stays the same but the direct sound decreases. The end result is perceptually the same: with more distance the room sound becomes more apparent. When we move the mic(s) further from the sound source we increase the gain to bring the direct sound back up to the desired level, and the increase in gain brings the reverberation up with it unless we change to a polar response with a higher Distance Factor.

Comparing Distance Factors

The illustration below provides a visual explanation of the Distance Factor values. On the left there is a single sound source (a speaker) placed in a large space. The reverberation of the space, which is evenly distributed throughout the room, is represented by the opaque blue background. Extending out from the speaker is a horizontal green line indicating the direct sound, on-axis from the speaker. A series of dots appear along the green line, each representing the distance and location that a particular polar response must be placed – relative to the omnidirectional polar response – to ensure that each polar response captures the same balance of direct and reverberant sound.

THE THREE Rs OF ACOUSTICS

Acoustics is the study of sound behaviour in enclosed spaces (i.e. rooms). Most of that behaviour depends on a) the frequency of the sound, b) the dimensions and shape of the room, c) what the room’s surfaces are made from, and d) the amount of sound absorptive materials within the room. The interaction of these parameters brings us the well-known acoustic phenomena of resonance, reflections and reverberation – which collectively form the Three Rs of Acoustics.

Acousticians and architects use the term ‘cuboidal room’ to describe any room that has six surfaces (four walls, a floor and a ceiling), and in which all adjacent surfaces meet at 90° – even if the room is not actually a cube. So why do they call it cuboidal? If all of the room’s surfaces were adjusted to the same dimensions the room would have six surfaces of equal size, all connecting at 90° – which is a cube. Hence a room with six surfaces and in which all adjacent surfaces connect at 90° can be described as cuboidal because it shares many of the same properties as a cube.

For the following shallow dive into room acoustics we’re going to assume a cuboidal room of rectangular shape (as used in the preceding illustrations), which is referred to as a rectangular cuboidal room. We’re also going to assume the room’s surfaces have sufficient mass and rigidity to reflect frequencies below 20Hz – a theoretically convenient assumption that is actually quite difficult and expensive to achieve in practice.

With those qualifying remarks out of the way, let’s take a closer look at the Three Rs of Acoustics…

R1: Resonance

At low frequencies, where the wavelength is relatively large within the room, the sound energy behaves like huge waves moving back and forth between the room’s surfaces. At these frequencies resonant behaviour dominates, resulting in resonating frequencies or simply resonance.

Resonance occurs at any frequency that has a half-wavelength equal to one or more of the room’s dimensions (it also occurs at frequencies that have a half-wavelength equal to diagonal combinations of the room’s dimensions, but we’re not going to get Pythagorean here). Every resonance repeats at integer multiples of its fundamental frequency, creating harmonic resonances up until the wavelength becomes relatively small within the room – at which point the sound behaviour transitions from resonance to reflections (more about reflections shortly).

When a frequency is resonating the positive peaks of its waveform will always occur at one place within the room, and the negative peaks of its waveform will always occur at another place within the room. As a result, the waveform appears to be standing still – hence it is referred to as a standing wave. It appears to be standing still, but the resonating sound energy is actually moving back and forth over itself, re-tracing and overlapping the same waveform with every repetition. The overlapping waveforms reinforce, resulting in SPL increases of up to +6dB at the positive and negative peaks. Meanwhile, the points where the waveform crosses the zero point (between the positive peaks and the negative peaks) represent areas of no SPL (-∞dB) and are essentially nulls for that frequency.

If we place the microphone in a positive or negative peak of a standing wave we’ll capture a sound in which notes at or near the resonant frequency will boom out over other notes, and we’ll need to use EQ to fix them. Conversely, if we place the microphone in a null of a standing wave we’ll capture a sound in which notes at or near the resonant frequency will be too soft compared to other notes, and, again, we’ll need to use EQ to fix them. Moving the microphone to different positions within the room will capture different balances of the peaks and nulls of the standing waves.

A cuboidal room has three ‘modes’ of resonant behaviour, known as the axial modes, the tangential modes and the oblique modes. The axial modes are the most significant and the most problematic, and are therefore the modes we’ll be focusing on in this shallow dive into resonance…

The axial modes occur between any two opposing surfaces, therefore a cuboidal room has three axial modes: one along the axis of the room’s length, one along the axis of the room’s width, and one along the axis of the room’s height. Each axial mode will have a fundamental resonance at the frequency that has a half-wavelength equal to the room dimension it occurs within (i.e. length, width or height). If we know the room’s dimension we can calculate the fundamental resonant frequency for the axial mode with the following formula:

fr₁ = v / (2 x d) Hz

Where fr₁ is the fundamental resonant frequency in Hertz, v is the velocity of sound propagation in air in metres per second (344m/s at 21°C), and d is the length of the room dimension in metres.

Let’s say a room has a length of 10m, a width of 5.8m and a height of 5m. Its fundamental axial mode resonances are shown in the illustration below:

The SPL of each resonant mode is represented with coloured shading. Darker shading represents higher SPLs (up to +6dB against the walls), while the white area through the centre of each illustration represents a null in the SPL (-∞dB). The axial mode for the room’s length is represented in red, the axial mode for the room’s width is represented in green, and the axial mode for the room’s height is represented in gold. Each of these fundamental axial mode resonances will be accompanied by harmonic resonances that extend higher into the frequency spectrum until reaching a frequency where the sound behaviour transitions from waves to reflections.

Contrary to popular belief, the surfaces do not have to be strictly parallel to create resonance; if they are facing each other and have sufficient mass and rigidity to reflect the sound energy, a resonance will occur between them. Hence they are usually referred to as ‘opposing surfaces’ rather than ‘parallel surfaces’. [Parallel reflective surfaces create the familiar ‘ping’ of flutter echo, which is a form of reflection not resonance.]

What does this have to do with Distance Factor? The following examples demonstrate the combined effects of Distance Factor, polar response and resonance. For these examples we will primarily focus on the axial mode resonances for the room’s length, with occasional reminders that the same process is occurring for the room’s width and height – each with its own fundamental resonance and harmonic resonances.

The illustration below is the same as the earlier illustration for Distance Factor except the reverberation (opaque blue) has been replaced with shades of red representing the SPL of the fundamental axial mode for the length of the room. As with the preceding illustration, darker shades of red represent higher SPLs for fr₁ (up to +6dB), lighter shades of red represent lower SPLs for fr₁, and the white areas represent nulls where fr₁ is theoretically non-existent (-∞dB). The intensity of the red shading seen within each polar response shows how much of fr₁ will be captured by that polar response at that position.

As a matter of interest, unwanted resonances are controlled by the strategic placement of tuned absorption. This typically consists of a sealed enclosure with a port or diaphragm that’s designed to resonate at the frequency that needs to be absorbed, and is typically placed in a peak of the resonance’s SPL. The enclosure contains absorptive material to dissipate any sound energy that is resonating within it, which it has, of course, taken out of the room. To understand why we need to use tuned absorption rather than a sheet of foam, we have to understand the scale of the problem. For example, let’s consider a resonance occurring at 20Hz. At a room temperature of 21°C, one cycle of 20Hz is 17.2m long and is travelling through the air at a velocity of 344 metres per second (that’s the velocity of sound propagation, aka ‘the speed of sound’, at 21°C). There are 20 of them occurring every second, and they’re all joined end-to-end to form the equivalent of an acoustic freight train travelling at the speed of sound through the room. No matter how much we want to believe the wish-casting for the cheap and easy ‘sheet of foam’ solution, the reality is that we’re not going to stop something that big and that fast by sticking a sheet of foam on a wall. That’s as futile as trying to stop a runaway bus by putting a line of traffic cones across the road. Resonance is just one part of the physics of sound, and that is why we have acousticians – but let’s get back to microphones…

R2: Reflections

As the frequency gets higher its wavelength gets shorter, eventually becoming relatively small within the room. At these frequencies the sound becomes more directional. Rather than creating resonance, it behaves like a ray of light reflecting off a mirror and therefore ray theory applies.

The basic rule for reflections is:

Angle of Reflection = Angle of Incidence

If the sound energy hits the wall at, say, 45° to the left side of the reflection point, it will be reflected at 45° to the right side of the reflection point. Similarly, if the sound energy hits the wall at 30° to the left side of the reflection point, it will be reflected at 30° to the right side of the reflection point. The reflected sound energy will be the mirror image of the incident sound energy.

The illustration above shows what happens when we change the angle of the microphone. In this case, we have rotated the bidirectional polar response by 90°; the kind of thing that might happen when a well-meaning non-engineer mistakes your Royer R121 for a shotgun mic and re-adjusts its angle to aim the end of the mic at the sound source. As we can see, the direct sound (green) has been completely rejected by the bidirectional’s side null, while the balance of the reflections it captures is significantly different. We’ll delve further into these kinds of on-axis and off-axis polar response calculations in a forthcoming instalment of this series.

As a matter of interest, unwanted reflections can be controlled by the strategic placement of broadband absorption to absorb the reflection (i.e. sticking sculpted open cell foam on the reflection point), or by the use of appropriately angled surfaces to re-direct the reflection elsewhere (angled walls, portable baffles and gobos with a reflective surface), or by the use of diffusion to scatter the reflected energy in numerous directions (irregular surfaces, quadratic residue diffusors, etc.). Reflections are just part of the physics of sound, and that is why we have acousticians – but let’s get back to microphones…

R3: Reverberation

If the sound source is continuous (let’s say the speaker is reproducing a 1kHz sine wave at a constant SPL) the sound energy will continue reflecting around the room, creating new pathways in accordance with the ‘angle of reflection = angle of incidence’ rule, until the reflections eventually fade out. Each reflection is like a billiard ball rolling across the table and bouncing off the cushions until it eventually dissipates all of the energy that made it start moving – at which point it has rolled to a stop. [The difference between the reflection and the billiard ball in this analogy is that the reflection does not slow down as it loses energy, it maintains the same velocity but loses SPL instead. Where the billiard ball rolls to a stop, the reflection fades to inaudibility.]

Eventually there will come a point where the sound energy travelling around the room is being dissipated ‘out’ of the room (by absorption, transmission through walls, and the Inverse Square Law) at the same rate that it is being put into the room by the sound source (e.g. a speaker). The overall sound energy in the room reaches a ‘break-even point’ where energy in = energy out, resulting in a consistent SPL. This point in time is known as the onset of steady state energy, and is the beginning of reverberant behaviour in the room. If the sound source suddenly stops we’ll clearly hear the characteristic sound of reverberation as hundreds, perhaps thousands, of individual reflections are absorbed out of the room – fading to silence one after another.

For any given room, the level of the reverberation and how long it takes to dissipate after the sound source stops (aka the reverberation time or Rt₆₀) is determined by the amount of absorption in the room. This includes the absorptive contribution of tuned absorbers that are designed to control resonances, the absorptive contribution of broadband absorption and diffusion that has been placed to control early reflections, the absorption of soft furnishings, and also the absorptive contribution (if significant) of people within the room. In most cases, additional absorption and/or diffusion will be placed around the room to achieve the desired reverberation curve (a graph of reverberation time vs frequency). Getting the correct reverberation curve (as represented on a graph of reverberation time versus frequency) for the room’s intended purpose is just part of the physics of sound, and that is why we have acousticians – but let’s get back to microphones…

R is for Revision

So the Three Rs of Acoustics are resonance, reflections and reverberation. What do they have to do with Distance Factor?

We know that reverberation is used as a reference to define the Distance Factor, and we know that the reverberation’s SPL won’t change no matter where the microphone is placed within the room – assuming it is a true diffusive field.

We also know that, for any given location of the sound source within the room, different microphone locations will result in different balances of the direct sound, the resonances and the reflections relative to the level of the reverberation. As a matter of interest, it also works the other way: for any given placement of the microphone within the room, different locations of the sound source will result in different balances of the direct sound, the resonances and the reflections relative to the level of reverberation captured by the microphone. In other words, moving the microphone and/or the sound source will affect the balance of direct sound, resonance and reflections (relative to the reverberation) captured by the microphone.

This same acoustic behaviour has major ramifications in control room design because the placement of the monitor speakers and the placement of the listening position both have an impact on the monitored sound heard by the engineer. Getting those monitor and listening positions right is just part of the physics of sound, and that is why we have acousticians – but let’s get back to microphones…

MICS ARE ACOUSTIC SUMMING MIXERS

The illustration below shows an omnidirectional polar response placed at a distance d from the sound source. We can think of this microphone as a two-channel acoustic summing mixer with one input for the direct sound and one input for the reverberation.

The ‘fader’ for adjusting the level of the direct sound is the distance between the sound source and the microphone: changing the microphone’s distance from the sound source changes the level of the direct sound it captures without affecting the level of the reverberation.

The ‘fader’ for adjusting the level of the reverberation is the Distance Factor: for any given distance, changing the microphone’s Distance Factor will change the level of the reverberation it captures without affecting the level of the direct sound.

To represent a frequency properly we must be able to fit at least half a wavelength of that frequency into the room. Therefore, for the purposes of this discussion, we will consider a room to be ‘acoustically small’ if any of its dimensions (i.e. length, width or height) is less than 8.6m and therefore cannot fit a half-wavelength of 20Hz – which is the lowest frequency of interest for most audio applications. A room may seem big to us as human beings, but if one or more of its dimensions is less than 8.6m it will be sonically claustrophobic to sound energy at 20Hz (remember, one cycle of 20Hz is 17.2m long in the air). In acoustically small spaces we can expect audible room resonances that will require tuned absorption to control them. We can also expect problems from first order reflections because they have travelled relatively short distances and will therefore have short arrival times accompanied by significant SPLs, meaning we need to listen carefully for comb filtering problems and a general ‘roomy’ or ‘boxy’ tonality. Broadband absorption and/or diffusion will be required to control the first order reflections, and more will then be added to bring the room’s reverberation curve to specification.

Most multitrack studios that are designed for recording popular music use acoustically small rooms. The engineer deals with the above-mentioned problems by a) careful placement of instruments and microphones within the room to minimise the effects of resonant modes, b) close-miking techniques with directional microphones to minimise the capture and significance of off-axis sounds, and c) the use of portable gobos (used as isolators, absorbers, diffusors and/or deflectors) to prevent first order reflections and spill from reaching the microphones. Similar close-miking and isolation techniques are used on stage when providing sound reinforcement. We’ll be looking at these studio and stage techniques in a forthcoming instalment of this series.

In most of the above cases (the concert hall and the multitrack recording studio) there has been acoustic treatment applied to control some or all of the Three Rs, which can make a significant improvement if done right and might even make many of the above-mentioned problems go away.

SUMMING IT ALL UP…

Let’s get back to a worst-case scenario where there has been no acoustic treatment. The illustration below is the same as the previous illustration, but the opaque blue background that represents the room’s reverberation has now been overlaid with the fundamental resonance of the room’s length, fr₁, in red, and the first order reflections from the sound source to the microphone in dark blue.

Moving either of the microphones in the above illustrations to different positions within the room will result in different balances of direct sound, resonances and reflections relative to the level of the reverberation – as will changing the polar response or even simply changing the direction the microphone is facing. The microphone is, essentially, a passive summing mixer with an EQ on the output, and we control the mix and the EQ by where we place the microphone in the room and which polar response and Distance Factor we choose.

SUMMARY

Distance Factor is a simple yet binding concept that brings together a significant amount of audio theory and practice in a way that few other audio concepts can. There’s not a lot to say about the Distance Factor, but there’s a lot to say around it.

The placement of the sound source within the room determines which resonances and reflections it creates, and where we place the microphone determines which resonances and reflections it captures. The polar response determines how much of the early reflections and indirect sound the microphone captures, and the Distance Factor determines how much reverberation it captures. Small changes in distance, angle, polar response and Distance Factor can make big differences to the captured sound.

The next time you’re making a slight change to a microphone’s distance or angle and some dumbass musicians cynically scoff “as if that’s going to make any difference”, remember those same dumbasses are paying you to do something they cannot do – capture an acceptable sound quickly and consistently based on an understanding of the complex relationships between the sound source, the polar response, the resonances, the reflections and the reverberation. That is why we are sound engineers – but let’s get back to microphones…

Acceptance Angle

In an earlier instalment of this series we discussed a microphone specification called Sensitivity, which tells us how much signal voltage will come out of the microphone when an on-axis sound source is reproducing a 1kHz sine wave with an SPL of 94dB at the diaphragm. We learnt that to minimise the risks of noise and distortion from our mics and/or preamps we should use mics with high Sensitivity for capturing soft sounds, and we should use mics with low Sensitivity for capturing loud sounds.

The Sensitivity specification assumes the sound source is arriving on-axis to the diaphragm, i.e. the angle of incidence is 0°. We can think of the polar response as an off-axis Sensitivity measurement, showing how the microphone’s Sensitivity changes depending on the angle of incidence.

As we already know, the polar response measurement begins at 0° (on-axis) with the microphone’s output gained up to reach a metered level of 0dB. If the microphone has any directionality (i.e. it’s not omnidirectional), we will see a reduction in the metered level as we move the sound source away from 0° and around the microphone. The sound source hasn’t changed its frequency, its SPL at the diaphragm, or its distance from the mic. The only change has been its angle of incidence to the microphone’s diaphragm, and this has created a decrease in the microphone’s output level that ultimately represents a decrease in the microphone’s Sensitivity; we can say that the microphone becomes less sensitive when the sound source is moved off-axis.

Rejection Null(s)

In addition to being most sensitive to sounds arriving at 0°, most directional microphones have one or more angles of incidence at which the microphone is least sensitive. These angles of lowest sensitivity often appear as deep notches or nulls in the polar response, and are called rejection nulls because they offer the highest rejection of incident sound. (The use of the word ‘null’ might seem extreme because it implies a complete rejection, which only occurs with the bidirectional polar response. It was the first of the directional polar responses, and every other directional polar response contains a bidirectional component, so the word ‘null’ remains valid.)

Understanding how to use a microphone’s rejection nulls is one of the most important aspects of microphone choice and placement. Anyone can point the front of a microphone at the sound they want; a monkey can be trained to do that, and therefore so can you. The real challenge, and reward, lies in choosing a polar response that allows us to aim the front of the mic at the sound we want while simultaneously aiming its rejection null(s) at the sound(s) we don’t want. Capturing more of the sound we want and less of the sound(s) we don’t want results in cleaner sounds overall and less work downstream. We’ll learn more about doing that in the forthcoming instalments of this series…

All of the following polar response illustrations have their rejection nulls (if any) indicated with blue arrows.

Distance Factor

The Distance Factor specification is a simple way of representing and comparing the directionality of different polar responses. As a broad generalisation, a higher Distance Factor means a higher on-axis directionality and, therefore, a narrower Acceptance Angle. There are some exceptions to this generalisation, but before we can understand those exceptions we must become familiar with the common polar responses – which we’re about to do. We’ll look at Distance Factor in detail in the next instalment of this series…

Small and/or short shotgun mics are often seen mounted on top of cameras for on-the-go vlogging purposes. This on-camera placement is good when the microphone/camera combination is held at an arm’s length and facing the presenter, but when shooting at distances that put the camera more than an arm’s length from the voice it is best to keep the microphone close to the voice by removing it from the camera and placing it on a microphone stand (Youtubers) or a boom pole (film/TV/documentary applications). The camera goes where the camera needs to go for the best visuals, and the microphone goes where the microphone needs to go for the best sound. The best placement for the camera is rarely the best placement for the microphone, and vice versa. It’s physics, not magic…

Hemispherical Polar Response

As with the lobar/shotgun polar response described above, the hemispherical polar response takes one of the existing polar responses and combines it with an acoustic modifier, in this case a flat surface or boundary. Microphones that offer a hemispherical response are often referred to as boundary microphones, Pressure Zone Microphones or PZMs (note that ‘Pressure Zone Microphone’ and ‘PZM’ are trademarks of Crown International).

The simplest form of the hemispherical polar response is created by embedding a microphone with an omnidirectional polar response into a boundary such that its diaphragm is flush with the boundary, as shown below:

Microphones with hemispherical polar responses are designed to be flush-mounted on a flat surface such as a wall, a floor or a desk. This placement increases the size of the boundary and extends their low frequency response. They are commonly placed on conference room desks to capture what is being discussed without placing a microphone in front of each person. They can also be placed on the wall or window of a recording studio to capture a very useable room sound.

It’s worth noting that Crown has pushed the boundary idea further and created a range of specialised polar responses for different applications. The PCC160 (shown below) is an interesting variation that replaces the boundary-mounted omnidirectional capsule with a boundary-mounted supercardioid capsule, creating a half-supercardioid polar response. It’s often used for theatrical sound reinforcement where two or more are placed across the front of the stage floor to capture the sounds of footfalls (dancing, acrobatics, flamenco, etc.), or to capture large groups singing in music theatre applications where it is impractical to fit a lavalier microphone on every performer. If placed slightly forward of any floor monitors, and/or angled appropriately, the rear nulls can be used to increase gain-before-feedback considerably.

We’ll discuss boundary mics and their applications in further detail in a forthcoming instalment.

CONCLUSION

In this instalment we’ve looked at the eight most commonly used polar responses throughout the numerous aspects of the audio industry. Some of these are very well known (cardioid), some are far more popular than we would assume (every mobile phone contains an omnidirectional microphone), and others offer varying degrees of speciality that make them commonplace in some aspects of professional audio but unheard of in others.

In the next instalment we’re going to dive deeper into polar responses and their Distance Factors. After that we’ll explore the topic of ‘off-axis response’ which helps us understand why microphones don’t always perform as their polar responses would suggest.

If the delay time is between 25ms (0.025s, half the period of 20Hz) and 25us (0.000025s, half the period of 20kHz) the cancellation will be somewhere between 20Hz and 20kHz, placing it within the audible bandwidth and possibly causing a problem.

The frequency that is delayed by half of its period is not the only frequency affected by the delay; it is simply the lowest frequency that complete cancellation will occur at (assuming both signals have the same magnitude). For this reason it is referred to as the fundamental cancellation frequency or fc. Cancellation also occurs at all odd-numbered integer multiples of fc (i.e. 3 x fc, 5 x fc, 7 x fc, etc.), and reinforcement occurs at all even-numbered integer multiples of fc (2 x fc, 4 x fc, 6 x fc, etc.). How and why does that happen? Read on…

Cancellation & Reinforcement

The illustration below shows how a single delay creates fc and its integer multiples of cancellations and reinforcements, in this case up to 7fc (i.e. 7 x fc). In theory the pattern of cancellations and reinforcements would repeat infinitely, but we don’t have enough on-screen bandwidth for that so we’ll stop at 7fc.

At the top of the illustration we see two sine waves with a delay between them. The original signal is shown in green, and is the frequency with a period equal to twice the delay time – therefore the delay time is equal to half of the period, putting this frequency 180° out-of-phase with itself. This is fc. [Note that the illustration shows two cycles of fc to help illustrate the comb-filtering effect.] The delayed signal is shown in blue and we can see that, because of the delay, it begins exactly half a cycle – or 180° behind – the original signal. Both signals have the same magnitude, but the 180° phase difference between them means they have opposing polarities. We can correctly say that they are ‘180° out-of-phase’. When both signals are added together they will cancel each other out, causing a null in the frequency response at that frequency.

Beneath that we see what happens at 2fc (i.e. 2 x fc, meaning the frequency is now twice fc and therefore it completes two cycles in the time taken for fc to complete one cycle). The same delay time that was equal to a half cycle of fc is equal to a full cycle at 2fc. Therefore the delayed signal (blue) has been delayed by one full cycle, or 360°, behind the original signal (green). We can correctly say that these two signals are ‘360° out-of-phase’. Both signals have the same magnitude, and the 360° phase shift means they both have the same polarity. When both signals are added together they will completely reinforce each other, resulting in a combined signal that has 6dB higher magnitude than either the original signal or the delayed signal. In this example we see that the same delay that caused cancellation at fc causes reinforcement at 2fc.

Moving down, we see what happens at 3fc. At this frequency the delayed signal is 1.5 cycles, or 540°, behind the original signal. We can correctly say that the two signals are ‘540° out-of-phase’. Both signals have the same magnitude but opposing polarities, resulting in cancellation when added together. The same delay that caused reinforcement at 2fc causes cancellation at 3fc.

Moving further down we see what happens at 4fc. The delay time that was equal to a half cycle of fc is equal to two full cycles at 4fc. Therefore the delayed signal (blue) has been delayed by two full cycles, or 720°, behind the original signal (green). We can correctly say that these two signals are ‘720° out-of-phase’. Both signals have the same magnitude, and the 720° phase shift means they both have the same polarity. When added together they will completely reinforce each other, resulting in a 6dB increase of magnitude for the combined signal – just as we saw at 2fc. The same delay that caused cancellation at fc and 3fc creates reinforcement at 4fc just as it did at 2fc.

This pattern of cancellation and reinforcement repeats as we continue down the illustration (and therefore up the frequency spectrum). At 5fc the delayed signal is 2.5 cycles behind the original signal, resulting in cancellation. At 6fc the delayed signal is three full cycles behind the original, resulting in reinforcement. At 7fc the delayed signal is 3.5 cycles behind the original signal, again resulting in cancellation.

At all odd-numbered integer multiples of fc the phase shift caused by the delay puts the delayed signal into the opposite polarity of the original signal and therefore creates cancellation, while at all even-numbered integer multiples of fc the phase shift caused by the delay puts the delayed signal into the same polarity as the original signal and therefore creates reinforcement.

SEEING COMB FILTERING

We can see what comb filtering looks like on the frequency spectrum by using the test system shown in the illustration below. It consists of an oscillator generating a sine wave that sweeps from 20Hz to 20kHz. The output of the oscillator goes directly into a mixer, but also goes through a delay that goes into the same mixer. Both signals have the same magnitude and the mixer combines them equally – simply adding them together.

The illustration below shows the effect that comb filtering has on the frequency response. The green line represents the frequency response of the original signal. The blue line shows the effect of adding the delayed version of the original signal to itself, assuming both signals have the same magnitude (shown as 0dB on the graph).

At the far left of the graph the frequency is so low – and therefore its period is so long – that the delay causes an insignificantly small phase difference between the original signal and the delayed signal. The two signals reinforce strongly, approximating +6dB.

As the frequency gets higher its period gets correspondingly shorter and the delay starts becoming significant – therefore so does the resulting phase difference between the two signals. They are still reinforcing but their combined magnitude starts falling, creating a downward curve.

The downward curve eventually intersects the 0dB line. This occurs at the frequency where the delay is equal to one third of the period, which creates a phase difference of 120° (i.e. one third of 360°) between the original signal and the delayed signal – as shown in the illustration below.

At this ‘break even’ frequency the combined signals neither reinforce nor cancel. In other words, if the original signal has a peak amplitude of +1 and the delayed signal has a peak amplitude of +1 then the combined signal (shown in gold) will also have a peak amplitude of +1. There is no difference in peak amplitude between the original signal, the delayed signal and the combined signal – that’s what 0dB means: ‘no difference’.

Beyond the 120° ‘break even’ frequency the process of cancellation begins, eventually reaching maximum cancellation at the frequency where the delay time is exactly half the period. The phase difference between the original signal and the delayed signal is 180°. If the two signals have the same magnitude they will cancel out completely, causing the null seen in the frequency response curve. This frequency is, of course, fc.

Moving beyond 180°, the curve moves upwards representing a reduction in cancellation. Eventually it reaches another ‘break even’ frequency where the curve intersects the 0dB line. At this frequency the delay is equal to two thirds of the period, creating a phase difference of 240°. As with the previous ‘break even’ frequency at 120°, the combined signals neither cancel nor reinforce.

The curve continues upwards, now showing reinforcement as the frequency gets higher and the delay exceeds two thirds of the period. Eventually we reach a frequency where the delay is equal to one full period, creating a phase difference of 360° between the two signals. The delayed signal is now exactly one cycle behind the original signal. The positive and negative half-cycles of the two signals are aligned, resulting in reinforcement that brings the combined signal’s amplitude up to +6dB. The frequency this occurs at is 2 x fc, aka 2fc. From this point onwards the cycle repeats as explained above, with cancellation occurring at all odd-numbered multiples of fc and reinforcement occurring at all even-numbered multiples of fc.

HEARING COMB FILTERING

We’ve seen what comb filtering looks like, but what does it sound like? As with many other problems in audio, it’s hard to identify if you haven’t knowingly heard it before. Here are some simple ways to hear comb filtering in action…

Stand about 30cm in front of a smooth reflective surface such as a window or a plasterboard wall. While facing the surface, make a continuous loud ‘sshh’ sound with your mouth while slowly moving closer to the wall and back again. Listen to how the tonality of the ‘sshh’ sound changes. You will notice a subtle effect that rises in ‘pitch’ (for lack of a better word) as you move closer to the wall, and lowers in ‘pitch’ as you move further away. It sounds similar to phasing or flanging – that’s comb filtering. The sound that travels directly from your mouth to your ears is being combined with the sound that travels from your mouth to the reflective surface and bounces back to your ears. The latter travels a longer distance and therefore arrives a short time later; it is a delayed version of the same sound. Slowly moving away from and towards the wall causes the comb filtering to sweep through the frequency response (just like the modulation control in a phasing or flanging effect), making it easier to identify.

See if you can still notice it when standing still. Holding a pillow or cushion in your hands, move it into the space between your mouth and the reflective surface and take it out again. You’ll hear the comb filtering stop when the pillow or cushion is moved into the space, and resume when the pillow or cushion is removed. Practice at different distances and see if you can identify the comb filtering without moving your head closer or further from the reflective surface at the same time. This is a useful skill because most instances of comb filtering in audio engineering are due to fixed distances, meaning they are not rising or falling in ‘pitch’ and are therefore harder to identify. In most cases, the first thing you’ll notice is that something doesn’t sound right; typically it sounds a bit hollow or nasally.

Alternatively, you can create a test system as shown above. Using white or pink noise as a sound source, pass it through a simple delay (no feedback or similar) and blend the delayed sound with the original sound at equal perceived loudnesses. Set the delay to 1ms and listen to how the sound changes when you switch the delay in and out of the mix. Increment the delay in 1ms steps and notice how the tonality of the sound changes. As you increase the delay time, the ‘pitch’ of the effect will get lower but the characteristic comb filtering effect remains.

If you want to take it a step further, try panning the original signal to the left channel and the delayed signal to the right channel. If using monitor speakers that are correctly set up you should still hear some kind of problem while seated in the sweet spot because the two signals will be combining in the air. It will be harder to notice in headphones because there is little chance of the two signals adding together. Switch your monitoring to mono (or pan the two signals back to the centre) and the effect will be easy to identify – which also reinforces the need to always check our work in mono, especially when monitoring with headphones.

After doing the above exercises a few times you’ll familiarise yourself with the characteristic sound of comb filtering. You’ll know what to listen for, and you’ll be able to identify it when it happens.

DETERMINING fc

To further our understanding of comb filtering we need to go beyond fc as a concept and give it an actual value. How? As we know, fc occurs at the frequency that has been delayed by half a cycle. We can define and measure that ‘half a cycle’ in two ways. One way is to define it as being half of fc’s period in which case it is measured in seconds, and we can use what is known as the Arrival Time Difference to determine fc. The other way is to define it as being half of fc’s wavelength in which case it is measured in metres, and we can use what is known as the Path Length Difference to determine fc. If we get the maths right, both approaches will give us the same value for fc.

The illustration above shows two microphones (Mic 1 and Mic 2) placed at different distances from a speaker enclosure. The fundamental cancellation frequency, fc, is the frequency that takes half a period to travel from one microphone to the other, which means it fits half a wavelength into the distance between the two microphones. At this frequency the signal from Mic 2 will be 180° behind the signal from Mic 1. Although each microphone’s signal might sound good on its own, the combined signal does not sound good due to comb filtering. To calculate fc we need to put some values into the illustration, as shown below.

Mic 1 is placed 0.1m from the enclosure, while Mic 2 is placed 0.444m from the enclosure. This is all the information we need to calculate fc. We’ll start by using the Path Length Difference, and confirm our calculations using the Arrival Time Difference.

PLD: Path Length Difference

The Path Length Difference is the first choice to use here because we already know the distances, or the Path Lengths, between the sound source (speaker enclosure) and each of the individual microphones. We can see from the illustration that the Path Length from the speaker enclosure to Mic 1 is 0.1m, and the Path Length from the speaker enclosure to Mic 2 is 0.444m. The Path Length Difference, or PLD, is simply the difference between the two individual Path Lengths. We can calculate the PLD as follows:

PLD = 0.444 – 0.1 = 0.344m

Let’s add that to the illustration.

Now that we know the PLD we can use the PLD formula to solve fc:

fc = v / (2 x PLD)

Where fc is the fundamental cancellation frequency in Hertz, v is the velocity of sound propagation in metres/second (m/s) and PLD is the Path Length Difference in metres.

Mathematically astute readers will see that this is simply a variation of the wavelength (λ) formula shown in the previous instalment (λ = v / f), transposed to solve for frequency (f = v / λ) followed by substituting (2 x PLD) for λ because we know the PLD is equal to half a wavelength of fc, therefore (2 x PLD) is equal to the wavelength of fc.

Let’s use the PLD formula to calculate fc.

fc = 344 / (2 x 0.344) = 344 / 0.688 = 500Hz

From this we can see that a PLD of 0.344m causes comb filtering with a fundamental cancellation frequency (fc) of 500Hz. There will also be cancellation at all odd-numbered integer multiples of 500Hz, starting at 1500Hz (3fc) and repeating at 2500Hz (5fc), 3500Hz (7fc), 4500Hz (9fc) and so on. Reinforcement will occur at all even-numbered integer multiples of fc, starting at 1000Hz (2fc) and repeating at 2000Hz (4fc), 3000Hz (6fc), 4000Hz (8fc) and so on. The illustration below puts these figures into the frequency response shown earlier, in this case assuming the signals coming from each microphone have been matched to the same magnitude before combining them together.

If we imagine that the green line on the graph represents the frequency response of each individual microphone, we can see that the comb filtering created by combining them together creates a real mess of the resulting frequency response. Bad luck if any notes in the music land on any of those cancellation dips or reinforcement peaks. More about that later, for now let’s confirm our fc calculation using the Arrival Time Difference…

ATD: Arrival Time Difference

In the previous example we used the PLD formula because we knew the Path Lengths (distances) between the speaker enclosure and each microphone. Sometimes we don’t know the Path Lengths but we do know the time it takes for the sound to travel from the sound source to each of the microphones. In those cases we can use the Arrival Time Difference.

We don’t know any time values for the current example, but we can calculate them. In the previous instalment we saw that the velocity of sound propagation is 344m/s (at 21°C). In other words, sound travels 344 metres in one second. From physics we know that:

Velocity = Distance / Time

Therefore, if we know the velocity and distance we can transpose the formula to calculate the time it takes the sound to travel a given distance – for example, from the speaker enclosure to each of the microphones in the previous illustrations. The transposed formula is:

Time = Distance / Velocity

The Path Length from the speaker enclosure to microphone 1 was 0.1m. How long will it take sound to travel that distance?

t = 0.1 / 344 = 0.00029s = 0.29ms

The Path Length from the speaker enclosure to microphone 2 was 0.444m. How long will it take sound to travel that distance?

t = 0.444 / 344 = 0.00129s = 1.29ms

We now know that the sound from the speaker enclosure takes 0.29ms to reach Mic 1, and 1.29ms to reach Mic 2. These are the Arrival Times. The Arrival Time Difference, or ATD, is the difference between the Arrival Times and is calculated as follows:

ATD = 1.29ms – 0.29ms = 0.00129 – 0.00029 = 0.001s

The ATD in this example is 0.001s, or 1ms.

We can use the ATD to calculate fc with the following formula:

fc = 1 / (2 x ATD)

Where fc is the fundamental cancellation frequency in Hertz, and ATD is the arrival time difference specified in seconds.

Mathematically astute readers will see that this is simply a variation of the period formula shown in the previous instalment (t = 1 / f), transposed to solve for frequency (f = 1 / t) followed by substituting (2 x ADT) for t because we know the ATD is equal to half the period of fc, therefore (2 x ATD) is equal to the period of fc.

What is fc for this example?

fc = 1 / (2 x 0.001) = 1 / 0.002 = 500Hz

Bingo! It’s same answer (500Hz) as the PLD calculation, which means we got all the maths right.

We can see that for any given PLD and its corresponding ATD, we get the same result. In this example, a PLD of 0.344m creates an ATD of 0.001s, and both formulae give us the same fc of 500Hz – along with its corresponding cancellations at all odd-numbered integer multiples, and reinforcements at all even-numbered integer multiples. It’s just physics…

The comb filtering illustration above is identical to the previous comb filtering illustration because they are both the same situation. In the first example we used PLDs to determine that fc was 500Hz, and in the second example we used ATDs to confirm that fc was 500Hz.

MUSICAL IMPLICATIONS

In case you’re still wondering what all of this means, here’s a musical perspective. Let’s say we moved Mic 2 slightly further from the amplifier, increasing its Path Length from 0.444m to 0.4909m. What is the PLD?

PLD = 0.4909 – 0.1 = 0.3909m

What is fc?

fc = 344 / (2 x 0.3909) = 440Hz

We’ll double-check that fc figure with the ATD formula. The PLD between the two microphones is 0.3909m. The ATD is the time it takes sound to travel that distance. What is it?

t = 0.3909 / 344 = 0.001136s = 1.136ms

Now we can use the ATD formula to calculate fc.

fc = 1 / (2 x 0.001136) = 1 / 0.00227 = 440Hz

So fc is definitely 440Hz, also known as A440 or Stuttgart pitch. It is the tuning reference for most forms of Western music. In scientific pitch notation it is known as A₄ because it is the A note in the fourth octave. An fc of 440Hz (or any other note in the chosen scale) is not good from a musical perspective. Why not?

If the signals from both microphones in this example were combined together at equal magnitudes, A₄ (440Hz) would be completely cancelled out. E₆, C#₇, G₇, B₇ and others would suffer varying degrees of cancellation due to being very close to the odd-numbered integer multiples of fc (440Hz) as shown in the table below (3fc, 5fc, 7fc and 9fc). Meanwhile A₅, A₆, A₇ and others that are even-numbered integer multiples of 440Hz (2fc, 4fc, 8fc) would be reinforced by up to 6dB. E₇ and C#₈ would also get some reinforcement due to being very close to even-numbered multiples of 440Hz (6fc and 10fc).

Due to the comb filtering, all of the notes mentioned above – and/or their harmonics – would not be reproduced at the levels and tonalities the musician intended when playing them. They will sound okay in each individual microphone’s signal (assuming the microphone and placement are good), but they won’t sound okay when the two signals are mixed together. Some will be louder than the musician intended, and some will be softer than the musician intended.

As stated in the previous instalment, pressing the switch on your preamplifier that is incorrectly labelled ‘Phase Reverse’ (or similar nonsense) is not going to fix this problem because, despite its name, that switch does nothing to the signal’s phase; it simply inverts the signal’s polarity. It is applying an amplitude-based solution (polarity inversion) to a time-based problem (phase shift due to delay), and is the wrong tool for the job. As a result of using this switch on one of the two signals, all of the frequencies that were cancelling will now be reinforcing, and all of the frequencies that were reinforcing will now be cancelling. One of those options might sound better than the other, but neither will sound as the musician intended.

PRACTICAL MAGNITUDES

All of the comb filtering examples shown so far – in this instalment and the previous one – are based on worst-case scenarios that assume the original (or ‘direct’) sound and the delayed (or ‘reflected’) sound have been combined at the same magnitudes, resulting in complete cancellation at fc. That’s rarely the case in practice. If the two signals are not combined with the same magnitudes then the cancellations will not be complete nulls and the reinforcements won’t reach the full +6dB – therefore the comb filtering effect is less significant. We’ll explore this practical aspect of comb filtering in the next instalment…

Comb filtering can occur when a microphone captures an additional version of the sound source, typically one that has reflected off a nearby surface. The reflected sound travels a longer distance to the microphone than the direct sound, which means it arrives some time after the direct sound and therefore becomes a delayed version of it. When both versions of the sound are combined at the microphone’s diaphragm, comb filtering occurs.

Comb filtering can also occur when two or more mics are used to capture the same sound from different distances, as shown below. The sound arrives at the further microphone a short time after it arrives at the closer microphone, creating a delayed version of the sound. Each mic’s signal might sound good on its own, but adding both together creates the characteristic comb filtering effect – resulting in a bad sound and a perplexing problem for the novice. Surely two good sounds added together should create an even better sound!

The example above uses just two mics. Consider a close-miked drum kit, a situation that typically results in four or more mics all placed within a radius of a meter or so from the snare. Every mic will be capturing some spill from the snare. The snare might sound great through its own microphone(s), but as each other mic is added to complete the drum mix it introduces its own unique comb filtering with the snare – reducing the snare’s impact and clarity. When solo’d or PFL’d the snare sounds focused and punchy, but in the mix with the other mics it becomes blurred and spongy.

We’ll discuss these problems and their solutions in the next instalments. For now, we need to understand how and why comb filtering occurs, and that means diving in to some fundamental audio theory. Grab your SCUBA gear and weights, because we’re about to dive deep…

WHAT IS SOUND?

Musicians and sound engineers use two different languages to describe what something sounds like. One is the subjective language that attempts to describe intangible things (such as sound, which we can’t see, touch, taste or smell) by borrowing words from our more tangible senses, particularly sight and touch. For example “This guitar sounds too bright”, “That bass isn’t fat enough” or “The snare sounds blurred and spongy…” The other is the objective language that refers to the definable and measurable aspects of sound, and brings with it eye-glazing terms like Hz, dB, wavelength, polarity and phase. Sound engineers have to be fluent in both the subjective and objective languages when discussing sound, because musicians use the subjective language to describe what they’re hearing but audio equipment uses the objective language to describe what it’s doing. So we must translate the musicians’ subjective language through the objective language of our audio equipment to achieve the desired result.

In this and the following instalment we’ll be focusing on the objective aspects of sound – the measurable and definable things – with the goals of understanding what causes comb filtering, how to recognise it when you hear it, and how to prevent it. Let’s delve into those eye-glazing terms…

GOOD VIBRATIONS

From an objective point of view, sound is created by vibrations. If something is vibrating strongly enough and at the right speed (i.e. between 20 and 20,000 vibrations per second), there’s a good chance that we’ll perceive those vibrations as ‘sound’. If those vibrations are repeating at a consistent rate it means they exhibit periodic motion – which, in turn, means they can hold a note and are therefore good for musical applications. Let’s take a closer look at those musically good vibrations by studying something at the heart of many musical instruments…

The Vibrating String

The illustration below shows a string suspended between two points. The string will have a certain length and a certain mass (i.e. weight), and it will be held under a certain amount of tension. Collectively, the combination of the string’s length, mass and tension will determine how fast it vibrates, which determines the note it plays. Faster vibrations mean higher notes, and slower vibrations mean lower notes.

The contemporary grand piano has 88 notes, covering just over seven octaves. Conceptually, each of those 88 notes has its own string, and each of those 88 strings uses a different combination of length, mass and tension to determine how fast it vibrates – which determines its note. Longer and heavier strings are used for lower notes, while shorter and lighter strings are used for higher notes. That’s the concept: 88 strings for 88 notes. In reality there are over 200 strings in a contemporary grand piano. The lowest bass notes use a single long and heavy string, but the other notes use multiples of shorter and lighter strings playing together to increase the volume and richness of their sound.

In comparison to the grand piano, the acoustic guitar has only six strings and they are all the same length. However, each string has a different thickness and weight to give it a different mass, which gives it a different note. We adjust each string’s tuning by altering the tension with the tuning pegs. We change the note of any given string by pressing the string onto the fretboard, which changes the length of the vibrating section of the string – as we already know, a shorter length means a higher note. The acoustic guitar uses a combination of mass and player-adjustable length to deliver over three octaves of notes from just six strings, and uses tension to adjust the fine-tuning of each string.

The illustration below reduces every string instrument to its most basic element: a string held under tension between two mounting points. In this example the string is stationary, otherwise known as being in its state of rest. It is not vibrating and therefore it is not creating any sound.

If we place our finger on the centre of the string, pull it down and hold it in place, we are transferring energy into the string. As long as we hold the string in place with our finger, the energy is being stored in our finger and in the string. Something interesting happens when we let go of the string…

Like many things in physics, the string is fundamentally lazy and simply wants to return to its state of rest. However, to do that it must first use up – or dissipate – the energy we’ve just put into it. And so it vibrates up and down until the stored energy is dissipated through a combination of kinetic energy (movement) and thermal energy (heat). When all of the energy is dissipated, the string will be back at its state of rest.

The illustrations below track the movement at the centre of the string as it goes through the vibration process. The graph’s vertical axis represents how far the centre of the string has moved away from — or has been displaced from – its state of rest, hence it is called displacement. For these examples, upwards displacement is considered a positive value (+) and downwards displacement is considered a negative (-) value. We will consider the state of rest as the point of minimum displacement, represented as zero.

The illustration above shows the string being pulled down to a point of maximum downwards displacement, which we’ll call point A. When the string is released it attempts to return to its state of rest (minimum displacement), but it contains too much energy to stop there and must continue moving upwards. The illustration below shows the string passing through its state of rest but heading upwards. We’ll call that point B.

The next illustration shows that the string has continued moving upwards until it has reached the point of maximum upwards displacement, which we’ll call point C.

From the point of maximum upwards displacement the string changes direction and attempts to return to its state of rest again, but it still contains too much energy to stop there. We’ll call this point D; the string is passing through its state of rest but is heading downwards, as shown below.

Eventually the string reaches the point of maximum downwards displacement, which we’ll call point E.

From here the string once again changes direction and attempts to return to its state of rest (point F) but it still contains too much energy and must continue upwards, moving towards point G (maximum upwards displacement) as shown earlier.

Eventually the string reaches the point of maximum upwards displacement again, and the cycle repeats itself.

As we can see from points E to G, the process repeats itself but with every repetition a small amount of the energy is dissipated, so each point of maximum displacement is slightly less than the previous one. If we were to plot points A to G on a graph of displacement versus time and join the dots we’d expect it to reveal how the centre of the string moves over time. Based on the points we’ve identified so far, it would look something like this:

Although the graph shown above seems to make sense, it’s incorrect because it is not based on enough information – it only uses the points of maximum and minimum displacement. If we took many more measurements of the string’s displacement at regular time intervals throughout the vibration, rather than just the points of maximum and minimum displacement, the resulting graph would look like this:

Let’s simplify this graph to a single cycle of vibration that starts from the state of rest (point B), moves to maximum upwards displacement (point C), changes direction, passes through the state of rest (point D), moves to maximum downwards displacement (point E), changes direction again, and returns to the state of rest (point F).

We have now isolated a single cycle of vibration and can see that the movement at the centre of the string creates the classic sinusoidal shape, in other words, a sine wave. That doesn’t mean that a vibrating string sounds like a sine wave (it doesn’t), it just shows us that the movement at the centre of the vibrating string follows a sinusoidal shape. The vibrating string on a musical instrument will do many of these cycles of vibration per second, each one taking the same amount of time but each one with slightly less displacement than the previous one as the energy gets dissipated. The amount of displacement ultimately determines the perceived loudness of the sound and the amplitude of the captured audio signal. So as the displacement reduces, so too does the perceived loudness of the sound and the amplitude of the signal captured by a microphone or pickup. As the energy is dissipated, the note fades out to silence and the string returns to its state of rest.

FREQUENCY

In statistics, the term frequency is used to describe how often something happens within a given amount of time. In audio we use frequency to describe how many cycles of vibration happen in one second. Therefore, frequency means ‘cycles per second’. In old-school audio terminology frequency was often measured as cps, for ‘cycles per second’, and you might still see cps on some vintage audio gear. In contemporary audio terminology cps has been replaced with Hertz, named after the German physicist Heinrich Hertz. It’s abbreviated to Hz, so 100Hz = 100 Hertz = 100cps = 100 cycles per second.

The frequency range of human hearing is said to extend from 20Hz to 20kHz; in other words, from 20 cycles of vibration per second to 20,000 cycles of vibration per second. That’s a huge range – the highest frequency we can hear vibrates 1000 times faster than the lowest frequency we can hear.

The tuning reference for Western music is A440. It is the A above Middle C on the piano keyboard (A₄) and has a frequency of 440Hz, hence ‘A440’. If you play the A440 note on a piano, the appropriate strings will be doing 440 cycles of vibration per second – assuming the piano is in tune. If all of the musicians in an ensemble tune their instruments to the same reference note/frequency of A440, they should all be in tune with each other. As a matter of musical perspective, Middle C (C₄) has a frequency of 261.6Hz…

PERIOD

The frequency tells us how many cycles of vibration occur in one second, which allows us to determine how long it takes to complete one cycle of vibration. This is known as the period. It is measured in seconds and represented by a lower case t (for time). We can calculate the period with the following formula:

t = 1 / f

Where t = period in seconds, and f = frequency in Hertz. The ‘1’ represents one second, so we can see that the formula is simply turning the frequency into a fraction of one second. For example, a frequency of 440Hz has 440 cycles per second and each of those cycles has a period of 1/440th of a second.

At 20Hz, the lower limit of human hearing, the period is:

t = 1 / f = 1/20 = 0.05s

At 20kHz, the upper limit of human hearing, the period is:

t = 1 / f = 1/20,000 = 0.00005s

At A440, the tuning reference for Western music, the period is:

t = 1 / f = 1/440 = 0.00227s

At Middle C the period is:

t = 1 / f = 1/261.6 = 0.0038s

At 1kHz, the standard frequency used for many audio specifications, the period is:

t = 1 / f = 1/1000 = 0.001s

WAVELENGTH

The frequency tells us how many cycles occur in one second, and the period tells us the time taken to complete one cycle. These are both important concepts for understanding comb filtering, but there are three more concepts we need to understand before we can understand comb filtering. One of those is wavelength, which tells us the length of one cycle of vibration (i.e. a wave) as it travels through the air. To understand wavelength we need to know how fast sound travels through the air. This is generally known as the speed of sound, but it’s more correctly termed the velocity of sound propagation and is measured in metres per second (m/s).

In his book Room Acoustics, Heinrich Kuttruff defines the velocity of sound propagation as follows:

v = 331.4 + (0.6 x T) m/s

Where v = velocity in metres per second (m/s), and the upper case T = temperature in degrees Celsius (°C)

We can see from the formula that the velocity of sound propagation is dependent on temperature – in fact, temperature is the only variable in the formula. How significant is it? Let’s find out by calculating the velocity at two different temperatures. We’ll start with 0°C:

v = 331.4 + (0.6 x 0) = 331.4 + 0 = 331.4m/s

What about at 40°C?

v = 331.4 + (0.6 x 40) = 331.4 + 24 = 355.4m/s

So a 40° increase in the temperature, from 0°C to 40°C, creates a 24m/s increase in the velocity (from 331.4 to 355.4 m/s). That’s quite significant. As the formula shows us, every increase of 1°C in temperature results in a 0.6m/s increase in the velocity of sound propagation.

For most audio calculations we assume a room temperature of 20°C, which gives us a velocity of:

v = 331.4 + (0.6 x 20) = 331.4 + 12 = 343.4m/s

For the purposes of this discussion we’re going to ‘turn up the heat’ (so to speak) up by just one degree to 21°C, increasing the velocity by 0.6m/s to give us a more convenient velocity value of 344m/s, as shown below:

v = 331.4 + (0.6 x 21) = 331.4 + 12.6 = 344m/s

We’ll use that conveniently simplified velocity value of 344m/s throughout the rest of this discussion about comb filtering…

Calculating Wavelength

The velocity tells us how far the sound has travelled through the air in one second, and the frequency tells us how many cycles of vibration occurred in the air during that second. Knowing these figures allows us to calculate the length of one cycle as it passes through the air. This is known as the wavelength. It is represented by the Greek symbol λ (lambda) and is calculated with the following formula:

λ = v / f

Where λ is wavelength in metres (m), v is velocity in metres per second (m/s), and f is frequency in Hertz (Hz).

Let’s calculate the wavelengths at the lower and upper limits of human hearing, starting with 20Hz…

λ = v / f = 344/20 = 17.2m

Imagine that you are one cycle of 20Hz. You’re a massive 17.2m long, you’re racing through the air at 344m/s (i.e. the speed of sound, how exhilarating!), and there are 20 of you joined end-to-end every second. You’re not going to be stopped by a pane of glass, some heavy drapes, or a sheet of open cell foam glued to a plasterboard wall. You’re going to pass through all of those things without hesitation because, when you’re 17.2m long and hurtling through the air at 344m/s, those ‘obstacles’ simply don’t matter. Containing and controlling low frequencies within a room is difficult – that’s why we have acousticians.

What happens at 20kHz?

λ = v / f = 344/20,000 = 17.2mm

Now imagine that you are one cycle of 20kHz. You’re still racing through the air at 344m/s, of course, but now there are 20,000 of you joined end-to-end every second and each of you is a tiny 17.2mm long. If you’re lucky you might make it to the other side of the room without being absorbed by the air. A pane of glass or a simple plasterboard wall is a serious obstacle that you’re going to bounce off, just like a light beam reflecting off a mirror. If the surface has a rough textured finish you’re going to get scattered in numerous directions, similar to a light beam reflecting off a mirrorball at a dance party. If you encounter a sheet of open cell foam, some heavy drapes, a carpeted floor, some cushioned furniture, a fleece hoodie or some band members sporting respectable ‘fros, you’re going to be absorbed into non-existence and so are thousands of other cycles behind you. All of those absorptive obstacles spell ‘Game Over’ for 20kHz. Sustaining and distributing high frequencies within a room is difficult – that is also why we have acousticians.

Although we cannot see or touch sound, the concepts of frequency, period, velocity and wavelength help to give it dimension and make it more tangible.

PHASE & POLARITY

The concepts of phase and polarity are often confused. It’s a problem that’s been exacerbated for decades by manufacturers who continue to label a certain switch as ‘phase reverse’ or similar phase-related terms despite the fact that what it actually does is invert the polarity – which is a very different thing that has nothing to do with phase and, not surprisingly, creates a very different end result. They know it inverts the polarity because they designed it to do that, but they continue to label it as ‘phase reverse’, ‘phase invert’ or similar phase-related names that imply a form of time travel or similar magic, as we’ll see shortly. This confusion between phase and polarity is one of the reasons why people have a hard time comprehending comb filtering. Let’s get to the bottom of it…

Combining Signals

Altering an individual signal’s phase or polarity rarely has much of an audible impact on the individual signal itself, and it’s not until we combine it with other versions of itself that we notice a problem.

Whenever we combine two signals, the amplitude of the resulting signal at any point in time is simply the mathematical addition of the amplitudes of the two signals at that point in time. The illustration below shows two sine waves of the same frequency being combined together. In this example both sine waves have the same values at the same time, and the resulting signal is the addition of them. Because both signals have the same amplitudes at the same time the resulting signal will have twice the amplitude of the individual signals.

The following illustration shows the same two signals, but now one of them is negative when the other is positive, and vice versa. Because they have opposite amplitudes at any point in time, when added together they will cancel each other out.

The illustration below shows the same two signals as the illustration above, but now the blue signal has less amplitude than the green signal and the resulting waveform is the difference between them. The green signal reaches a positive peak of +3 at the same time that the blue signal reaches a negative peak of -1. The result is the addition of the two: +3 + -1 = +2

In both of the previous two illustrations it would be tempting to jump the gun and say that the blue signal is 180° out-of-phase with the green signal, but it could be simply inverted polarity – which creates a very different result in real-world audio situations. They are both simple and symmetrical waveforms, and because we cannot see the start or end of each signal in these illustrations (they are just excerpts from a signal for the purposes of these three illustrations) we cannot tell if the difference between them is due to phase or polarity. That’s what we’re going to look at next, because it’s a very important distinction…

What Is Polarity?

When it comes to audio signals, the term polarity refers to whether a point on the cycle is positive or negative relative to the reference (which is considered to be zero). The illustration below shows one complete cycle of a sine wave.

Note that the first half of the cycle (green) is positive, and is therefore known as the positive half cycle. The second half of the cycle (blue) is negative, and is therefore known as the negative half cycle. At any point within the positive half cycle the polarity is considered positive, while at any point in the negative half cycle the polarity is considered negative.

In the interests of being technically precise we have to introduce the term magnitude, which is the same as amplitude but without a polarity value. So a signal with an amplitude of +3 would have a magnitude of 3, and a signal with an amplitude of -3 would also have a magnitude of 3. For the purposes of this discussion, we can consider magnitude to be the same as amplitude but without any indication of the signal’s polarity. The magnitude is simply the numerical value of the amplitude, without the + or – sign.

When we invert the polarity of a signal we simply flip it upside down so that the positive half cycle becomes negative and the negative half cycle becomes positive. If we combine a signal with a polarity inverted version of itself (i.e. the same magnitude but with inverted polarity) the result will be complete cancellation.

The illustration above shows a signal consisting of two cycles of a sine wave (green), that is being combined with an inverted polarity version of itself (blue). We can see that both waveforms begin and end at the same time, as indicated by the flat lines showing the start and end of the signal. The resulting signal (yellow) shows that total cancellation has occurred because both signals have the same magnitude but one signal has inverted polarity.

The illustration below shows a signal consisting of four cycles of a sine wave (green) over the same time duration as the earlier example. It completes twice as many cycles as the previous example, therefore it has twice the frequency. In musical terms, it is an octave higher. It is being combined with an inverted polarity version of itself and, again, the resulting signal (yellow) indicates that adding the two signals together results in total cancellation.

At first glance some readers will say that the inverted polarity signals (blue) in the two illustrations above are “180° out-of-phase” with the original signals (green). Bzzzt! Incorrect…

This reveals the long-held confusion between polarity (amplitude) and phase (time). In both of the above illustrations the blue signals are not out-of-phase with the green signals. In fact, they are perfectly in phase – we can see both signals start and end at the same time, they both reach maximum magnitudes at the same time, and they both cross the zero points at the same time. The blue signals are simply inverted polarity versions of the green signals, and that’s the only difference between them. As shown here, when any signal is combined with an inverted polarity version of itself at the same magnitude the result will be total cancellation – regardless of frequency. That’s not what happens when signals are out of phase, as we’re about to see…

What Is Phase?

There are 360° in a cycle, just like in a circle, and when vibrations are occurring with periodic motion we can consider one cycle of those vibrations to be similar to following the outline of a circle: it starts at a certain point and goes through an entire cycle before returning back to where it started.

The term phase is used to describe a point within a cycle, and is expressed in degrees to give us a phase angle that we can use to represent that point within the cycle. For example, 0° is the start of a cycle, 90° is one quarter of the way through a cycle, 180° is halfway through a cycle, 270° is three quarters of the way through a cycle, and 360° is the end of a cycle. In the case of periodic motion, 360° is also 0° – the start of a new cycle.

The illustration below shows a number of sine waves, all of the same frequency but starting at different phase angles relative to the first sine wave, and therefore all having different phase relationships with it and with each other.

The second sine wave (B) is 90° behind the first one (A), and its phase relationship with the first one can be correctly described as being “90° out-of-phase”. It could also be said that the second sine wave is lagging the first sine wave by 90°, or that the first sine wave is leading the second one by 90°. Similarly, the third sine wave (C) is 180° behind (or “out-of-phase” with) the first sine wave (A), the fourth sine wave (D) is 270° behind the first sine wave (A), and the fifth sine wave (E) is 360° behind the first sine wave. Note that they are all versions of the same signal but with different start times due to each one being delayed, or phase-shifted, 90° behind the previous one.

The two illustrations below show the same two sine waves used in the earlier illustrations to demonstrate inverted polarity, but this time they’re being combined with delayed or phase-shifted versions of themselves instead of inverted polarity version of themselves. The delay time is the same for both examples.

The sine wave (green) in the illustration above completes two cycles of vibration. The delayed signal (blue) also completes two cycles but it has been delayed so that it starts half a cycle after the green signal. In other words, the delay puts it 180° out-of-phase with the green signal. Both signals have the same magnitude, and we can see that adding them together results in total cancellation – except for the first half cycle of the green signal and the last half cycle of the blue signal, where only one signal exists and therefore no cancellation. The cancellation occurs because the original signal (green) is in its negative half cycle when the delayed signal (blue) is in its positive half cycle, and vice versa. The delayed signal looks like its polarity has been inverted, but it has not. It simply begins half a cycle after the first signal – putting the delayed signal 180° behind, or 180° out-of-phase with, the original signal. It is correct to say that the two signals are “180° out-of-phase”. The resulting cancellation would cause a dip in the frequency response at the frequency that is 180° out-of-phase. If both signals have the same magnitude, the cancellation will reach a complete null. (It’s important to note that for any given delay time, only one frequency will actually be 180° out of phase – more about that later…)

So far so good, but things get interesting in the illustration below. Here we see a sine wave (green) with twice the frequency of the previous example. The blue signal has been delayed by the same time duration used in the previous illustration. However, because the original signal is twice the frequency of the previous illustration, the delayed signal (blue) is now 360° behind the original signal. In other words, it has been delayed by one full cycle. Because the sine wave is a symmetrical waveform it looks as though the two signals are in phase and it is therefore tempting to say that they are “back in phase” when, in fact, they’re 360° out-of-phase – the delayed signal begins one full cycle after the original signal.

Because the delay is equal to the duration of one full cycle at this frequency, the original signal (green) and the delayed signal (blue) both have positive polarities at the same time, and both have negative polarities at the same time. Therefore, adding them together results in addition, otherwise known as reinforcement – which causes a peak in the frequency response at this frequency. If both signals have the same magnitude and polarity, adding them together will result in a 6dB increase in amplitude.

The two illustrations above show the effect of delaying the signal, i.e. shifting the phase. Both signals have the same delay, which is equal to half a cycle of the first sine wave (i.e. half the period or half the wavelength) but is equal to a full cycle of the second sine wave (i.e. one full period or one full wavelength). This delay causes a cancellation null in the first illustration but a +6dB reinforcement in the second illustration. As we will see in the next instalment of this series, that simple delay causes cancellations at all odd-numbered multiples of the first frequency to cancel, and reinforcements (up +6dB) at all even numbered-multiples of it – resulting in a series of peaks and dips throughout the frequency response that is otherwise known as comb filtering. It is very different to the complete cancellation caused by inverted polarity.

Phase Invert & Other Nonsense

As we have just seen, phase is ultimately an indicator of time. It is a relative measurement of the elapsed time within a cycle, given in degrees and referenced to a starting point of 0°. With this in mind we can see that the term ‘phase invert’ means ‘turn time upside down’, which is nonsense. Similarly, the term ‘phase reverse’ implies ‘making time go backwards’, which is also nonsense – at least when it’s offered as a function on a microphone preamplifier.

The switch on a microphone preamplifier that is often called ‘Phase Reverse’, ‘Phase Invert’, ‘Phase’ or is indicated by the Greek letter φ (Phi, which is used to indicate ‘phase’ in maths and science) is actually inverting the signal’s polarity and should be called ‘Polarity Invert’, ‘Polarity’ or simply ‘Invert’. We’ll come back to that incorrectly named switch in the next instalments when we dive deeper into comb filtering. All we need to know for now is that pressing that switch doesn’t prevent or fix comb filtering, it just makes it sound different by inverting the polarity of the offending signal – thereby turning all of the comb filtering peaks into dips, and all of the comb filtering dips into peaks. It’s up to us to choose whichever of the two versions we find less offensive, or, better yet, take whatever action is necessary to prevent the comb filtering from happening in the first place.

If you have finally understood the distinction between phase and polarity due to reading this, hold your hand at arms length and bring the tips of your thumb and forefinger towards each other until there is a 1mm gap between them. Congratulations, you are now that much smarter than you were before because you have finally grasped a ridiculously simple concept suitable for ages 10 and over: phase exists on the time axis, and polarity exists on the amplitude axis. Inverting a signal’s polarity and asking how much it has put the signal out-of-phase is like someone asking “How tall are you?” and answering with “6 o’clock”. It’s nonsense. The next time you hear someone say they’re going to “flip the phase” or similar ‘baffle you with science’ nonsense, rejoice in the knowledge that you are 1mm smarter than they are. You cannot ‘flip phase’ any more than you can ‘shift polarity’ (or measure knowledge in millimetres, for that matter). However, you can ‘flip the polarity’ because polarity exists in the amplitude domain and can be either positive or negative, and you can ‘shift the phase’ because phase exists in the time domain – in fact, every time you slide a signal along the horizontal axis in your DAW you are moving it through time and therefore affecting its phase relationship with other signals, aka ‘shifting the phase’. That is exactly what engineers do when time-aligning close mics and distant mics that are capturing the same signal, or when calibrating delay speakers in a PA system…

INVERTED POLARITY OR PHASE SHIFTING?

An inverted polarity signal is perfectly in phase with the original signal – there is no time delay between the two signals and therefore there can be no phase difference. They start and end at the same times, they both reach maximum magnitudes at the same time, and they both pass through zero at the same times. The only difference between them is that the signal’s polarity has been inverted, turning it into a mirror image of the original signal – when one signal has a positive polarity the other has a negative polarity, and vice versa. Adding them together will cause a cancellation that affects all frequencies equally. If both signals have the same magnitude but one has inverted polarity, total cancellation will occur. Adding a signal to an inverted polarity version of itself does not cause comb-filtering, it just affects the overall amplitude of the signal.

A phase-shifted signal is a delayed version of the original signal. Its polarity has not been inverted, but, due to the delay, there will be some frequencies where the delayed signal has the opposite polarity to the original signal and other frequencies where it has the same polarity. Adding the original signal and the delayed signal together will cause cancellations (dips in the frequency response) at the frequencies that have the opposite polarity, and reinforcements (peaks in the frequency response) at the frequencies that have the same polarity. That is what causes comb-filtering.

The switch on your preamplifier that is incorrectly labelled ‘Phase Reverse’ (or similar nonsense) is not doing anything to the signal’s phase, it is simply inverting the polarity. It is an amplitude-based solution to an amplitude-based problem. We’ll look at that amplitude-based problem, and comb filtering, in more detail in the next instalment. In the meantime, remember that using an amplitude-based solution (inverting the polarity) to fix a time-based problem (comb filtering) is like using SCUBA gear to go skydiving. You’re diving, but you’re using the wrong tools. Hang on to your SCUBA gear, however, because we’re about to dive even deeper…

A microphone’s frequency response is an expanded version of its Sensitivity measurement, using frequencies throughout the range of human hearing (20Hz to 20kHz) rather than just 1kHz. It ultimately shows us how the microphone’s Sensitivity changes with frequency – in other words, which frequencies the microphone is more sensitive to and therefore produces a higher output signal level, and which frequencies it is less sensitive to and therefore produces a lower output signal level.

The method for measuring a microphone’s frequency response is simple in concept. The microphone is placed in front of a speaker that reproduces a ‘sweep tone’, i.e. a sine wave that typically starts at 20Hz and slowly increases, or ‘sweeps’, up to 20kHz while maintaining a consistent SPL at the microphone’s diaphragm. As the frequency sweeps from 20Hz to 20kHz, the amplitude of the signal coming out of the microphone is measured and plotted on a graph of frequency versus amplitude.

The result is typically referred to as a frequency response curve (it’s still called a ‘curve’ even if it’s a straight line), and shows us how well the microphone responds to some frequencies compared to other frequencies. It provides an overall impression of the microphone’s tonality (bright, dull, etc.) which is useful for comparison and mic selection purposes. It does not factor in harmonic distortion and other parameters that contribute to a microphone’s tonality, but those parameters make relatively small contributions compared to the frequency response.

The frequency response measurement is typically made in an acoustically-isolated anechoic chamber that prevents interference from external sounds and does not create any resonances, reflections or reverberation of its own that would adversely influence the sound captured by the microphone.

The amplitude of the microphone’s output signal at 1kHz is used as the reference, which becomes the 0dB reference line for the frequency response curve. Therefore, a frequency response curve should always read 0dB at 1kHz – although some manufacturers prefer to use the absolute value of SPL (e.g. 94dBSPL) rather than the relative value of 0dB as the reference level for 1kHz.

The illustration above shows a theoretically perfect frequency response curve, as expected of a microphone designed to capture a sound very accurately (i.e. for speaker test and measurement purposes, making very accurate recordings, etc.). The frequency is shown on the horizontal axis; in this example it extends from 20Hz to 20kHz. The amplitude of the microphone’s output signal is shown on the vertical axis; in this example it extends from +15dB to -15dB (also referred to as ±15dB) with 0dB in the middle. The frequency response curve (shown in blue) is a straight horizontal line extending from 20Hz to 20kHz. Projecting up to the frequency response curve from any frequency on the horizontal axis and looking across to the vertical axis shows us that the amplitude of the microphone’s output signal remains the same regardless of the frequency. This microphone captures all frequencies within the range of human hearing equally well – it does not favour some frequencies over others, and therefore should not affect the tonality of the captured signal. This is referred to as a flat response because it is essentially a flat line.

The illustration below shows three different frequency response curves that are all perfectly straight lines, but only one of them is a flat response.

The green response tilts upwards, indicating a steady increase of output level from the microphone as the frequency gets higher. A microphone with this frequency response would sound very bright and lacking in low frequency energy, and might be described as sounding tinny or thin due to the way it exaggerates high frequencies – although it might be a good choice for use with a sound source that is too dull or boomy.

The red response tilts downwards, indicating a steady decrease of output level from the microphone as the frequency gets higher. A microphone with this frequency response would sound dull and lacking in high frequency energy, and might be described as sounding boomy due to the way it exaggerates low frequencies – although it might be a good choice for use with a sound source that is too tinny or thin.

The blue response is a horizontal line, meaning it reproduces all frequencies equally well and therefore offers a flat response – a microphone with this frequency response would be described as providing an accurate representation of the sound at the microphone position. Interestingly, however, many sound engineers would not say it sounds ‘natural’ because, subjectively, ‘accurate’ does not necessarily equate to ‘natural’. Ribbon microphones, with their gentle high frequency roll-off, are more often described as sounding ‘natural’ – a phenomenon we’ll return to later in this instalment.

Smoothing

A microphone’s frequency response curve is rarely a perfectly straight line, even when it’s meant to be ‘flat’. As we saw in the earlier instalments of this series, microphones contain parts that need to move very fast (i.e. capturing up to 20,000 vibrations per second), and moving parts introduce the problem of resonance – which will exaggerate some frequencies and thereby affect the frequency response. Furthermore, the microphone’s physical construction provides its own acoustic environment that also affects the frequency response – think of it as room acoustics on a miniature scale.

Due to these things the frequency response curves of most microphones will contain numerous peaks and dips within the audible range, many of which will manifest as spikes (upwards or downwards) and ripples. Some of these will be due to the microphone itself, others will be due to artefacts caused by the measuring equipment or the measurement process. Many of these irregularities are too low in amplitude or too narrow in bandwidth to have any sonic significance, and including them on a frequency response curve only causes unnecessary concern. For this reason a process known as smoothing is often applied to remove or downplay these insignificant irregularities – essentially ‘smoothing out’ the frequency response curve (like going over it with sandpaper) to provide a better indication of what the microphone sounds like in practice. However, be aware that the smoothing process can be over-used to deliberately downplay peaks and dips that are significant and audible.

Deviation Window

There are times when it is not necessary to have a graphical representation of a microphone’s frequency response – we are simply interested in knowing how much a microphone deviates from the theoretical ideal of a flat response, and we’re not concerned with the actual frequencies it deviates at. In these cases, a written specification is sufficient. It provides a ‘big picture’ of how much the microphone’s frequency response curve deviates either side of the 0dB reference within a certain bandwidth (typically 20Hz to 20kHz).

In the illustration below we can see that the peaks and dips of the curve never exceed 1dB either side of the 0dB reference, from 20Hz to 20kHz. This microphone’s frequency response could be summarised as ‘20Hz to 20kHz ±1dB’. From its highest peak to its lowest dip, the deviation window never exceeds 2dB (from +1dB to -1dB) from 20Hz to 20kHz.

The curve shown below is more extreme and deviates up to 3dB either side of the 0dB reference. Its frequency response would be summarised as ‘20Hz to 20kHz ±3dB’. From its highest peak to its lowest dip, the deviation window never exceeds 6dB (from +3dB to -3dB).

The curve below is for a microphone that has a very good response but slightly narrower bandwidth than the earlier ±1dB curve. We can see that the response remains within the ±1dB window except at the upper and lower frequency extremes, where it rolls off to -3dB at 20Hz and 20kHz respectively. This response would be described as ‘20Hz to 20kHz +1dB/-3dB’, meaning it never rises more than 1dB above the 0dB reference and never falls more than 3dB below it. In this example the frequency response is actually very good (remaining within ±1dB from 30Hz to 10kHz), and those 3dB drops are purely due to roll-offs at the high and low frequency extremes. They’re probably not worth worrying about unless the intention is to accurately capture the low and/or high frequencies that exist below 30Hz and above 10kHz.

Frequency Range

When a microphone’s frequency response is specified in text as upper and lower frequency limits within a deviation window, as described above, it is often referred to as a frequency range.

Some manufacturers have dumbed this down to the point that the specification is devoid of any deviation window, rendering it meaningless. For example:

Frequency Range: 20Hz to 20kHz

It’s not a problem if the published specifications include a frequency response curve where the viewer can see how the microphone responds to different frequencies, but without a frequency response curve and without a stated deviation window this type of specification is nothing more than a ‘feel good’ exercise for a technically uninformed market. “Does this car go fast?” “Yes.” “I’ll take it.”

PROXIMITY EFFECT

No discussion of microphone frequency response would be complete without considering the proximity effect. It was discussed briefly in the first instalment of this series, so let’s start by re-visiting that…

As the name suggests, the proximity effect refers to the effect of the distance between the microphone and the sound source. It’s responsible for the well-known boost in low frequencies that occurs when speaking very close to a microphone. It’s also responsible for the lesser-known loss of low frequencies that occurs when miking from a distance. As a generalisation, as the microphone’s polar response becomes more directional the proximity effect becomes greater.

The cause of the proximity effect will be explained in a forthcoming instalment that discusses how microphones create their polar responses. For now, think of the proximity effect as a dynamic EQ that progressively boosts the low frequencies as you get closer to the microphone and progressively cuts the low frequencies as you move away from it. Typically beginning somewhere below 1000Hz and reaching boosts or cuts of 12dB or more at 50Hz, the proximity effect has a major effect on the tonality of the sound captured by the microphone – especially when close-miking a sound source that is capable of moving closer to and further from the microphone, such as a vocal or any hand-held instrument (e.g. saxophone, flute, etc.). Many musicians learn to ‘play’ the proximity effect during their performance, moving closer and further from the microphone to get the desired tonality for any given moment. Changing the distance literally changes the microphone’s frequency response.

The proximity effect should always be kept in mind when measuring or considering the frequency response of a directional microphone, because it affects the amount of low frequencies captured by the microphone. A measurement made very close will have an exaggerated low frequency response, while a measurement made at a distance will have a poor low frequency response. For this reason, it is always important to know what distance the frequency response was measured at and how that relates to your application.

The illustration above shows how the low frequency response of a microphone with a cardioid polar response changes with distance – in this case the microphone is DPA’s 4011 small single diaphragm cardioid condenser. At a distance of 10cm the 4011’s response rises to +12dB at 20Hz, while at 100cm it falls to -18dB at 20Hz. That’s a difference of 30dB (from +12dB to -18dB) over a distance of 90cm (from 10cm to 100cm), and is typical of most microphones with a cardioid polar response. Note that the response is flat at 30cm, which is a pivotal distance for measuring the frequency response of a cardioid microphone because it’s the transitional distance where the proximity effect is not increasing or reducing the low frequencies. This brings us conveniently to…

MEASUREMENT DISTANCE

The illustration above, from DPA’s 4011, shows how a microphone’s low frequency response changes with distance due to the proximity effect. Note that each curve includes the distance it was measured at – without that information we’d have no idea what the frequency response would be for any particular application and distance.

For many decades every reputable manufacturer included the measurement distance with their microphone frequency responses. Nowadays we have to drill down deep into a manufacturer’s website to find such important qualifying information, often to discover it’s simply not there.

The illustration above demonstrates this problem. It overlays the frequency response curves of two popular small single-diaphragm cardioid condenser microphones, both of similar dimensions and applications but at significantly different price points. They are both real mics that have been on the market for many years, but for the purpose of this demonstration we’ll refer to them simply as the Red mic and the Green mic in accordance with the colour of their response curves. Both mics offer a flat response from 300Hz to 4kHz, followed by very similar upper midrange humps reaching around +2dB before starting a gentle roll-off at 10kHz and falling a dB or two below 0dB at 20kHz. The Red mic would have slightly more output than the Green mic between 5kHz and 6kHz, and slightly less output between 15kHz and 20kHz. We could expect very similar midrange and high frequency tonality from each microphone – at least as far as we can determine from the frequency response curves and their contribution to a microphone’s tonality. So far so good, but what about below 300Hz?

The Red mic drops 4dB from 300Hz down to 80Hz, at which point it levels out and remains consistent down to 20Hz. The resulting curve is reminiscent of a cut being applied by a low frequency shelving EQ. Meanwhile, at 300Hz the Green mic begins a low frequency roll-off that falls to -12dB at 20Hz. Which mic offers the best low frequency performance? The Green mic appears to offer better performance from 300Hz down to 55Hz, while the Red mic offers better performance below 55Hz. However…

Right about now alarm bells should be ringing in the heads of every reader who knows how to interpret a microphone’s frequency response graph. Something doesn’t look right… The Green mic’s low frequency roll-off looks like something we’d expect to see from a ‘free field’ measurement (see below) of a cardioid at 60cm or more from the sound source, where the proximity effect is rolling off the low frequencies significantly. Meanwhile, the Red mic’s extended low frequency response from 80Hz down to 20Hz looks like something we’d expect to see from a measurement made at 30cm or thereabouts, where the proximity effect is not boosting or cutting the low frequencies.

Drilling down into the respective manufacturer’s websites and downloading manuals, we find that the Green mic’s frequency response was indeed measured under ‘free field’ conditions (in accordance with the IEC60268-4 specification as discussed below). Unfortunately there is no mention of the measurement conditions on the Red mic’s web page or in its downloaded manual. This means we cannot make confident comparisons of these two frequency response curves because a) we don’t know if they were measured under the same conditions, and b) they don’t appear to be measured under the same conditions. Specifications are only comparable if everyone follows the same measuring techniques and/or includes the vital qualifying information in their marketing materials.

As shown above, the measurement distance is a crucial piece of information for evaluating the frequency response of any microphone that exhibits the proximity effect…

APPLICATION PROFILES

In the sixth instalment of this series we saw that there’s an in-depth International Standard for microphone specifications that’s been in place since the 1960s. Known as IEC60268-4, it’s published by the IEC (International Electrotechnical Commission) and regularly updated by the AES (Audio Engineering Society). It describes precisely how every microphone specification should be measured, the units those measurements should be presented in, and what qualifying information should be included with the measurements – all with the goal of enabling meaningful objective comparisons between different microphones.

Interestingly, it also includes recommendations for describing a microphone’s application profile – in other words, what application the microphone is designed for. This is an important consideration because if we know the application that a microphone is designed for we can measure it in a way that’s relevant to that application. IEC60268-4 provides three example application profiles – free field, performance and close-talking – and each comes with a recommended measuring technique and distance.

Free Field Application Profile

The first application profile is for free field microphones, where ‘free field’ refers to a space that is free of any reflections, and the sound is arriving ‘on axis’ to the microphone, i.e. the microphone’s diaphragm is directly facing the sound source.

IEC60268-4 specifies that microphones designed for free field applications have their measurements made in ‘approximately plane progressive wave conditions’ – in other words, where the sound energy is free to propagate away from the sound source without encountering any interference that could create reflections. This can be achieved with a specially designed and acoustically treated duct, or in an anechoic chamber – provided it is large enough to support a half-wavelength of the lowest frequency being measured. The free field application profile doesn’t state a specific distance for microphone placement when measuring the frequency response, but does require it to be in the free field. This will typically place the microphone at a distance where we see the characteristic low frequency roll-off due to the proximity effect.

The most obvious use of this application profile is for test situations such as measuring the frequency response of a loudspeaker – which is done in an anechoic chamber similar to the approach shown earlier for measuring a microphone’s frequency response. The anechoic chamber has no reflections and the microphone is directly facing the sound source, both conditions that satisfy the requirement for a free field.

Performance Application Profile

The second application profile is for performance microphones. The implication here is hand-held vocal microphones, where the performer is able to change the microphone distance during the performance to take advantage of the proximity effect – although those same microphones are often mounted on a stand for performers whose hands are not free to hold a microphone (e.g. brass and woodwind players), and the performer moves the instrument towards or away from the microphone while performing to it.

The recommendation for measuring performance microphones is similar to the anechoic chamber method described earlier, but the speaker is replaced with an ‘artificial mouth’ or ‘mouth simulator’ – which is essentially a speaker mounted into an object that’s shaped to recreate the reflections and diffraction of a human face, perhaps even a dummy head and upper torso with a speaker where the mouth would be. This application profile requires a measurement distance of 30cm – the ‘break even’ distance for a cardioid where the proximity effect is not boosting or cutting the low frequency energy.

Close-Talking Application Profile

The third application profile is for close-talking microphones, which, as the name suggests, are intended for use at very short distances. As with the performance application profile described above, the measurements for close-talking microphones require the use of an artificial mouth but require it to be placed at a very short distance of 25mm to the microphone – which will definitely bring the proximity effect into play if the microphone is directional.

Other Applications…

You may have noticed that there’s no application profile for close-miking musical instruments that are fixed in position during a performance (drums, piano, guitar amplifiers, etc.), or that can move around the microphone but are not voices (e.g. brass and woodwind instruments) as is commonly done in the studio and on stage. The free field application profile does not rely on close-miking, while the performance and close-talking application profiles are clearly intended for vocals/voice and therefore require the use of an artificial mouth – which makes no sense for measuring the frequency response of a microphone intended for close-miking a drum kit, piano, guitar amplifier, saxophone, trumpet, or most other instruments for that matter…

For these situations the free field application profile provides all the information we need, especially if it includes the distance the measurement was taken at so we can consider the influence (if any) of the proximity effect at that distance. Miking an instrument in a studio or on stage is not using the microphone in a free field environment, but a microphone specification made in a free field environment remains useful because it tells us how the microphone responds in an ideal ‘on-axis’ situation with no reflections. This provides a basis we can use for selecting microphones for applications that are not free field. If the signal coming out of the microphone doesn’t sound like we’d anticipate (by mentally superimposing the microphone’s free field frequency response over the sound arriving at the microphone’s diaphragm while also considering the proximity effect), then we know something else is the problem – such as comb filtering due to reflections off nearby surfaces, or perhaps the microphone is damaged.

The purpose of the application profiles is to allow for situations where a free field measurement is not relevant, such as close-miking a voice. The IEC standard states that a manufacturer may create their own application profiles to measure and determine specifications of microphones that are designed for a specific application, as long as qualifying details about the measurement conditions are provided with the measurements.

Diffuse Field

Although not an application profile, some microphone frequency responses include a diffuse field curve. What is it and what does it mean? We’ve already seen that a free field measurement requires no reflections, so that the only sound that reaches the microphone is the direct sound from the sound source. Free field measurements are typically performed in an anechoic chamber, which is a room with highly absorptive walls to prevent any reflections or reverberation (as shown in the first image in this instalment).

The diffuse field is the opposite to the free field. In a diffuse field, sound energy can arrive at the microphone from any direction with equal probability and amplitude – the contribution of the direct sound is considered negligible relative to the contribution of the reflected sounds and the reverberation.

For diffuse field measurements the anechoic chamber is replaced with a reverb chamber (a large and highly reverberant room), and the sweep tone is replaced by third-octave bands of noise in short bursts that are intended to create reverberation. The measurements are taken immediately at the end of each noise burst, when there is no direct sound and the only sound in the room is the reverberation (i.e. a ‘diffuse field’).

The IEC standard recommends that the measurement room has the following reverberation times:

Some manufacturers, particularly those who make microphones intended for distant miking applications (such as recording orchestral, chamber and choral music), provide two frequency response curves: one measured in accordance with the free field application profile described above, and one measured in a diffuse field. DPA’s 4006A small single diaphragm omnidirectional condenser provides a good example, as shown below.

A frequency response graph like this is helpful when choosing a microphone for distant miking. The on-axis frequency response curve (blue) provides an indication of how the microphone responds to sounds arriving on-axis, while the diffuse field frequency response curve (green) provides an indication of how the microphone responds to the early reflections and reverberation arriving from different directions throughout the room. Note that the 4006A’s diffuse field frequency response curve shows a high frequency roll-off that begins at around 4kHz and falls to around -8dB at 20kHz. This is mostly due to air absorption of high frequencies, which we’ll look at shortly.

DPA provide a number of diffraction grids for the 4006A. These fit over the front of the microphone and alter its frequency response to suit different applications – there’s one for free field applications, one for diffuse field applications and one for close-miking applications. The frequency response curves shown above were made with the free field grid fitted, which is useful for capturing a balance between the sound coming off stage and the room’s reverberation – such as making a two-mic direct-to-stereo recording of an acoustic performance in a concert hall.

The frequency response curves shown below were made with the diffuse field grid fitted. Note the increased level at 10kHz. The diffuse field grid boosts the diffuse field frequency response by about 4.5dB at 10kHz, from -2.5dB (free field grid) to +2dB (diffuse field grid), which provides a more detailed capture of the diffuse field. It also adds a similar boost to the on-axis frequency response curve, but that shouldn’t be too significant in a diffuse sound field application. This grid is suited for applications where the 4006A is being used as a room microphone to be blended with closer microphones. In these applications the intention is to capture a diffuse room sound by placing the microphone(s) at a distance where the room’s reflections and reverberation are the dominant sound and there is very little direct sound, allowing the captured sound to be blended with the close mics without causing any problems – rather like adding reverb from a plug-in. Aiming the microphones away from the performers (e.g. directly upwards or to the back of the room) uses the grid’s on-axis boost to provide a more detailed capture of the diffuse field rather than emphasising the direct sound from the performers.

To be in the diffuse field, the microphone must be placed at a sufficient distance to ensure the contribution of the direct sound is negligible, as illustrated below.

As we move away from the sound source the direct sound’s SPL decreases in accordance with the Inverse Square Law, dropping by 6dB for each doubling of distance (shown in red). However, the reverberation’s SPL remains consistent throughout the room and therefore is not affected by the distance from the sound source (shown in green). As we move further away from the sound source and into the room, we reach a point where the direct sound’s SPL is equal to the reverberation’s SPL. In acoustics terminology this is known as the critical distance. At distances less than the critical distance we are in the near field, where the direct sound is dominant. [As a matter of interest, this is also the goal for ‘near field monitoring’.] Beyond the critical distance the reverberation becomes dominant and we have entered the far field. As we move further into the far field the direct sound becomes less and less significant. When the direct sound’s SPL is significantly lower than the reverberation’s SPL, the contribution of the direct sound becomes negligible and we are in the diffuse field.

DEVIATING FROM FLAT

Earlier in this instalment we discussed the importance of using a microphone with a flat response to capture the sound’s tonality as accurately as possible from the microphone position. However, there are many times when we rely on the microphone’s frequency response to alter the sound’s tonality – turning it into something more useful, more acceptable or more fashionable. Let’s look into that…

We’ll continue using DPA’s 4006A, as discussed above. The illustration below is the 4006A’s on-axis frequency response with the free field grid fitted, as shown earlier but this time without showing the diffuse field response.

From 10Hz to 5kHz the frequency response is ‘ruler flat’ (i.e. as straight as the edge of a ruler), just like the theoretical ideal. Above 5kHz we see a gradual rise in the microphone’s output level, reaching a peak of +2.5dB around 15kHz before rolling off to about +1dB at 20kHz (it continues down to -6dB at 40kHz, making it a good choice for those who create sound effects by lowering the pitch of recorded sounds). The peak in the high frequency response ultimately represents an increase in the microphone’s Sensitivity at those frequencies, which means the microphone exaggerates those higher frequencies. Why? The 4006A is primarily intended for recording acoustic instruments at a distance, sometimes many metres away. As we move further away from the source the sound becomes duller due to air absorption (i.e. for any given distance, the air absorbs more high frequency energy than it absorbs low frequency energy). The 4006A’s high frequency boost is intended to compensate for the loss of high frequencies over distance. It’s a very popular microphone with sound engineers who need to record orchestras and pipe organs – two applications that require distant miking while maintaining high frequency detail.

Neumann’s KM183 (above) is a small single diaphragm omnidirectional condenser microphone designed for similar applications as DPA’s 4006A. It offers a flat response from 20Hz to 2kHz, then gently rises to about +8dB at 9kHz before rolling off to -1dB at 20kHz. It’s very similar to the on-axis response of DPA’s 4006A with the diffuse field grid added.

Due to their high frequency boosts, both of the above microphones might be considered too bright, too harsh or too detailed for close-miking applications. Fitting the close-miking diffraction grid to DPA’s 4006A helps considerably, as shown below. It extends the free field grid’s flat response from 5kHz up to 8kHz, rises to a gentle peak of a dB or two around 12kHz (air compensation), then rolls off to -5dB at 20kHz. This would probably be a preferable tonality than the free field grid or the diffuse field grid when close-miking, but there are many applications where it would still be considered too bright. For example, close-miking metallic and wooden percussion or finger-picked steel string guitar – all situations that create fast attack transients that are rich in high frequency detail. Much of this high frequency detail is absorbed in the air by the time it reaches a listener some metres away, but a microphone placed 30cm or so from the instrument is going to capture the full brunt of it. That’s not likely to be the sound we want to capture unless we’re making a sample library or similar.

BeyerDynamic’s M130 ribbon microphone offers the opposite characteristic at high frequencies. Its frequency response (shown below) is essentially flat from 400Hz to 6kHz, then we see the high frequency roll-off that’s inherent in the design of all ribbon microphones – in this case falling to -10dB at 20kHz. The M130 is not a popular choice for the distant miking applications that DPA’s 4006A and Neumann’s KM183 are suited for – it is too dull and its Sensitivity might be too low – but it’s very popular for close-miking wooden and metallic percussion and similar sounds with very fast attack transients, and also for capturing the sound of electric guitar amplifiers. Its high frequency roll-off provides a tonality that could be described as mellow, dull or dark, depending on your application. It has the benefit of taming bright attack transients in a similar way as the air does over distance, often making it a preferable choice for close-miking than the more ‘accurate’ small single diaphragm condensers.

The result is a sound that is often described as ‘natural’; it provides the detail, focus and minimised spill of close-miking, but with a high frequency roll-off that approximates the effect of the air between the instrument and the listener. It’s up close but doesn’t feel like it, hence ‘natural’…

We’ve just looked at how high frequency boosts and roll-offs can be used to our advantage, but what’s happening at the low frequencies? DPA’s 4006A and Neumann’s KM183 both have flat responses down to 20Hz or lower, but BeyerDynamic’s M130 has a low frequency roll-off that begins at 100Hz and falls to -7dB at 50Hz – which is where their response graph ends. Projecting further down the slope, we can expect the roll-off to reach -18dB at 20Hz. Why is this?

The 4006A and KM183 are single diaphragm omnidirectional microphones that belong to a family of microphones known as pressure transducers. One characteristic of pressure transducers is an extended low frequency response that remains consistent regardless of the distance from the sound source, because they do not have any proximity effect. It’s one of the reasons why small single diaphragm omnis are popular with engineers who need to capture sounds from a distance – such as recording orchestras, chamber music ensembles, and nature soundscapes.

The M130 is a bidirectional ribbon microphone, and belongs to a family of directional microphones known as pressure gradient transducers. A fundamental characteristic of pressure gradient transducers is that their low frequency response changes with distance – when close to the sound source (typically less than 30cm) the low frequencies are exaggerated due to the proximity effect, but when used at a distance (typically more than 30cm) there’s a low frequency roll-off that causes the captured sound to lack low frequency energy.

We’ll discuss pressure and pressure gradient transducers in a forthcoming instalment of this series. The important thing to understand for now is that most directional microphones use pressure gradient transducers, which means they are prone to the proximity effect. We must keep that in mind when considering their suitability for our intended application.

In the examples given above, DPA’s 4006A and Neumann’s KM183 are both omnidirectional pressure transducers and therefore have no proximity effect, so their low frequency response remains the same at any distance. Beyer’s M130 is a bidirectional pressure gradient transducer and therefore has proximity effect, so its low frequency response changes with distance. There is no measurement distance given in the M130’s specification sheet, so we don’t know what distance provides the low frequency response shown here.

TAILORING FOR SPECIFIC APPLICATIONS

Let’s look at some microphones that have their frequency responses tailored for specific applications. For the following examples we’ll be focusing on dynamic microphones. Why? As we saw in an earlier instalment of this series, a dynamic microphone’s frequency response consists almost entirely of carefully controlled resonances. This makes it difficult to create dynamic microphones with theoretically ideal flat responses from 20Hz to 20kHz, but it does make them ideal for creating microphones with frequency responses that are tailored for specific applications. By placing the resonances appropriately, we can put peaks and dips where we want them in the frequency response. If we factor in the microphone’s intended application and consider the proximity effect, we can make microphones that excel at doing very specific things.

Shure SM58

Shure’s SM58 provides a good example of a microphone with a frequency response that has been tailored for a specific application, as shown below. It’s a dynamic cardioid microphone designed for handheld vocal use, and fits the performance application profile described earlier.

Below 400Hz its frequency response is quite similar to BeyerDynamic’s M130 ribbon mic shown earlier. We see a similar low-frequency roll-off from 100Hz down to 50Hz, with a subtle hump in the low frequencies from 100Hz up to 400Hz. On the SM58 this subtle hump is followed by an equally subtle dip between 400Hz and 1kHz. Neither of those is worth discussing at this point in time – some manufacturers might smooth them out altogether – but things get interesting above 1kHz. The response gradually rises, creating a large upper midrange hump that reaches +5dB at 5kHz. At first glance this seems intended to maximise vocal intelligibility, allowing the vocal to compete with heavily distorted electric guitars, crashing cymbals and so on – to ‘cut through the mix’ as live sound engineers are fond of saying – but there’s more to it than that, as we’ll see shortly. The response dips 4dB from +5dB down to +1dB at 7.5kHz, possibly to minimise essing, then climbs to about +4dB at 10kHz before rolling off to -6dB somewhere around 15kHz. The graph ends there, having covered the vocal range, but if we project further downwards we can expect to see it falling to -15dB at 20kHz. Without that high frequency roll-off (i.e. if the response remained at +4dB from 10kHz onwards) the microphone would be exaggerating spill from cymbals and similar sounds from the drum kit – which is usually placed behind the vocalist in a typical live band set-up on stage. This high frequency roll-off is essentially a low pass filter for frequencies above the vocal range.

The above interpretation is based on a casual glance at the SM58’s frequency response, which makes it look like a microphone with a relatively extreme upper midrange boost. However, that assumption ignores its intended use scenario, i.e. its application profile. When placed less than 30cm from the voice the proximity effect comes into play, boosting the low frequencies and bringing them back into perspective with the boosted upper midrange seen in the frequency response curve. Experienced vocalists learn how to ‘play’ the proximity effect, adding more or less low frequency energy to their voice to achieve the desired tonality. This clever balancing of the proximity effect with the upper midrange boost allows a close-miked voice to have a full and detailed sound without getting boomy or muddy. Meanwhile, low frequency spill from the drums and bass is too far away from the mic to benefit from the proximity effect’s boost and receives a reduced low frequency response instead, resulting in an effect that’s similar to applying a high pass filter to maintain vocal intelligibility.

When used up close and factoring in the proximity effect, the SM58 ends up with a frequency response that’s tailored for close-miking the human voice – along with a bandpass filter (the HF and LF roll-offs) to minimise the audibility of sounds beyond the vocal range. Regardless of whether these things are by fault or by design, it’s not hard to understand why the SM58 has remained a firm favourite ever since its introduction in 1966.

Shure Beta52A

Shure’s Beta52A provides another good example of a microphone tailored for a specific application. It’s a dynamic mic with a supercardioid polar response, specifically designed for use with kick drums and similar bass instruments. Let’s take a closer look at it…

Ever since the late 1970s it’s been common practice in popular music to add an upper midrange boost to the kick drum sound, typically around 4kHz, to bring out the impact of the beater hitting the skin and give the kick some definition. That peak has been built into the Beta52A. In fact, it’s the most striking feature of the frequency response shown above: a +7dB peak at 4kHz. Above that peak the response rolls-off rapidly, which, by fault or by design, minimises the audibility of spill from the snare bottom. A small hump in the roll-off at 8kHz, an octave above the 4kHz peak, helps to keep the overall peak a bit broader and more ‘musical’ – although it might simply be the effect of a resonator cap or similar added to extend the high frequency response (as discussed in the earlier instalment about dynamic microphones).

When close-miking a kick for popular music applications it’s also common (depending on the genre) to remove some low midrange energy around 300Hz to 400Hz to prevent the kick from sounding too boxy – and we can see that a subtle dip around that area has been built into the Beta52A’s response.

Between the upper midrange peak and low midrange dip, we can see that two of the most commonly used EQ points when mixing kick drums for popular music have been built into the Beta52A, helping it to deliver an acceptably fashionable sound straight out of the microphone.

If judged by the frequency response curve shown above you’d be forgiven for dismissing the Beta52A as being too bright and clicky, but, as with the SM58, that judgement does not factor in the proximity effect. The frequency response graph shown above was measured at a distance of 60cm from where the beater hits the skin, which places the mic somewhere outside the front skin where the sound is usually woolly and dull. This is typical of the kick mic placement for Modern Jazz and similar applications, where the kick needs to sound natural and there is often no hole in the front skin to pass through the high frequency transients caused by the impact of the beater. At this distance the prominent 4kHz boost adds some much-needed definition without sounding clicky.

The graph below shows how the proximity effect alters the Beta52A’s low frequency response at distances of 5cm (+5dB at 50Hz), 2.5cm (+8dB at 50Hz) and 0.3cm (+14dB at 50Hz) from where the beater hits the skin. We can see how the proximity effect increases the amount of low frequency energy coming out of the microphone, making that 4kHz peak a less significant part of the overall frequency response as the mic is moved closer. At these distances the impact of the beater on the skin is so strong that it doesn’t require any help from the mic’s upper midrange boost anyway.

The Beta52A’s combination of proximity effect, low midrange dip and upper midrange peak creates a kick drum microphone that provides an acceptably fashionable sound across numerous genres, changing tonality in accordance with the miking distances typically used for those genres.

ElectroVoice RE20

Many directional microphones intended for close-miking have similar characteristics to the SM58 and Beta52A – an exaggerated upper midrange that is ultimately balanced out by the proximity effect when the sound source is close. When using these microphones for voice, brass, woodwind and other sound sources that are capable of moving closer and further from the mic, the musician is able to ‘play’ the proximity effect to create the desired tonality.

However, there are times when this is not a desirable quality – for example, radio announcers, podcasters and Youtubers. In these situations the announcer or presenter could be required to move around a little while talking, and is unable to maintain a consistent distance to the microphone. This results in unintentional variations in the tonality of their voice due to the proximity effect. They might also have one or two guest speakers who are not familiar with speaking into a microphone and won’t maintain a consistent distance, again unintentionally changing the tonality of their voices. Omnidirectional microphones don’t have any proximity effect and would not cause this problem (which is one of the reasons why handheld dynamic omnis are commonly used for ‘on the street’ interviews and news-related sound bytes), but are not a good choice when there are not supposed to be external noises such as traffic, air conditioning, untreated room acoustics and similar. For situations where directionality is needed without any significant proximity effect, ElectroVoice’s RE20 provides a good solution. It’s a dynamic cardioid that uses ElectroVoice’s ‘Variable-D’ technology (the D is for ‘distance’) to minimise the proximity effect, making it a popular choice with broadcasters and podcasters. Announcers can move closer or further from the RE20 without any significant changes in tonality at low frequencies.

The illustration above shows the frequency response of the RE20. Unlike Shure’s SM58 and others there is no significant boost in the upper midrange because there is no need to balance the upper midrange against the proximity effect’s low frequency boost when used up close.

The RE20’s frequency response curve is relatively even from 70Hz up to about 1.5kHz. Most microphones designed for voice tend to have peaks in the upper midrange (aka ‘presence peaks’), but, instead, the RE20 features subtle dips in the upper midrange — there’s one around 2kHz and another around 4kHz. These dips are followed by a rise of about 1dB between 5kHz and 10kHz (probably to aid intelligibility and provide a sense of air) before rolling off to -5dB at 20kHz.

The RE20 offers directionality without the proximity effect, making it an ideal choice for voice applications where it’s not possible to maintain a consistent distant between the voice and the microphone, and where there’s no desire to ‘play’ the proximity effect as part of the performance. Its directional polar response and lack of proximity effect also make it a popular choice with double bassists who need to be close-miked on stage while pivoting their instrument back and forth on its pin. Most double-bassists will show you exactly where to put it in front of their instrument, and they’ll do the rest of the work for you – moving in for quiet parts and using the bow, and pulling back for loud parts, all without any change in low frequency energy.

The RE20’s combination of a directional polar response, a relatively smooth frequency response with no significant proximity effect, and the ruggedness of a dynamic microphone, collectively make it a unique and valuable addition to any microphone collection.