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Comb Filtering, Acoustical Interference, & Power Response in Loudspeakers

by September 03, 2012
Contributors: Steve Feinstein , Paul Apollonio
Line Array Mid

Line Array Mid

Comb Filtering and Acoustical Interference are two audio terms that relate to the manner in which two or more sound sources (such as two speakers or two drivers within a speaker system) interact and affect each other. The importance and audibility of these phenomena are the subject of this article, and they are a source of a continuing difference of opinion among well-respected equipment designers and acoustic theorists/researchers.

Before we debate the issues surrounding Comb Filtering and Acoustical Interference, it’s prudent to first clearly identify how these two terms since more often than not people just lump both phenomena into the term comb filtering.  Although they are both similar, it’s really more accurate to break them into two terms based on the listening conditions we are setting out to describe as follows as follows:

more often than not people lump comb filtering and acoustical interference together as the same phenomena

Comb Filtering: This is basically a delayed version of a primary signal that is produced when two or more loudspeakers are playing the same signal at different distances from the listener. In any enclosed space such as a music or theater room, listeners hear a mixture of direct and reflected sound. Because the reflected sound takes longer to reach our ears, it constitutes a delayed version of the direct sound and a comb filter is created where the two combine at the listener.  The extent of its audibility depends on how lively the room is to allow the reflected sounds to average out the overall response.  Note that this interference may be constructive (additive) or destructive (subtractive).

Acoustical Interference:  This phenomenon occurs when a single sound source such as a loudspeaker shares the same bandwidth across multiple drivers within the cabinet separated by a physical distance greater than the wavelength of propagation.  If the interference is destructive at some given frequency, it will also be destructive at multiples of this frequency.  This gives rise to a graph such as shown below, which takes on the appearance of a comb.  The extent of audibility depends on the position of the listener relative to the speaker and the physical distance between the offending drivers relative to the lowest frequency the commonly produce.

In order to generate the high degree of cancellation shown, the sound sources must generally be within the same enclosure, for reasons to be explained later.  This is why the term “acoustical interference” which is really a subset of comb filtering is generally applied to the behavior of a particular speaker, whereas “comb filtering” is applied to the behavior of a set of speakers.

 

 Combing

 Acoustical Interference / Comb Filter Measurement

Comb Filtering is also known as “picket fencing,” but this is due to the appearance of the above graph.    This should not be confused with radio wave multipath, which results in reception coming and going in response to signal variations as the receiver (your car radio) is traveling.  This combine-cancel-combine-cancel phenomenon is known as “picket fencing,” because if the listener moves across the soundstage, it sounds like the “rat-tat-tat-tat” as you drive past a picket fence in a car with the window open.

Acoustical Interference pertains more to where a common signal in the same frequency range is reproduced by two physically separate sources, such as two drivers operating in the same frequency range, or the frequency overlap of two drivers in the crossover region. If the drivers are separated by a distance greater than ¼ (90 degrees) wavelength of the highest frequency being reproduced, then the time/distance issues that manifest themselves at those frequencies mean that at some angles relative to directly on-axis, their outputs combine in phase, and at some angles, their outputs cancel out of phase.

Audibility of Comb Filtering & Acoustical Interference

There seems to be two schools of thought on the topic of comb filtering.  Some engineers use this term interchangeably with acoustical interference implying the audible effects of comb filtering between a pair of speakers playing in a room is similar to multiple high frequency drivers spaced further apart than their common wavelengths of operation in the same cabinet.

School #1:  It’s Audible

Some believe comb filtering is harmful and avoid designing multi-driver loudspeaker systems that share the same bandwidth of operation thus featuring a single woofer for bass, single midrange for vocals, and a single tweeter for the highs. Their argument is that having one driver over a specified bandwidth is better than having multiple drivers performing that task.   There is nothing wrong with this approach but if more output and higher sensitivity is required, there is absolutely no reason why multiple woofers cannot be employed in the design.  Not only will comb filtering not be an issue at these lowest frequencies, but the overall system distortion will be reduced because for every doubling of identical bass drivers, each driver will only have to work half as hard for a given output level.

Editorial Note on soundwave behavior: 

λ = C/F (The wavelength of the sound is equal to the speed of sound divided by the frequency of the sound).  All pure tones have a 360 degree cycle which can be represented by the height of an arrow above the horizontal axis as the arrow rotates at a constant speed proportional to the frequency in a complete circle). Bigger arrow = bigger amplitudes, and faster rotation = higher frequency.  If the arrow starts ON the horizontal axis, and spins one complete circle, that is 360 degrees of rotation.  That is a very simple explanation of phase. (Good enough for us right now).

School #2: It’s NOT Audible

On the flip side there is an alternative viewpoint that comb filtering is “inaudible” and nothing more than a measurement artifact. Saying comb filtering is inaudible is a bit like saying cars can go fast.  It doesn't tell us much.  To qualify that statement a bit more, it is possible that with a complex signal like stereo music, in a normal room with a good amount of reflective energy, those dips that occur from comb filtering are impacted by the mathematically inevitable fact that at some frequencies in some locations one speaker will be pushing the air (in phase), while simultaneously the other is pulling the air (out of phase). You might not perceive the dips as abnormal or undesirable.  The problem with this theory of course, is that in a real room it is impossible to separate the two.  If we put two speakers at some distance apart and play stereo, what we hear will no doubt include the effects of comb filtering from the room.

This will not be or sound as bad as for example, the out of phase behavior that occurs when one uses two tweeters in a system, separated by a distance which is significant relative to the wavelengths they radiate.  (Wavelengths decrease with increasing frequency: High frequencies have short wavelengths, and low frequencies have very long ones.)  For this reason it is quite possible to mount two 12” subwoofers side by side, or even a few feet apart, and have them act as one speaker.  At 2000 Hz, where most two-way woofer and three-way midranges  are playing, that wavelength is only 6.78 inches, meaning 180 degrees is half of that or 3.39 inches.  As the frequency increases, the wavelengths become proportionally smaller. (The wavelength at 4000 Hz is half the size of 2000 Hz).  The formula for calculating the wavelength in inches is 13560/frequency in Hz. So 13560/2000= 6.78 in for a 2000 Hz frequency.

For example, if we are 3.39 inches farther from the left speaker than the right speaker, we should expect a cancellation in the sound at 2000 Hz. (180 degrees out of phase).  Again at 6000 Hz, where we are now 540 degrees out of phase (180 plus one full cycle) so we can expect another dip in the response.  At 10,000 Hz, we are now 900 degrees out of phase (180 plus two full cycles).

So, if at some distance from the acoustic center of each speaker, we are exactly as far away from one as the other, and if the outputs at our listening location are not dominated by room reflections, then their outputs can be expected to combine in phase for up to a +3dB increase in SPL. 

However, if we move off to an angle on one side, we have changed the distance that wave must travel to reach us, so the phase between the two sources will no longer be in perfect synchrony.  If the phase difference is 90 degrees, there is seen a phase change (relative to either speaker alone),  and up to a +1.5dB SPL change.  At 180 degrees out of phase, we should expect a complete cancellation of the sound. Since real rooms at distances of more than a few inches away are predominated by room effects and reflections, this complete cancellation does not happen in practice.  What this means in actuality is that one will have a frequency response which—even if it started out as a flat line with one channel playing—once we turn on the second speaker, our composite frequency response may then look like anything but – although it may well still sound just fine.

Editorial Note: The Math behind adding signals out of phase

Let's add two vectors, C1 and C2.  First one (reference, in phase) is  C1 = 1 <0 ; second (90 deg out of phase) is  C2 = 1 < 90.

Converting to rectangular form gives  C1 = 1 + j0 ; and  C2 = 0 + j1.

Adding gives   C1 + C2 = (1 + 0) + j(0 + 1), which is 1 + j1

Converting to polar gives   Magnitude = square root of ( 1squared + 1squared ), which is  1.414

and    phase = arctangent of 1/1,  which is 45 degrees

and this is      1.414 <45

Converting magnitude to dB gives   db = 10 log 1.414, which is  1.504dB

It’s important to note that this description applies only to a microphone, or to a one-eared listener.  Humans have two ears separated by an acoustical obstacle, the head, and therefore are somewhat prepared to deal with the issue because the interference peaks and dips occur at different frequencies in each ear.  Perception in this case is determined by what is called a “central spectrum” – a cognitive (involving thought) combination of the sounds at both ears.  Hence we begin this discussion with a problematic relationship between what is heard by humans with two ears and what is measured by a single microphone.

multiple sound sources separated by a large distance is much different than a single source loudspeaker producing sound from multiple drivers separated by a relatively large distance with respect to the frequencies they are producing.

Now if those two tweeters are very close, the difference in arrival time at your ear is so small, you cannot distinguish the sound from one as direct, and the sound from the other as indirect or coming at you from an entirely different location.  Thus we cannot equate the two phenomena, (room reflections and acoustic interference) and declare, “Comb filtering is inaudible.” What we can say is there are some people who misapply the studied science of comb filtering.  Multiple sound sources in a room separated by a large distance vs. acoustical interference issues of single source loudspeaker producing sound from multiple drivers (separated by a relatively large distance compared to the wavelengths they are producing) are two different phenomena and should not be confused or used interchangeably despite their similarities.  This is akin to announcing there is no difference between direct and reflected sound, and all sound perceived as echoes are simply artifacts, not something you can actually hear.

AR Dual Dome

AR “Dual Dome” assembly

AR was the first major speaker company to recognize this phenomenon, with the invention of the “Dual Dome” midrange-tweeter assembly in the 1982 AR-9LS. 1978’s AR-9 introduced the first intentionally vertical array of midrange/tweeter drivers, to eliminate interference between the drivers in the horizontal plane. But AR realized that there was still interference between the upper range drivers in the vertical plane as well, because of the physical distance separating the upper midrange dome and the tweeter. So AR produced the “Dual Dome” unit which mounted the 1 ½”upper mid and the ¾” tweeter domes very close to each other—well within the 2” wavelength of their 7000 Hz crossover frequency—by building a massive magnet assembly with two VC carriers which drove both domes at once. Thus, the upper mid and tweeter domes operated as a single acoustic unit, with no horizontal or vertical acoustical interference or picket fencing throughout their combined frequency ranges. That was 30 years ago, but few manufacturer really pay much attention to that degree of detail anymore.

A programmer by the name of Paul Falstad has actually written a program to allow a PC user to hear acoustic cancellations, and has the utility online, and best of all, for free.  For those of you adventurous enough to test the theory yourselves, you can go here to find a link to the program.  

http://www.falstad.com/mathphysics.html

http://www.falstad.com/interference/

Now someone is going to rightly point out (as Paul Klipsch did many years ago) at a high enough frequency, your ears are many degrees out of phase.  True enough.  That we do not hear like a microphone measures, is not in dispute.  Our ear, will take the amplitude of the varying wave, and integrate it over time.  We don't hear 2000 Hz as 2000 separate pushes and pulls of the air.  What we hear instead is a constant tone, despite the fact that the pressure at our ears is changing very rapidly.  So, how does the ear brain mechanism deal with this?  Are we simply incapable of hearing it?  No.  Below about 1-2 kHz the ear/brain progressively becomes able to track the waveform. At higher frequencies it cannot, but the ability to recognize pitch accurately is uncanny, so there is more going on than meets the eye.  At high frequencies we track envelopes, and this allows us to localize amplitude-modulated and transient high frequency sounds with great precision – in fact it is the dominant factor in sound localization in rooms. So, although we don’t track the detailed structure of high-frequency sounds, we do track the modulation envelopes.  Much of the perceptual “averaging” that happens when listening to music exists because music is not a stationary signal, and there is an ever-changing pattern of inputs. What we listen to is music, filled with many frequencies at once (which are constantly changing, and even have vibrato, so the interference patterns never really stabilize long enough to be clearly audible), in a room where reflections create a similar kind of alternating plus and minus of the amplitude of the signal that reaches us.  It is because we listen to music in reflective rooms, that we have become accustomed to this effect.  If the music signal's Q is 0.1 (wideband) while the effect of the comb-filtering is to spread the dips apart at narrow intervals (Q = 20 for example), then this will not predominate over what we hear. (In other words, our ears are averaging the energy that reaches them not only over a specific time, but over a specific range of similar frequencies!) If we as humans were equipped to hear all these acoustical effects as destructive, our voice and sound recognition system would be so fragile and sensitive to the environments in which we found ourselves, we would probably have been unlikely to survive as a species.

What direction is the danger coming from?  I can hear mom calling, or is that someone else's mom?  With a narrow enough steady state as opposed to transient signal, we can demonstrate that comb-filtering is audible.  If a transient is very brief, the direct sound will come and go before a reflection may arrive and produce no interference.  Traditional frequency response measurements end up being “steady state” so they don’t necessarily depict what we will hear with real program material.

In a non-anechoic room, we hear an increased sense of space due to reflections from the separated stereo pair of speakers.  It is an effect of real rooms we deal with in everyday life when listening to sounds that are rather wideband in their energy distribution vs. frequency.  Every room has a multitude of reflections and peaks and dips.  There is no survival advantage for us to be able to hear them all, so the ear-brain tends to average the SPL (peaks and dips both) over a given bandwidth averaging the amplitude of the signal.  Multiple tones within a critical bandwidth are not identifiable as separate tonal events but they do beat together at rates determined by the frequency differences.   At low frequencies we have all heard this as the cyclical tone; at higher frequencies it is called “roughness” and is the basis for “rosin on the bow” kinds of sounds, which are important aspects of music. 

Assuming this is true, what it means is that our ear-brain mechanism is going to average those peaks and dips together, so assuming their distribution is evenly spaced, the effect on the tonal character of music will be negligible.  (Assuming the music signal is wideband, and not very narrow in bandwidth like a pure tone)  Something to remember is that interference peaks and dips do not ring.  Resonance peaks ring, and therefore are the things we easily hear.  That is also why, in measurements it is essential to do spatial averaging so that one can identify whether a peak is due to a resonance (get busy and fix it) or interference (it may or may not even be audible).

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About the author:

Gene manages this organization, establishes relations with manufacturers and keeps Audioholics a well oiled machine. His goal is to educate about home theater and develop more standards in the industry to eliminate consumer confusion clouded by industry snake oil.

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Recent Forum Posts:

gotchaforce posts on September 09, 2012 20:55
Heh, no attention given to this article because it flies over most peoples heads.

It was explained VERY well most people just dont have the patience to take it in.

They rather talk about how pretty speaker with horrible headroom and power response measurements compares to the other pretty speaker with horrible headroom and power response measurements.
Beatmatcher247 posts on September 08, 2012 11:01
Sorry it didn't link in the post above.

Beatmatcher247 posts on September 08, 2012 10:58
A while back, I asked about adding another set of Synchrony One towers to the front would be and was advised against it because of comb filtering. I don't understand that much about it, but would the following setup sound like a disjointed mess because of comb filtering?

MinusTheBear posts on September 07, 2012 20:29
Is it a far assumption that the difference between acoustical interference occurring within the driver layout of a loudspeaker will ALWAYS share the same signal and amplitude while listening to a pair of speakers in stereo, the Left/Right speaker might not always share the same signal and/or amplitude. You talked about two sound sources sharing the same signal, say you change the amplitude of the one sound source, what implications does this have on comb filtering and/or acoustical interference?
agarwalro posts on September 07, 2012 00:52
Gene, from article
on the topic of comb filtering. Some engineers use this term interchangeably with acoustical interference implying the audible effects of comb filtering between a pair of speakers playing in a room is similar to multiple high frequency drivers spaced further apart than their common wavelengths of operation in the same cabinet.
Must be the same “engineers” who use speaker sensitivity/ efficiency or phase/time aligned as interchangeable terms.

Acoustic interference is a physical phenomenon resulting from interaction of sound waves moving in air, whereas comb filtering is an electrical phenomenon resulting from summing a signal with a delayed version of itself. Acoustical interference of single frequencies under controlled conditions can be made to graphically look similar to a comb filters' response. To be fair, in an ABX test the physical and electrical outcomes may be audibly indistinguishable.

In a real life listening scenario, the acoustic interference, like room modes and floor/ceiling/wall bounce will swamp out all but the most egregious electrical errors, like incorrect polarity between drivers and amp clipping.
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