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Technical Article: Listening Room "Modes" (Frequency Response Changes)

DonH56

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#1
Room interactions are often discussed as one of the primary reasons similar (or even dissimilar) systems sound different. If you read the “Reflections and DACs” article you saw how reflections and standing waves can interact along a transmission line. As it happens, sound waves in a room also interact, affecting the amplitude of sound you hear at different frequencies. Sound waves from more than one source (for example, two speakers) will meet and interact. Sometimes they add, sometimes they subtract (cancel), but there will be interactions in any room. “Ah, but what about absorption?” you might ask. Ah, but remember I said “more than one source”. If I put two speakers in a perfect anechoic chamber, absorbing all sound when it interacts with any surface (walls, floor, ceiling), there are still those two sources to consider. If I sit between them, waves from one interact with waves from the other, despite having no other reflections to contend with. See Figure 1; sound waves from the two speakers spread out and interact at the listener’s location.


Figure 1. Sound wave interaction.

Depending upon their phase, the sound waves may add constructively, making the sound louder, or destructively, sounding quieter. The phase depends upon the source, naturally, but also the frequency and distance from the speakers. Take a look at Figure 2, showing three different frequencies (fo, 2fo, and 5.9fo). The vertical axis shows amplitude and the horizontal axis distance. All is relative for this example.



Figure 2. Amplitude vs. distance for three frequencies.

All three waves are launched at the same instant and in phase (this is not generally true). Now, there are several interesting observations we can make from this picture:

At an arbitrary distance, the sound waves do not line up perfectly. This is the way the world works and is not really important, so long as the phase relationship is maintained. That is, if your components (from source through speakers) alter the phase/frequency relationship, then what you hear may be different from what was originally recorded. However, even if that is not true, chances are you won’t notice… As an aside, speakers typically dominate the phase picture, and speakers with excellent pulse (or impulse) characteristics do best at maintaining phase relationships across all frequencies (linear phase, constant group delay, to be technical). I do like my Magnepans!

As frequency increases, the peaks and valleys get closer. At 20 Hz there are over 56 feet from peak to peak; at 20 kHz the distance from peak to peak is less than an inch. At low frequencies, the waves are longer than most rooms and room modes dominate. At high frequencies, most any little surface will cause reflections, breaking up the waves so that by the time they reach you the reflections are pretty random with respect to the source and don’t really bother us. In between, the same sound from two different sources interacts as a function of frequency (actually wavelength, velocity of sound/frequency) and distance. If we are sitting such that two peaks interact, the sound will be louder; if a positive peak and negative peak interact they will cancel and no sound is heard at that frequency. While perfect cancellation in the real world is rare, deep nulls and large peaks do occur. The effect looks like the teeth in a comb, and thus the name “comb filter effects”. Unfortunately, comb filter effects tend to be worst right through the middle of the audio band, right where we hear best. When you move your head an inch, and the sound changes by a mile, that’s almost always what is causing the effect. The good news is that sound absorbers and diffusers can go a long way toward reducing comb filter effects, and proper speaker positioning minimizes interactions from the desired direct sources (your speakers).

Finally, when the sound wave hits a reflecting surface, it inverts and takes off at an angle equal to the incoming angle but on the other side: it makes a triangle. For the simplest case, consider a constant sound wave that comes from the speaker and hits the back wall, coming back along the same path but inverted (180 degrees out of phase). It’s like a mirror image of the sound… It travels along interacting with the incoming wave, sometimes adding, sometimes subtracting. Think of sitting somewhere in Figure 1 while signals bounce around, creating peaks and valleys at your listening position. What we hear depends upon where we sit with respect to the distance from the wall, and the frequency of the sound.

If we have a sound source in a closed room, the frequencies at which interactions occur (the modes) can be predicted since the dimension are known. Since we know the velocity of sound for a given frequency, we can calculate wavelengths, and in turn predict the modes of that room. Those are the frequencies at which peaks and valleys will occur. These peaks and valleys will occur at integer submultiples of the room’s dimensions, and even multiples generally cause the biggest problems. Thus sitting in the exact center of the room is where we are most likely to have problems with them. That is also the reason many sources suggest sitting 1/3 from either wall in the longest dimension of the room to minimize the impact of the lowest mode.

Calculating room modes is straight-forward if somewhat tedious:

Fmode = v/2 * m / D where

Fmode is the frequency of the mode
v is the velocity of sound (1130 ft/sec in dry air at sea level)
m is the mode (an integer: 1, 2, 3, …)
D is the room dimension (width, length, height)

The fundamental mode (m = 1) creates a standing wave in the middle of that dimension, a peak or null (usually a null, but it is sometimes hard to predict which as the modes increase). A mode of two indicates a wave that has traveled twice along that dimension, and so forth. There are tangential and oblique modes reflecting from other dimensions and such; it can get complicated quickly. For now, consider a simple room with dimensions 10’ W x 20’ L x 9’ H and calculate the first few modes in each dimension:

Fmode = (28, 57, 57, 63, 85, 113, 113, 126, 141, 170, 170, 188, 198, 226, 226, 251) Hz

These are frequencies at which sound in the room will peak or null. Note that peaks can easily reach 10 dB (10 times) or more, but physical factors (absorption, wall vibrations, etc.) usually prevent peaks much larger than that. Nulls due to cancellation can be quite deep; 30 dB (1/1000) or more is not uncommon. Thus, fixing the nulls is often harder than bringing down the peaks. It is often easier to move the listening position…

Note that several frequencies are duplicated. This is because 20’ is an integer multiple of 10’, leading to multiple modes at the same frequency. This will exaggerate the effects at those frequencies, and indicates why good sound design requires room dimensions that are not multiples. Prime numbers are often used to prevent mode doubling.

Because closely-spaced modes are not heard as separate frequencies, knowing the difference frequency (Fd) between successive nodes is useful:

Fd = (28, 0, 6, 22, 28, 0, 13, 16, 28, 0, 19, 9, 28, 0, 25) Hz

Most texts agree that differences of 10 Hz or less are problematic as our ear/brain system does not separate them, making one big dip or peak. This room clearly has several problem frequencies…

Sound absorption or diffusion can be used to reduce or “break up” room modes and reduce their impact on frequency response. Either way, they must be physically large to handle low-frequency problems due to the very long wavelengths involved. This is why solving bass problems requires large diffusers and/or a lot of bass traps. Other folk, such as our own Ethan Winer, are better equipped to discuss mitigation of these modes in your room. His website, www.realtraps.com, also has a calculator to help determine the modes of your room. There are numerous other calculators online.

Reading back, this may a bit hard to follow, but hopefully presents a picture of room modes and why they matter.

HTH - Don
 
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#2
A visual way to see this is to drop 2 stones or rocks at the same time in a pond or a lake and watch the reaction as the waves cross paths.
 

DonH56

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#3
A visual way to see this is to drop 2 stones or rocks at the same time in a pond or a lake and watch the reaction as the waves cross paths.
At home you can use a pan of water and a couple of marbles, or just stick (poke) a couple of fingers in the pan.
 

amirm

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#5
A “conclusion” (as Amirm does) would be welcome... Thanks!
Here you go. :)

Every listening room has modes which conspire to substantially change the frequency response of any speaker. Variations can be huge, as much as 25 dB! You don't have correct sound reproduction in your room unless you reduce their effects.
 

Theo

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#6
Primary correction steps should be physical (diffusers or bass traps), at least when confronted with strong mode amplitude.
It is relatively easy to correct for constructive standing waves with a computer: just eq them down as per model (or measurement).
Destructive ones are more difficult to handle, as you would need to boost those frequencies by up to 25dB, as pointed out by Amir. Your amp/speakers may not like it at all, and in the best case (that is with no smoke involved) distortion will probably rise a lot...
 
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#7
Here a calculator for room modes: https://amcoustics.com/tools/amroc
And here a page with more info regarding room modes: http://www.sengpielaudio.com/calculator-roommodes.htm with a good footnote: "An equalization cannot be a substitute for good acoustics. "
And here a calculator for absorption and Helholtz resonators if you wish to acoustically treat a room (fibreglass and rockwool will have a gfr between 5000 and 40000 or so depending on density, the fluffiest blow in fibreglass has an even lower gfr): http://www.acousticmodelling.com/
 

MRC01

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#8
Good intro. One way to visualize it is to imagine a rope tied to the center of one wall. Extend the rope across the room and hold the opposite end. If you pump it up and down to make a standing wave, you can only make waves that have an integer number of "humps" in the rope.

The biggest peaks and nulls are typically easily audible. Slowly walk around the room while sounds (test signals or music) are playing and you can hear the sound changing in different locations in the room. When we say that 60 Hz is a room mode, it means a wave of that frequency is resonating between walls just like your rope. But that doesn't mean 60 Hz is louder everywhere in the room. It will be louder in some places, and quieter in others. Just like a standing wave in the rope has certain points that aren't moving at all, and other points that are leaping from the floor to the ceiling.

This means the listener position is as important as speaker position; listening to the sound change as you walk around the room demonstrates this. For example if you sit 3' in front of a reflective back wall, you'll get a null at about 92 Hz because at your position, the wave bouncing off the wall behind you has traveled 6' which is 1/2 wavelength of 92 Hz. You'll also get a boost at 184 Hz because at this frequency that 6' is now a full wavelength.

It's best to solve it (flatten or reduce modes) using room arrangement and treatment first, before applying EQ. The first fixes the problem at its root, the second is a band-aid over the top of the problem. This is true of all speakers, but especially for dipoles which are even more sensitive to room position (this is both a blessing and a curse).

Because we hear frequency logarithmically (the difference between 4,000 and 8,000 sounds the same as the difference between 40 and 80), the modes get perceptually closer together with increasing frequency. So most of this is below around 300 Hz (more or less depending on the room). You can have peaks & dips at higher frequencies but that's a different problem with different solutions.
 
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Cosmik

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#9
When you move your head an inch, and the sound changes by a mile
Does that really happen? Not with 99% of music, I think. If I play steady tones, then yes, the level varies noticeably, but I wouldn't say 'the sound' has changed - just the level, and because I am accepting the addition of the room's acoustic to the sound (I'm listening on speakers) that doesn't bother me - it's what I want, in fact.

But if I want the recording beamed into my ears directly, it can be arranged.
 

MRC01

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#10
Does that really happen? Not with 99% of music, I think. ...
I've heard this effect before.

One potential cause can be certain speakers, if the driver isn't smaller than the wavelength of the sound it's emitting, the dispersion pattern gets uneven. For example, when a big panel driver emits a treble frequency, the dispersion pattern can get uneven to the point where moving your head a few inches is like sliding a treble knob up and down (the lower frequencies are unaffected).

Room modes also cause this, but they're usually far enough away from each other you don't get the effect by just moving your head. You have to relocate to a different part of the room. Or at least slide to the opposite end of the couch. More than an inch.
 

DonH56

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#11
Does that really happen? Not with 99% of music, I think. If I play steady tones, then yes, the level varies noticeably, but I wouldn't say 'the sound' has changed - just the level, and because I am accepting the addition of the room's acoustic to the sound (I'm listening on speakers) that doesn't bother me - it's what I want, in fact.

But if I want the recording beamed into my ears directly, it can be arranged.
Has happened to me many times over the years and virtually always with music (I rarely listen to test tones). Maybe I just more sensitized to it. It is mostly when single instrument (or singer) is soloing so that probably exacerbates the issue. May also be due to the jazz music I like that often has solos over the band. What I have used as a self-test and teaching/training exercise is to listen on headphones then again to the speakers when I suspect comb filtering or other speaker imaging issues. If the sound is consistent over the frequency range and instruments/voices stay fixed in the image using headphones, but wander around using speakers, then something is messing up the image.

Fixing placement and/or adding room treatment usually stabilizes the image. I have demonstrated it many times to other people so I don't think I am completely crazy. Or maybe all of us are.

Room modes are usually at lower frequencies so the effect is just as noticeable, but you have to move maybe a foot or three, instead of just an inch or three.

IME - Don
 

LTig

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#12
When you move your head an inch, and the sound changes by a mile
Does that really happen? Not with 99% of music, I think. If I play steady tones, then yes, the level varies noticeably, but I wouldn't say 'the sound' has changed - just the level, and because I am accepting the addition of the room's acoustic to the sound (I'm listening on speakers) that doesn't bother me - it's what I want, in fact.

But if I want the recording beamed into my ears directly, it can be arranged.
I once listened to Martin Logan CLS full range electrostatic speakers, and the sweet spot was just an inch or two wide. Moving the head a little to the side and the really wonderful soundstage collapsed totally.
 

MRC01

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#13
I once listened to Martin Logan CLS full range electrostatic speakers, and the sweet spot was just an inch or two wide. ...
That's expected since the driver is wider than the wavelength of treble frequencies. Not by a little either, but around 10:1. They curve the panel to mitigate this.
Magnepans use a long vertical ribbon tweeter which avoids this issue. But of course requires a x-over. Choose your poison.
 

Blumlein 88

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#14
I had some Acoustat Two's. Not really a flat panel. Two flat panels side by side about 30 inches total width. So half that for each panel. Each was angled very slightly, maybe 5 degrees off center. An inch or two would alter the imaging. Moving to the next seat on the sofa would mean you only heard the nearest channel as if the other quit playing. When having audiophile friends over I had a chair ahead of and behind the sofa so three could listen in stereo at once. My curved Soundlabs aren't like this though favoring the middle. Quad ESL63s with their delayed concentric rings weren't that way either.
 

Cosmik

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#15
OK, maybe it does happen with panel speakers - I have very little experience with them. With reference to another thread, I don't think they are a speaker that would emerge from a typical set of requirements for an audio playback transducer. They exist, and people use them and test them, but they have peculiar properties.
 
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#16
I have experience listening in a near anechoic room (nearfield and midfield listening without desk in a big high ceiling room with 50cm thick absorption full walls and ceiling, only floor untreated).
To share my experience. It is not even similar to listening in a normal room or partly treated room. It's as different as listening to speakers in a normal room and listening to headphones (which all lack natural HRTF, bass sensation and have all the breakup problems that come from using a single driver). Only it's way way better than both. You really have to experience it to understand the detail, dynamics and transparancy you get in such a room. Can't compare it with anything else, totally unique experience.
Then you understand how massively direct reflections and modes affect the sound you usually get in rooms. It masks most of the audio info.
I can say with confidence that having a good room and treating your room the right way (and listening position ofcourse) is by far the most important thing for audio quality, then speakers, then amps and DAC.
 

Cosmik

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#17
I have experience listening in a near anechoic room (nearfield and midfield listening without desk in a big high ceiling room with 50cm thick absorption full walls and ceiling, only floor untreated).
To share my experience. It is not even similar to listening in a normal room or partly treated room. It's as different as listening to speakers in a normal room and listening to headphones (which all lack natural HRTF, bass sensation and have all the breakup problems that come from using a single driver). Only it's way way better than both. You really have to experience it to understand the detail, dynamics and transparancy you get in such a room. Can't compare it with anything else, totally unique experience.
Then you understand how massively direct reflections and modes affect the sound you usually get in rooms. It masks most of the audio info.
I can say with confidence that having a good room and treating your room the right way (and listening position ofcourse) is by far the most important thing for audio quality, then speakers, then amps and DAC.
But would you want to live like that? I think that one of the underlying fantasies of the whole hi-fi phenomenon is that you are effectively summoning musicians to play for you. And part of that is for the experience to be two-way i.e. both you and the musicians are sharing something of the same acoustic. Your companion speaks to you and there is something similar in the sound of that to the music you are listening to. When you remove the room completely, all you have is the recorded acoustic and no 'bridge' between you and it.

(Of course I am retro-fitting an idea to the practical reality of stereo speakers in rooms, but it doesn't necessarily mean it's wrong... :)).
 
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#18
But would you want to live like that? I think that one of the underlying fantasies of the whole hi-fi phenomenon is that you are effectively summoning musicians to play for you. And part of that is for the experience to be two-way i.e. both you and the musicians are sharing something of the same acoustic. Your companion speaks to you and there is something similar in the sound of that to the music you are listening to. When you remove the room completely, all you have is the recorded acoustic and no 'bridge' between you and it.

(Of course I am retro-fitting an idea to the practical reality of stereo speakers in rooms, but it doesn't necessarily mean it's wrong... :)).
There are two aspects to this I think.
First is bare "soundquality". The limitless dynamics / complete dryness of sounds and especially treble is just crazy in an anechoic room. And no headphones don't get even remotely close (I think this due to the lack of correct HRTF and driver breakup modes in the treble). This gives a sensation of soundquality and tranparancy that is second to none.
Secondly, do you want the performers to be in your room or do you want to be transposed to the room in the recording. I want the second and while most recordings are lacking here, there are many recordings where you will be transposed so perfectly to the performers space that it is truly as if you are there. Big concert halls, churches, jazz clubs, etc.

Btw I think the top of professional studio's and mastering rooms get the idea too. As I understand it the best rooms are currently made by Northward Acoustics. These are near anechoic rooms (often more than a meter of absorption in layers, full walls and ceiling) and soffit mounted speakers.
http://www.northwardacoustics.com/portfolio/ (btw the diffusors you see in the pics are just for creature comfort for the person sitting in the listening spot, the do not have an audible effect on the sound coming from the speakers)
These are very expensive but one can do it for much less money by yourself if you study acoustics (building a new studio myself that is fully anechoic including floor). There is one caveat though in such rooms, when set up to measure flat the treble will most often be too forward / loud, only with natural far field recordings will it sound balanced. I've studied this effect and have come up with a psychoacoustic solution which I'll share at a later point, developing a product for this).
 
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#19
I've heard this effect before.

One potential cause can be certain speakers, if the driver isn't smaller than the wavelength of the sound it's emitting, the dispersion pattern gets uneven. For example, when a big panel driver emits a treble frequency, the dispersion pattern can get uneven to the point where moving your head a few inches is like sliding a treble knob up and down (the lower frequencies are unaffected).

Room modes also cause this, but they're usually far enough away from each other you don't get the effect by just moving your head. You have to relocate to a different part of the room. Or at least slide to the opposite end of the couch. More than an inch.
This is only true if beaming occurs at higher frequencies. The left-right sensitivity of human hearing is max in medium frequencies and diminishes to zero at low frequencies and high frequencies. If the music player is recorder in stereo, so 2 mikes of similar there is enough audio encoding in IT forcour Braun to perceives space and position. However if mono pannedcin the middle, moving your head will move the virtual position.
 

Krunok

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#20
I have experience listening in a near anechoic room (nearfield and midfield listening without desk in a big high ceiling room with 50cm thick absorption full walls and ceiling, only floor untreated).
To share my experience. It is not even similar to listening in a normal room or partly treated room. It's as different as listening to speakers in a normal room and listening to headphones (which all lack natural HRTF, bass sensation and have all the breakup problems that come from using a single driver). Only it's way way better than both. You really have to experience it to understand the detail, dynamics and transparancy you get in such a room. Can't compare it with anything else, totally unique experience.
Then you understand how massively direct reflections and modes affect the sound you usually get in rooms. It masks most of the audio info.
I can say with confidence that having a good room and treating your room the right way (and listening position ofcourse) is by far the most important thing for audio quality, then speakers, then amps and DAC.
I have tried listening music in a true anechoic room (we had one at university) and it sounded awful. Even a people voices sounded awful. I would definitely not want to have that kind of sound in my room.
 
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