All rooms of equivalent volume have the same first room mode

[Keith_W]

I was reading some articles on Earl Geddes website when I came across this document (warning, links directly to a document) which said this:

He has other interesting things to say about room modes. For example, monopoles, dipoles, and cardioid speakers have the same room modes at low frequencies in small rooms.

It was surprising for me to read this. So I reconsulted Toole Ch. 8. Toole does not explicitly confirm or debunk this claim, but his extensive discussion of room modes focuses on calculating modes depending on room dimensions.

I then picked up F. Alton Everest's book. In chapter 13 he reaffirms what Toole said - "[...] Thus far, only axial modes have been discussed, of which each rectangular room has three, plus a modal series for each. Axial modes reflect from two opposite and parallel wall surfaces, tangential modes reflect from four wall surfaces, and oblique nodes from all six surfaces [...]", etc.

So who is right? Toole and Everest or Geddes? I headed over to the Amroc room mode simulator and entered two room dimensions that equal 96 m^3 - 6m x 4m x 4m and 8m x 4m x 3m.

The room sim showed that the first mode was different - 28.58Hz vs 21.44Hz.

It may be possible that Amroc is making calculations by calculating room dimensions as per the same approach used by both Toole and Everest, and not whatever mathematical model Geddes was using.

But is Geddes right? Sadly, his paper does not link to his Ph.D thesis where he demonstrated his claim. It would be extremely difficult for us to determine the correctness of his claim by experiments. And I haven't the foggiest how I would model his claim with mathematics.

@3ll3d00d

 

[Frank Dernie]

I then picked up F. Alton Everest's book. In chapter 13 he reaffirms what Toole said - "[...] Thus far, only axial modes have been discussed, of which each rectangular room has three, plus a modal series for each. Axial modes reflect from two opposite and parallel wall surfaces, tangential modes reflect from four wall surfaces, and oblique nodes from all six surfaces [...]", etc.

This is true.
Also the frequency of room modes are not loudspeaker type dependant but their excitation is speaker location dependant in as much as how strong the fundamental is and the amplitude of the harmonics.

Being 3D it is very much more complicated than a 1D string instrument but if you are familiar with the way the timbre and tonality of a string instrument can be changed by where you pluck it it is similar, the pitch is the same but the strength and number of overtones excited is affected.

It is similar with listener position. In the room various modes are excited by music at their frequency and at different amplitudes.
Where you are sitting is unlikely to be at either a node or antinode of any of the modes - and certainly not all of them - so the magnitude of the peaks of the various modes is different at different listening positions.

IMO and IME, if you have the freedom to do so it is best to spend time on speaker and listener location to minimise the magnitude of the peaks before applying any room correction since the correction can only be spot on in one location.

The frequencies are determined by room dimensions and are a feature of the room, the magnitude of the peaks of the modes and harmonics excited is influenced by where in the room volume they are excited, and the magnitude of the peaks you hear depends where in the room you listen.

That is also one of the reasons why different minimalist microphone positions sound so much different when you make a recording with 2 microphones.

 

[wwenze]

Earl's statement is phrased more like a rule of thumb estimation that is not far off. It mentioned that one dimensions must not be (more than) twice of the other, which your simulation has violated.

Add: Anyway Amroc seems to be using just the longest dimension for that lowest first mode. So dimensions of 500x500x500, 500x200x500, and 500x333x300 all give 34.3Hz for the lowest mode.

 

[MarkS]

The statement is just wrong. The formula for the frequency of the lowest mode in a rectangular space is f = (v/2)(1/L), where v is the speed of sound and L is the longest of the three room dimensions. This formula holds no matter what the other dimensions are (provided only that they are shorter).

The general formula for any mode is

f = (v/2)√[(n1/L1)^2 + (n2/L2)^2 + (n3/L3)^2]

where L1, L2, L3 are the three room dimensions and n1, n2, n3 are nonnegative integers, not all zero.

 

[ZolaIII]

It's primarily influenced by the room length and it will move by little with shape, absorption coefficient and so on but not to the point you can replace them for something else.

 

[MaxwellsEq]

IMO and IME, if you have the freedom to do so it is best to spend time on speaker and listener location to minimise the magnitude of the peaks before applying any room correction since the correction can only be spot on in one location

I agree with this. DSP-based room correction is useful, but it's essential to get the speaker and listening position as good as possible first.

 

[Keith_W]

Earl's statement is phrased more like a rule of thumb estimation that is not far off. It mentioned that one dimensions must not be (more than) twice of the other, which your simulation has violated.

Add: Anyway Amroc seems to be using just the longest dimension for that lowest first mode. So dimensions of 500x500x500, 500x200x500, and 500x333x300 all give 34.3Hz for the lowest mode.

I did think about that "one dimension not being more than twice of another" so I did another sim.

First mode: 24.5Hz.

First room mode: 28.6Hz.

I accept that "rule of thumb" argument, if that's what Earl meant. But if he meant literally the same frequency, I can not see how he is correct.

 

[Frank Dernie]

Earl's statement is phrased more like a rule of thumb estimation that is not far off. It mentioned that one dimensions must not be (more than) twice of the other, which your simulation has violated.

A not very good rule of thumb since it depends on linear dimension not volume.

Why have a poor rule of thumb when the precise answer is simple?

 

[bigjacko]

Maybe what Geddes said about first room mode is the uniform pressure distribution, so pure tension or compression in a room. It is not the bad room modes that cancels some sound.

Just like harmonic distortion start from 2nd. 1st harmonic is also a harmonic, but it is the sound we want.

To make it more easily understand. A perfect speaker should only produce first harmonic but no other harmonics. A perfect room should only have first room mode for every frequency but not other room modes.

 

[Frank Dernie]

Maybe what Geddes said about first room mode is the uniform pressure distribution, so pure tension or compression in a room. It is not the bad room modes that cancels some sound.

Just like harmonic distortion start from 2nd. 1st harmonic is also a harmonic, but it is the sound we want.

To make it more easily understand. A perfect speaker should only produce first harmonic but no other harmonics. A perfect room should only have first room mode for every frequency but not other room modes.

The laws of physics would beed to be repealed!

Static reasoning applied to dynamic systems is common but wrong.

Uniform pressure distribution is silence.

Any room has inevitable modes depending on its dimensions. The extent to which they are excited mainly depends on speaker position. The extent to which they add to the sound at your ears also depends on where you are in the room.

Damping in the room effects the decay.

 

[3ll3d00d]

Given that he generally knows what he is talking about and that it's easy to show that modes are driven by dimensions then it seems reasonable to think that maybe something is lost in translation in his summary.

I guess someone can find his actual thesis somewhere online? It seems to be

An Analysis of the Low Frequency Sound Field in Non-Rectangular Enclosures Using the Finite Element Method
Ph.D. Thesis by Earl R. Geddes; supervised by J. Tichy

I found the abstract here

A Analysis of the Low Frequency Sound Field in Non-Rectangular Enclosures Using the Finite Element Method.

The details of the low frequency sound field for a rectangular room can be studied by the use of an established analytic technique--separation of variables. The solution is straightforward and the results are well-known. A non -rectangular room has boundary conditions which are not separable and...

ui.adsabs.harvard.edu

I think it's quite different to what he wrote in the pdf as he compared some variants of a given room rather than rooms with completely different dimensions but same volume

The solution results are used to construct the Green's function for the low frequency sound field in five rooms (or data cases): (1) a rectangular (Louden) room; (2) The smallest wall of the Louden room canted 20 degrees from normal; (3) The largest wall of the Louden room canted 20 degrees from normal; (4) both the largest and the smallest walls are canted 20 degrees; and (5) a five-sided room variation of Case 4.

 

[Frank Dernie]

Given that he generally knows what he is talking about and that it's easy to show that modes are driven by dimensions then it seems reasonable to think that maybe something is lost in translation in his summary.

Quite so, totally agree.

 

[Keith_W]

Well, I guess that's a rather short thread. Geddes is wrong, and that's it.

 

[René - Acculution.com]

It looks like a bit of a strange statement. I would say that "All rooms of equivalent volume, regardless of shape will have the exact same 'zeroth' mode", since the volume alone determines the static compliance, and this (0,0,0) mode does indeed affect the overall response. He also states that this is not true if one dimension is very different from the others, so he must be talking about the 'first' mode, i.e. the first non-zero frequency mode, and so this shows that is is not just about volume after all, which is trivial to show. So perhaps it is more about non-rectangular rooms with fairly standard dimensions having similar low-frequency modes as those of a rectangular room.

"He has other interesting things to say about room modes. For example, monopoles, dipoles, and cardioid speakers have the same room modes at low frequencies in small rooms."
I don't see him saying that. The speakers don't "have the same room modes". The room has the same modes regardless of the speaker.

 

[Frank Dernie]

The room has the same modes regardless of the speaker.

Quite so, we can influence the magnitude of excitation of each mode and harmonic by speaker location but the room modes are a characteristic of the room.