Non-parallel surfaces and resonances

[mefistofelez]

In a rectangular loudspeaker enclosure, parallel walls will cause standing waves development inside the enclosure. The standing waves will have frequencies inversly related to the wavelengths based upon the distance between the walls. These frequencies (and their combinations) will cause peaks and/or dips in the frequency response.

So far this is accepted theory confirmed by practice.

I have been wondering what happens when the opposing walls are not parallel. I was, therefore wondering if someone who has more knowledge in this area could point me to (at best) some references that studied the phenomenon, and (at worst) to some references that would enable me to model it.

Thank you,

M

[h-bar]

I just typed and lost a longer reply, so I'm afraid this one will be a bit terse.

Matlab can be useful for modeling standing waves in various structures. It's easier to work in two dimensions than in three. A lot can be learned even in the simplified system. The key result is that even if a shape has non-parallel walls (or edges) standing waves can still be supported. There seems to be a broadly held misunderstanding in audio circles on this topic. An equilateral triangle, for example, has a series of modes of oscillation that are reminiscent of the ones you'd expect in a square. The symmetries are different, of course, but the basic behavior is quite similar (higher frequency modes of more nodes; the symmetries of the modes are determined by the symmetry of the triangular shape...).

[Andy_G]

H-bar is correct, any enclosed structure will have standing wave frequencies associated with it.
With a rectangular cab there three distinct 1st order standing waves created. (at 3 distinct frequencies)
With other irregular shapes the SW frequencies tend to be more spread out, hence any individual one is of much less intensity.
This is also the idea behind differential bracing (non equal spacing), stressed panels, and irregular padding etc. The aim being to spread out any problems over as wide a range as possible so that there are hopefully no main resonance or SW frequencies.

[elefantino]

Hi mefistofelez - "Ich bin der Geist, der stets verneint!"

Visaton did a little study about this which confirmed that irregular shapes are pretty useless:



(from http://www.visaton.de/vb/showthread....&threadid=5143 )

Resonances are smeared a bit and pushed a little higher in frequency in this case but otherwise there is zero effect. I guess the physics behind this is quite simple: pressure is proportional to the area inside the enclosure and sound waves are pressure waves. The often seen beam analogy for sound waves is misleading.

[mefistofelez]

Gentleman,

thank you very much for your replies.

h-bar,

Matlab sounds fine to me. Would you have any references how to set up such a model?

Andy_G,

yes, this was my heuristic understanding that the "q" will be broader for the non parallel surfaces. I would just like to have a better qualitative understanding.

elefantino,

". . .
Und das mit Recht; denn alles, was entsteht,
ist wert, dass es zugrunde geht;
Drum besser wär's, dass nichts entstünde.
So ist denn alles, was ihr Sünde,
Zerstörung, kurz, das Böse nennt,
Mein eigentliches Element."

Thank you for the link. Where are you in Deutchland? I am in Muenchen.

M

[Dennis H]

Unless the enclosure is very large, the resonance frequencies are usually high enough that they are easily absorbed with some damping/stuffing material so it's not really a problem.

[crackyflipside]

So would the same findings from the German study relate to resonance in non-parallel wall rooms?

[Dennis H]

So would the same findings from the German study relate to resonance in non-parallel wall rooms?

Sure, same principle but lower frequencies because of the larger dimensions.

[mefistofelez]

Dear Dennis H,

you wrote: "Unless the enclosure is very large, the resonance frequencies are usually high enough that they are easily absorbed with some damping/stuffing material so it's not really a problem."

Well, maybe I am making a mistake in my calculations, but, for a length of the enclosure equal 18 inches, I get a first mode at 376 Hz. From the little I read, this low frequency is not easily absorbed.

Or, am I missing something?

Thank you,

M

[Dennis H]

3" of fiberglass will absorb 376 Hz pretty well. Keep in mind that 376 is the lowest mode. All the others will be higher and more easily absorbed. And, if the driver is mounted more than 1/4 the 18" length (4.5") away from the end of the enclosure, that 376 mode won't be stimulated at all.

http://www.bobgolds.com/AbsorptionCoefficients.htm

[---k---]

". . .
Und das mit Recht; denn alles, was entsteht,
M

Ack! Stop that! Ich habe alle meine Deutch vergessen.
And, I probably got that wrong too.

Dennis,
You aren't suggesting that 3" of fibreglass be used though, are you?

Also, can you explain a little further why the first mode won't be stimulated if the driver is further than 1/4 the wavelength away. And, isn't the first mode the most improtant to abosorb?

Thanks,

[Dennis H]

You aren't suggesting that 3" of fibreglass be used though, are you?

It's usually not necessary because the top-bottom resonance is usually weak. The most important one is the front back resonances behind the midrange where the sound tends to reflect back out the cone and that's higher frequency.

Also, can you explain a little further why the first mode won't be stimulated if the driver is further than 1/4 the wavelength away. And, isn't the first mode the most improtant to abosorb

It's just like room modes. Moving the speaker away from the wall avoids stimulating the mode. As well, for the top/bottom modes, a front-mounted woofer is pretty big compared to the enclosure so you don't have a single point source but rather signals arriving at the wall at different times, weakening the reflection. Kinda like a line array eliminates floor-ceiling bounce problems. The only time it's a big deal is with a bottom-mounted driver and then some stuffing at the top is a good thing.

This is only a factor with a ported box anyway. Most people stuff sealed boxes so all the reflections go away.

[h-bar]

mefistofelez:

To see some pertinent MATLAB demos, once you've started MTALB open the Help window. Click on the Demos tab (in the upper left quadrant of the help window). If you expand the MATLAB list you have Mathematics and Graphics as the first two options. The most useful might be Graphics. It contains "Vibrating Logo" as an option. If you click on that to bring up an explanation, you're also given the option to open up the source code (m-file). The option appears just above the point where the "Vibrating Logo" heading appears in the explanation window. I haven't read through the code but since it makes use of solutions to the wave equation it ought to put you on the right track.

As an alternative you can look in the Help window under: Demos>MATLAB>Mathematics>Finite Difference Laplacian

It's not precisely what you're looking for but it will show you some useful MATLAB tricks and commands.

h-bar

[mefistofelez]

Dear Dennis,

It's usually not necessary because the top-bottom resonance is usually weak.

That is good to know, but what is the mechanism? The driver is omnidirectional, no?

Unfortunatelly, in my case the 18" is the front to back. The intended crossovoer is at 300 Hz, so I am worried about this.

Dear h-bar,

Thank you.

M