Treatment of a small boxy room - REW file attached

#76

By the way if anyone works with Matlab and is interested in digging further, Trevor Cox has posted all the code from his book, along with a few other applications, on the Matlab File Exchange.

I have access to Matlab through my work (no idea how much it costs but suspect it's not cheap), but most of this code can probably also be run under the free Gnu Octave package.

#77

Re-re-reading Cox & D'Antonio, the following passage in the section on Helmholtz resonators jumped out:

"The perforated surface is divided into individual cells which are assumed to behave independently with a repeat distance D. D is defined in Figure 6.2, which shows a cross section through the absorber. The absorber is assumed to be perforated in two directions, with the repeat length being the same in both directions. The individual cells will not be entirely independent at low frequency, and consequently physical sub-dividing of the volume may be required as the wavelength becomes large. This is especially true if good oblique incidence absorption is required, as would be needed for good random incidence absorption, and lateral propagation within the cavity must be suppressed to maximize absorption. When a porous absorbent is placed in the cavity, sound propagation is generally normal to the surface as discussed in Chapter 5, and so the need for subdividing is less critical, except at very low frequencies."

Glen also alluded to this earlier, and it seems like this might explain the total lack of absorption of my test boxes. The text is vague on whether the problem with a non-divided volume will be a failure to achieve resonance, a failure to absorb, or both. Since my 45Hz mode is near the low end of typical playback systems, I guess it's safe to say it qualifies as a "very low frequency".

I'd read this section before, but there's nothing like having something not work to put the information into context.

#78

This information is superb, thank you.

Have you compared your matlab models with those on this site? He states Cox as an influence in the formulae used.

http://www.acousticmodelling.com/8layers/helmholtz.php

#79

if you can access the studiotips on archive.org, Eric Desart had posted quite a bit of information on HH resonators, chamber divisions impact and calculations and much more. yes, octave would be the way to go unless you can afford mathlab :-)

https://octave.org/

#80

endorka wrote:Source of the post This information is superb, thank you.

Have you compared your matlab models with those on this site? He states Cox as an influence in the formulae used.

http://www.acousticmodelling.com/8layers/helmholtz.php

Great question!

I have heard that this site is regarded as one of the more reliable calculators, and it looks to be really well thought out. If you dig into the parameters, it provides numerous options for both the porous absorber model and the Helmholtz model.

I have tried running the web calculator using the same parameters as the Matlab script, and selecting the same models (which are not the defaults on the web page). The porous absorber model shouldn't matter, since my initial tests are without any porous absorber (to simplify things as the flow resistivity values are a whole other can of worms). Nonetheless I specified "Delany and Bazley" as the porous absorber model, and "Transfer Matrix" as the Helmholtz model (the results don't depart much from the default settings though).

The web calculator gives a slightly different result, with a centre frequency of 45.6Hz versus 42Hz using Cox's Matlab script. I don't think the difference is hugely significant, given all the uncertainties involved, but am not sure where the difference arises (the Matlab result is a bit closer to what I observed with the candle). What seems sketchy is that both the web calc and Matlab imply strong absorption in this frequency range, even without a porous absorber, but my boxes seem to have zero effect on the sound levels (neither around the absorber holes nor for the room in general). This despite the fact that there is clearly something happening at a specific frequency in the expected range (based on the candle test).

In the C&D book, they start by deriving equations for the resonant frequency without considering a porous absorber. They go on to say "For most designs, the losses contributed by Equation 6.15 are very small, and in order to get good absorption it is necessary to add porous material." Equation 6.15 gives the resistive component of the impedance for a Helmholtz resonator without any porous material. Subsequent sections go into more detail on determining the acoustic impedance in the presence of a porous absorber.

So in a sense, my candle testing is consistent with what they ultimately say (the resonance frequency is as predicted, and there is no absorption). It's possible that the transfer matrix implementations used above are not suitable for the case where there is no porous absorber, which could explain why both the online calculator and Matlab code predict strong absorption when there should be little or none.

It's also worth quoting another earlier section from C&D:

"One problem with modal control using resonant absorption is knowing how much resonant absorption to use. Although the theories set out in Chapter 6 allow the absorption coefficient for Helmholtz absorbers to be estimated, the meaning of absorption coefficient at low frequencies is problematical. (Even more problematical is the lack of good prediction models for membrane absorbers, but that is another story.) At low frequency the sound field is not diffuse, and consequently the effect that the absorber has is not calculable through simple statistical laws."

One other point is that I'm realizing my "soda bottle and cotton" tests probably have little to do with absorption per se, although I still think they should give some insight into how Helmholtz resonance interacts with the local sound field. For one thing, the bottle mouth is a tiny speck in front of the 1.5m sound wavelength at 200Hz. That wave will normally diffract right around an object that size, so there never would have been any relection to speak of.

A more meaningful "bottle" test might be to measure the sound level in front of a reflective baffle, then check how it changes with the bottle mouth presented through a snug hole in the baffle. This would better represent a Helmholtz resonator at the room boundary.

#81

gullfo wrote:Source of the post if you can access the studiotips on archive.org, Eric Desart had posted quite a bit of information on HH resonators, chamber divisions impact and calculations and much more. yes, octave would be the way to go unless you can afford mathlab https://octave.org/

Thanks I will check that out! Matlab has pretty generous educational licensing, so if anyone has student or teacher status it's worth looking into (if you really want to get into the gory details).

#82

endorka wrote:Source of the post Have you compared your matlab models with those on this site? He states Cox as an influence in the formulae used.

So further followup on your question led to an interesting observation (which I should probably triple check).

In section 6.3.2, C&D point out that losses are determined by the resistive (real) term of the Helmholtz resonator's impedance. They then give a couple of equations, with references, for this resistance in the no-absorber case. They stress that the losses are negligible without an absorber (which they are, in my limited experience).

Plugging the values used in my Matlab code into Equation 6.16 for the resistance at resonance gives a value of 42 Pa·s/m3. This is a much smaller resistance than the corresponding values of 315 and 413 given, respectively, by the Matlab and web implementations of the transfer matrix method.

So it seems possible that some widely used algorithms for predicting Helmholtz absorption might be designed for the practical case where porous material is present, leading to invalid results for an "empty" resonator (over-predicting the absorption). This would be worth knowing, as it is tempting to perform initial tests on the resonator prior to adding absorption. Moreover, the gas flow resistivity values needed for accurate modeling are notoriously difficult to obtain for commercial insulation products that are widely used in DIY attempts. I would also hazard a guess that overdamping the cavity will prevent resonance, which will also lead to failure. So we really need to hit a magically narrow range of GFR values for this to work, under circumstances where we are basically flying blind. I think the only way to succeed is to come up with an approach for titrating the absorber load while continuously testing (somehow) for effective absorption.

All that being said, I'm still trying to get my head around all this so these comments should be taken with a grain of salt (especially from someone who mixes up 2x6 and 2x8 lumber :roll:

).

#83

there are also impact from position of the damping within the cavity including proximity to the openings, depth of the material, distance to "back wall" of the cavity from the material, etc. e.g. having the damping (say 3" of semi-rigid 703) behind the openings (say touching the front panel), then you would see a low absorption level but wide, if you put that same thing 1/2 deep into the box, you would see broad but higher, and final flush on the "back wall" more absorption than empty, sharp Q. you noted that velocity is one of those things happening with the candle test... "room mode" resonances within the box also play into the overall efficiency and workable bandwidth (e.g. having a large cavity used for higher frequency absorption). John Sayers always said - doesn't matter in terms of the absorption material used, soft rags tossed into the box will deliver. :-)

Eric D. of course agreed and disagreed on the finesse aspects ;-)

#84

Hi Glenn,

The C&D Book does give a nice discussion of the impact of absorber placement, and of course this requires more finesse in constructing the absorber system. I hadn't mentioned it, but I did try my boxes stuffed full of insulation that I happened to have on hand from a renovation project. Needless to say, both the choice of insulation and its placement were kind of arbitrary (spoiler: it didn't seem to make any difference acoustically).

For what it's worth, the insulation I used was RockWool Comfortbatt, which is supposed to be a bit less dense than Safe'n'sound and which comes in thicker versions (I'm not sure I've seen Safe'n'Sound thicker than the 2x4 stud variant). Now I remember where I got 2x6" stuck in my head - my insulation was for 2x6 studs and I cut a thin slice to put on top of a full 5.5" layer so the box would be full. I suspect that the small differences between ComfortBatt, Safe'n'Sound etc. are likely to be irrelevant, and there is probably also variation between lots and from handling in transport etc.

As noted above, the stuffed boxes did not do anything acoustically. One theory is that the boxes were overdamped, and there just wasn't much resonance happening. Unfortunately I took the stuffing out before doing the candle tests - I'm curious as to what the effect would have looked like with the insulation.

From reading countless threads (like we all have) it seems clear that obsessing over the "perfect" material is futile, and in most cases it seems to be the total resistance achieved that really matters. This can be achieved using varying amounts of different materials, and it seems like an empirical calibration approach would be most effective.

The cotton ball approach I used with my soda bottle might actually be interesting to scale up, as it's easy to gradually titrate the amount of absorber and achieve various levels of density/compression. It might be no more expensive than building insulation if sourced in bulk from an industrial supplier or fabric store.

Also you raise a good point about the velocity demonstrated by the candle test - C&D make the point that a Helmholtz absorber can be viewed as a device for converting pressure to velocity, as the air movement is forced through the small holes. Absorber placed in the high velocity zone should be more effective at yielding viscous losses.

#85

I keep referring to the book "Acoustic Absorbers and Diffusers - Theory, Design, and Application" by Trevor Cox and Peter D'Antonio, but as I'm sure many are aware it doesn't seem to be the only classic reference.

There is also a widely referenced chapter on HH resonators in the Master Handbook of Acoustics by Everest and Pohlmann. In Chapter 12, they give a specific example of a resonator that is purported to address a mode at 47Hz and show waterfall plots that demonstrate greatly improved ringing. The resonator is based on a concrete forming tube (commonly branded Sonotube in North America) with a single port at the bottom. No dimensions are given, but something like this would be easy to build and tune. That being said, the one online account of building this ended in a negative result that did nothing.

There seem to be pdf versions of Cox & D'Antonio kicking around on the web. I had access to the eBook version through my institution, but the typesetting was horrible and the pdf version (set like the actual book) is much better.

No doubt I am re-inventing multiple wheels here, but I suppose that's how we learn! :horse:

#86

I ran some additional tests using individual "cells" with the same target frequency as my boxes. I thought this might help show whether the lack of division between cells in the large boxes was having an impact.

I built one small cell, with a depth of 7.25" and inner dimensions of 4x4". The front face of the the cell had a single hole of 1/4" diameter, making it equivalent to the cells of my larger units.

I also built a second cell, with a depth of 12", inner dimensions of 4x4", and a single hole of 11/32". This hole size was indicated by my adaptation of Cox's Matlab as giving a roughly equivalent resonant frequency of 42Hz.

Finally I also included my trusty soda bottle (200Hz) in the testing. Here are all the contestants lined up:

First I did the candle test on the two mini-cells, and they both appeared to resonate at around the right frequency (I used the frequency sweep function in REW).

Next, I made some REW measurements with the resonator mouths facing my left main monitor (I bypassed the sub and right monitor - the mains can do 40Hz no problem). The mic was positioned close to the mouth of each resonator, like this:

The tests also included a run with one of the mini-cells flipped around to present its back (hole-less) face to the mic. Consistent with my past observations, the small low-frequency resonator cells did not appear to do anything to the sound field picked up by the mic:

However, you will note that the trace for the soda bottle (which was empty in this test) does show a pronounced resonance effect at 200Hz. It's cool because you can really see the phase reversal effect that Glenn talked about (from when the imaginary part of the impedance passes through zero at resonance).

So all of the resonators have been demonstrated to resonate around the right frequency, either by the candle test (for the boxes) or simply by blowing on the mouth of the bottle. However, the low frequency resonators differ from the bottle in having no measurable effect on sound levels.

One point that may be relevant is that only the low frequency boxes are able to move the candle flame. The soda bottle does not seem to have any effect on the candle, even though it audibly resonates and has an obvious effect on the local sound field. Perhaps this is due to the pressure levels and/or hole size.

Of course I will also run tests varying the amount of absorbent material in the mini-cells, which is a lot easier to do in these (with cotton balls) than in the full-scale boxes. Stay tuned...

#87

Another thing worth mentioning about the soda bottle SPL curve:

Although we are definitely seeing a Helmholtz resonator in action, and it makes sense in terms of the reactance passing through zero, this looks nothing like what you would expect from the typical "bell shaped" absorption curve output by the Helmholtz calculators we've been discussing. Perhaps that is because whatever I am measuring in my crude tests has nothing to do with absorption, but it would be nice to reconcile the different phenomena (which should at least be related).

#88

wrap the bottle (damp it) so it doesn't resonate the structure of the bottle.

#89

gullfo wrote:Source of the post wrap the bottle (damp it) so it doesn't resonate the structure of the bottle.

That's a really great point! The physics assume we are looking only at vibration of the air in the bottle. You can feel that the plastic is vibrating as well, while passing through resonance, when holding the bottle.

My "single-cell" low-frequency units are made from 3/4" MDF, which is quite heavy at this scale.

I will try it and post the results.

#90

gullfo wrote:Source of the post wrap the bottle (damp it) so it doesn't resonate the structure of the bottle.

So I tried this, using several ways of damping the bottle (wrapping it in a soft cotton T shirt, plunging the bottle into a bag filled with cotton balls).

It did not seem to change the response curve:

fwiw the cyan line is the "naked" bottle, and the magenta line is the "wrapped" bottle.

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