slat resonator questions..

[JasonFoi]

So, for quite some time I've been contemplating my rooms rear wall treatment, and feel that I may want to utilize some or all of the area as a slat resonator or simply as a slat absorber. The entire rear wall is currently 12'x8.2'x32" of fluffy fiber. Now, I dont necessesarily want to be specific to my situation, as Im still building the room and want to measure before i make a decision. I'm more interested in clarifyng some design principles that have bothered me for a long time. When calculating a slat resonator I always see the following parameters: slat width, slat thickness, slot width, and cavity depth, but I never see slat length, and i dont understand why. Surely the length has an effect on the tuning, or is it that all other parameters being equal, a slat length of 2' and 8' still have the same Fc? And then that leaves the question of the number of slats. My intuition says that a cavity 32" deep with a width of four 2' long slats and a cavity 32" deep with a width of twelve 2' long slats would have a different Fc, as the internal volume is considerably different, but i realize acoustics are not always intuitive. Any clarification would be greatly appreciated.

[Soundman2020]

I always see the following parameters: slat width, slat thickness, slot width, and cavity depth, but I never see slat length, and i dont understand why. Surely the length has an effect on the tuning,

Actually, it doesn't! Sounds strange, I know, but it's true.

Here's how it works: the equations for Helmholtz resonance are based on the volume of the resonant cavity, which makes sense: it is, after all, the volume of air that creates the spring! However, you can think of a SLAT resonator as a special case, where you don't just have one small "neck" on the device, but rather you have a whole bunch of devices next to each other: imagine that the slot consists of hundreds of individual resonators, all stacked next to each other, each with it's own imaginary cavity behind it. So, for each of those cavities, the volume is given by the length of the cavity, the depth of the cavity, and the width of the cavity. With me so far? So you could define a vast number of cavities, calculate each one, add them all up, then divide by the total number. That would give you the overall resonant frequency, right? But think about that: if you add up all the WIDTHS them divide by all the WIDTHS, then mathematically, it means that the width doesn't matter any more! If you divide any number by itself, the answer is always one....

So it's a mathematical curiosity that makes the length of the slat unimportant. You only need the depth and height of the cavity, to calculate the frequency. Curious...

or is it that all other parameters being equal, a slat length of 2' and 8' still have the same Fc?

Right. The 8 foot one would be more EFFECTIVE, since it exposes a larger surface area to the room, and has a larger internal volume, but they would both have the same frequency.

The same applies to perforated panel resonators: Width doesn't matter. Only cavity depth and hole spacing.

- Stuart -

[JasonFoi]

Hmm, that actually makes sense. So, if i varied slot and slat width across my entire back wall i could target all my lowest modes very effectively. Would there be a downside to doing that vs leaving the entire wall as a porus absorber or a slat absorber with a mls sequence? Or would it be better to do a mixture?

[Soundman2020]

So, if i varied slot and slat width across my entire back wall i could target all my lowest modes very effectively.

You can target a broad range of frequencies like that, yes. You can also vary the depth, by having one end of the cavity deeper than than other. However, there's a couple of other issues to take into account:

1) It's really hard to target modal frequencies with slat walls: the slot (gap between slats) has to become very small, and/or the depth has to become very large, and/or the size of the slat (height, or thickness) has to become very large, in order to get down to those low frequencies.

2) Also, it's notoriously hard to tune a Helmholtz resonator precisely to hit the mode exactly. Modes are very high Q: very narrow bandwidth, just a few Hz wide at best. Helmholtz resonators are very high Q: also just a few Hz bandwidth. So lining up those two Q peaks is a real challenge. Yes, you can reduce the Q of the device by tuning it more broadly, but that reduces efficiency, even though it will hit the target frequency better.

3) You need a very large internal volume to effectively deal with a mode. Some research suggest that you need at least 1% of the room volume to do that. So if you have to hit 6 modes, you'd need 6% of your room taken up by such devices. In a small room, that usually isn't feasible.

4) The dimensions of the device vs. the wavelength: The equations are only valid for the case where the device is considerably smaller than the wavelength being treated.

5) Open area: If the relationship between the total area of the slots an the total area of the slats+slots is large, (greater than about 20 to 30%), then the device acts mostly as a broadband absorber. If the open area is less than about 5 to 10%, then it acts as an array of individual resonators, each tuned to its own frequency.

Etc.

Lots of stuff to take into account with Helmholtz devices. Here's a link to a room that is in the process of being tuned right now, where you can see all of this theory in action, and how it works out in the real world: http://www.johnlsayers.com/phpBB2/viewt ... 68&start=0 You can see a couple of different types of Helmholtz device in there, and see the effect they have on a room.

Would there be a downside to doing that vs leaving the entire wall as a porus absorber or a slat absorber with a mls sequence? Or would it be better to do a mixture?

It depends on what the room needs! Slot resonators are very useful devices, but hard to tune, and I generally only use them for stubborn issues that aren't responding well to other treatment, or where I can get plenty of "bang for the buck" by combing several devices into one, as was the case with that room.


- Stuart -

[JasonFoi]

The slots ive been playing with expose 2% of the underlying absorbtion. Varying slat widths from 50mm - 350mm 18mm thick all with 3mm slots. Then a 75mm airgap and 700mm of fluffy fiber. I figured if i varied slats all across the entire back wall (8'x12') i could pretty much cover from 30hz-200hz with an absorbtion coeificient of about .8

Of course ill only go this route after i finish my basic build and test the room. Im working on the soffits now so hopefully not too much longer...

[Soundman2020]

The slots ive been playing with expose 2% of the underlying absorbtion.

... and therein lies the problem! Only 2% of the rear wall surface would be doing any absorbing: 98% would be reflecting! On the other hand, if you just used absorption on the rear wall, then 100% of the rear wall surface would be absorbing...

Which do you think would be more effective? Something that absorbs across 2% of it's surface area, or something that absorbs across 100% of its surface area?

And since this is the rear wall of the room, do you REALLY want it to be 98% reflective? Assuming you are planning on the "20/20" principle (sound coming of the rear wall should be delayed at least 20 ms, and arrive at -20 dB (with respect to the direct sound), it's hard to see how you'd get that 20 dB reduction from what is basically a solid surface.


- Stuart -