Slat resonator with various slot depths

[wzemon]

I am designing a slat resonator that will cover a range of low-to-mid frequencies.

It is known that the resonant frequency is affected by width of the slat, the depth of the slot, and the depth of the space behind the slats and the width of the slot.

My idea is to keep the depth of space behind the slats at 150 mm, the width of all the slots at 5 mm, and vary the width of the slats between 400 mm and 50 mm in order to broaden the bandwidth of absorbtion.

I have also considered varying the depth of the slot by using slats of 18 mm, 15mm, and 12mm.

My question is this: how will the resonance of the slot be affected when one side of the slot is 18mm and the other side is 12 mm? Will we end up with a resonant frequency somewhere between the two?

I feel like this is a good design because the various depths will also contribute to dispersion.

Anyone have any experience with this type of installation? Any solid technical information?

Thanks -- Bill

[Soundman2020]

Hi Bill. Please read the forum rules for posting (click here). You seem to be missing a couple of things!

My question is this: how will the resonance of the slot be affected when one side of the slot is 18mm and the other side is 12 mm? Will we end up with a resonant frequency somewhere between the two?

That's actually a really interesting question, and to be honest, I don't know the answer. I'm not aware of any research that has been done on that, but it's a fascinating question.

The issue is this: The "slug" of air trapped in the gap between the two slats is actually what resonates here. It's the "mass" that moves in and out, sort of like a piston, vibrating in sympathy with a certain tone. It's the mass of that air slug that defines the resonant frequency. With normal slats that measure the same thickness, that slug is uniform and relatively easy to calculate. In fact, it's not just the slug itself that moves: it also affect the air just outside, pushing and pulling on that such that it also joins in, so there's a "mouth correction factor" that is applied to the calculated mass of the slug, usually estimated at roughly 20% extra. But with slats of different thickness, it's not clear to me how you would calculate the mass of the slug, nor how you would calculate the mouth correction. You MIGHT be able to estimate this by taking an average dimension, half way in between the thicknesses of the two slats, but I'm not sure how valid that is. And since Helmholtz resonators usually have a fairly high Q, I'm not sure how much that would be affected either. Another way of looking at it might be to just pretend that your slot wall is actually a perf panel, an use the open percentage equations, instead of the Helmholtz equations. Once again, I'm not sure how valid that would be, considering the asymmetric hole geometry.

You might just have to experiment, and see how it really performs!

Sorry I can't be more help than that!

- Stuart -

[wzemon]

Sorry for the oversight. In my enthusiasm ( and rush) I failed to include some important details.

I'm working on an auditorium located in Riobamba, Ecuador that is used for educational purposes, but the interior is very stark, with no effort to control RT60. The volume is 11,325 m3 and has an
RT60 when empty of about 5.5s at 125Hz to 3.1 at 4kHz. (This was measured using Audio Tools by Studio Six Digital using their iTest mic, and full range pink noise produced by the in-house sound system).

Using the RT60 = .161 x V/Sa formula, I calculated that the empty auditorium has about 320 Sa absorption @ 125Hz evidently due to window glass and drywall; all other surfaces are painted cement walls, unpainted cement floor, and a corrugated metal roof.

Audiences range from 700 to 1500, and Audience Sa ranges from 176 to 345 @ 125 Hz, based on a coefficient of .23 per person @ 125 Hz. This is not enough to reduce the level of reverberation at the fundamental of male speaking voices (85-180) that I believe is interfering with the frequency response of professionally produced videos that contain music, speech and sound effects. These videos are an essential part of the educational program.

In a manner similar to how certain low frequencies on your car stereo are masked when on the highway due to tire noise, etc. at the same frequency, I believe that the speaking voices are being masked by the long RT60 as measured at 125 Hz.

Thus my interest in building a variety of slat absorbers that will treat the range of low to mid bass, and covering as much of the rear wall (35 meters wide, with a peak height of c. 6 meters).

I hope these details are useful for those who are studying this topic.

[wzemon]

Stuart,

Thanks for the insights. I continue to peruse my references on Helmholtz resonators, and your observations were useful.

Bill