Slot absorber slot width

J.J.McLeod · Post by **J.J.McLeod** » Sat Mar 22, 2003 2:49 am

I was using an Excel spreadsheet for calculating frequencies of slot absorbers that happened to be different than the one on the SAE site, and I noticed something interesting. There was a field for perforation percentage that was created by the slat width and slot width numbers. Remembering that pegboard can make a helmholtz resonator also, and that the perforation percentage determines frequency, I tried ignoring the slat widths and just entering different perforation percentages. In the spreadsheet it had the same effect on frequency as slat width, etc.

So doesn't using different width slats with different slot widths result in one perforation percentage for the whole enclosure? If so, doesn't that mean you can get the same percentage with 1"x4"'s with consistent gaps? Varing slat thickness and cavity depth make a difference, of course, but it seems that varying slat and slot width doesn't. Is this true?

Thanks,

J.J.

J.J. McLeod
Different Drummer Studios
www.differentdrummerstudios.com

barefoot · Post by **barefoot** » Sat Mar 22, 2003 4:38 am

JJ,

You raise a good point. The information on the SAE site regarding slot resonators is slightly erroneous. It implies that varying the slot width creates a broadband absorber. In most practical designs, however, the slat width winds up being rather small compared to the resonant wavelength. In this case the wavelength covers several slats and therefore only cares about the average slot width and the average cavity depth. So the resonant frequency will still be fairly sharp. The only way that varying the slot width will result a broadband response for a resonator whose slat width is small compared to the resonant wavelength is to also build partitions in the cavity perpendicular to the slats, as I have illustrated below.

Here the panel is now truly an array of isolated resonators of varying frequency.

SAE also mentions varying the depth from the wall as helping to create a broadband absorber. This will be effective only because the width of the wall is typically large compared to the wavelengths in question. That being said, however, smaller sections of the resonator will not be as broadband as the depth variation might suggest. The shallower side of the resonator will be skewed more towards the higher frequencies while the deeper side will be skewed towards the lower frequencies.

Believe it or not, the main thing that helps to create a broadband absorber in the SAE design is the Cloth Backing mounted against the rear of the slats. This cloth restricts the free flow of air in and out of the slot, acting as a damper. Damping in any resonant system has the effect of flattening and broadening the resonant peak, as well as shifting it to a slightly higher frequency.

Hope I actually answered your question!

Thomas

Post by **John Sayers** » Sat Mar 22, 2003 8:25 am

I'm happy to stand corrected.

Thanks barefoot;)

cheers
john

J.J.McLeod · Post by **J.J.McLeod** » Sun Mar 23, 2003 4:43 am

Thanks for clearing that up, Thomas. Of course, I still have a few questions:

and therefore only cares about the average slot width and the average cavity depth

The shallower side of the resonator will be skewed more towards the higher frequencies while the deeper side will be skewed towards the lower frequencies.

These two statements about cavity depth seem to be at odds. Does varying the depth vary the absorbed frequencies or, because the waves are so large, only the frequency that corresponds to the average depth is absorbed? Of course, skewing them helps high-end diffusion and standing waves, but does it really affect the lower frequencies?

This cloth restricts the free flow of air in and out of the slot, acting as a damper

Are we talking about acoustically transparent cloth that you can blow through, or should something denser be used?

On the subject of construction materials, the SAE site suggests using 1" MDF for the frame. Would 3/4" be o.k.? That's the thickest I found at Home Depot. And am I correct in assuming that the insulation inside should be rigid fiberglass like 703 - preferably 4" to absorb more lows?

Your answer about average slot width seems to support my plan of making modular smaller (4'x4' maybe even 2'x4') slot absorbers that I could stack, move around the room, etc. Seems like I could vary the frequency more in the bargain. But I'm still unclear about what percentage of the room should be slot absorbers. Every room is different, but is there a rough guide for what the ratio of 703, slot absorbers and hangers should be? In a 2000 cubic foot room with a fairly live floor and rigid insulation on an 8' drop ceiling, should, say 50% of the walls be slot absorbers?

Thanks again everyone for all your help. Maybe one day soon I'll run out of questions.

J.J.

J.J. McLeod
Different Drummer Studios
www.differentdrummerstudios.com

barefoot · Post by **barefoot** » Tue Mar 25, 2003 4:47 am

My two statements are not at odds because the basic resonance equation of a Helmholtz resonator assumes that all wavelengths are large compared any of the resonator's dimensions. In the case of a singe slat/slot unit this is true. Over the length of an entire wall, however, this is probably not true. For a midband resonator the wall would likely span several wavelengths. The simple Helmholtz model no longer holds. Still, it's possible to think of the panel in terms of an array of Helmholtz resonators. But now that the wavelengths are small compared to the dimensions of the whole panel, we need to think of it as an array of quasi isolated resonators. It's almost as if we built in those perpendicular partitions I illustrated in my first post. Now if we move along either the vertical or horizontal dimension of the panel and nothing changes (cavity depth, slat width, slot depth, etc,..) then everything is normal. Our quasi discreet resonators all sum together as if they are one big Helmholtz resonator, despite the fact that it's larger than the wavelengths in question. If one or more dimensions change however, like the cavity depth, then the resonance frequencies of our quasi isolated resonators will change as well. Make sense?

Acoustically transparent cloth is only transparent when the velocity of the moving air is very small. If you actually try that experiment of blowing through the cloth, you'll find the air movement is significantly hindered. The area in the direct vicinity of the slot (i.e. the neck of the Helmholtz resonator) is by design an area of increased air velocity. You can enhance the damping, and hence bandwidth, even more by using a heavier cloth or by mounting the rigid insulation a little closer to the slots/slats.

As far as your other questions, John has more expertise in those areas that I do.

Thomas

J.J.McLeod · Post by **J.J.McLeod** » Wed Mar 26, 2003 2:45 am

Thanks Thomas. That clears it up. I thought I saw a red flag when you said the slot absorbers only respond to the _average_ cavity depth.

So John, would smaller, stackable 4'x4' or 8'x2' slot absorbers be just as effective? Should the fiberglass be rigid like 703? And does the cloth have to be attached to the back of the slats, of can it just be covering the insulation, like a high frequency absorber with a wood box around it?

Thanks,

J.J.

J.J. McLeod
Different Drummer Studios
www.differentdrummerstudios.com

Post by **John Sayers** » Wed Mar 26, 2003 8:31 am

would smaller, stackable 4'x4' or 8'x2' slot absorbers be just as effective?

yes - it's a good way of breaking up a flatwall.

Should the fiberglass be rigid like 703?

the insulation in a slot isn't as critical as for wall treatment. It's a good way of using up your offcuts.

And does the cloth have to be attached to the back of the slats, of can it just be covering the insulation, like a high frequency absorber with a wood box around it?

like you said, make a box with insulation, cover with cloth then lay the slots over the top.

cheers
john

bolehnggak · Post by **bolehnggak** » Tue Apr 01, 2003 7:26 pm

Should the fiberglass be rigid like 703?

the insulation in a slot isn't as critical as for wall treatment. It's a good way of using up your offcuts.

Can I use usual rubber foam?

And does the cloth have to be attached to the back of the slats, of can it just be covering the insulation, like a high frequency absorber with a wood box around it?

like you said, make a box with insulation, cover with cloth then lay the slots over the top.

How should I lay the slot? Nailing them at the joint of the frame, or just glue them to the cloth?

Post by **John Sayers** » Tue Apr 01, 2003 10:38 pm

yeah - chopped up rubber foam might work - dangerous fire hazard though

Yes - Nail the slats down.

cheers
john

jc71 · Post by **jc71** » Wed Jun 11, 2003 9:41 am

Well.... now I'm really confused! I am interested in using pegboard instead of slats due to the fact that it would be considerably less expensive. Insterested in the pros & cons? My thoughts are these....
1. Flatter suface i.e. less diffusion ????
2. All same size holes less broadband???? or would varying the cavity depth change that???
3. Is it truely the perforation percentage that designates the frequency not the hole sizes???? and varying the hole sizes would only change the perforation percentage not necessarily make it broadband????
4. When using pegboard should I still use cloth behind it ????
Just some thoughts & questions! All help will be appreciated!!

Thanks!
Jeff

Eric Best · Post by **Eric Best** » Wed Jun 11, 2003 11:00 am

I will try to answer this, so correct me if I'm wrong. The frequency is determined by the combination of the area of perforation, and the depth of the cavity. Varying the hole size should not make it more broadband according to the math.

There are different schools of thought of whether a box of varying depth will make it a broadband absorber. I believe Everest says it will and he has tested these things, so I would go with that.

I would still use the cloth behind the pegboard.

Something else to consider is the thickness of the pegboard, this will also affect the frequency.

Someone else tell me if I'm wrong.

Post by **John Sayers** » Wed Jun 11, 2003 1:01 pm

sjoko used sheets like this

cheers
john

Henrik · Post by **Henrik** » Wed Jun 11, 2003 11:46 pm

Hmmm...great in depth-info on the secrets of Helmholz resonators.

Barefoot or whoever, do I understand this right:

If a Helmholzresonator is built across a wall (say 5 meters/about 15 ft) without partitions, and therefore is large (wide) compared to the wavelenghts that hits it, then angling it will make it affect a broader range of frequencies. But if the resonator consists of a comparatively small box (say 1.20 meters/about 4 ft), then angling it will be of little effect.

True?

OK, if so...using the Excel file on the SAE site you can experiment with different depths from the wall. Is it correct to assume that a large non-partitioned Helmholz resonator will affect the areas between the frequencies given by entering the largest and the smallest depth from the wall? Or does it reach lower because of its large width (volume)? Is there any way to put the total width of the resonator into the calculation?

Damn, this is interesting stuff.

Thanks
/Henrik