# Extraordinary Acoustic Transmission - Need Math Help

1. Nov 10, 2011

### Felgar

Hi everyone; I'm in need of mathematic assistance.

Background: I'm in the process of constructing a home theatre and I'm undertaking the building of a 12" high rear-seat riser that I will be filling with sound-absorbing material so that it can be used as a bass trap to reduce modal ringing in the room. My challenge is constructing the floor surface (the top of the riser) to be porous yet have small enough holes that they be carpeted over and walked on.

Problem: In reading this article http://apl.aip.org/resource/1/applab/v96/i13/p134104_s1?isAuthorized=no [Broken] it's clear that certain frequencies will pass entirely through a grated surface with sub-wavelength apertures, based upon the size and period of the apertures. What I'm hoping someone can help with is to solve the formulas presented in the article for the wavelengths and aperture sizes that are applicable in the design of my riser. In particular, 70 Hz is my room height mode and I'm wondering if I can design a surface through which a 70Hz wavelength can pass freely.

The article presents graphs that show Extraordinary Acoustic Transmission for a surface that is 10% open and 90% solid whereas I think I can probably make it 50% open, with 3/8" slats. The graphs only show a range where the frequency is 5 times larger than the aperture, but in my case the frequency is on the order of 250x the aperture. If nothing else, the graph might be showing that after a certain point (i.e. after the wavelength is a very large multiple of the aperture size), the wavelength penetration through the grating will become equal to the percentage of open space in the grating. If the math shows that this is indeed the case, that would still be important knowledge to be incorporated into my construction design.

Are there any mathematicians that can help interpret the article for me? Thanks a lot; very much appreciated!

Last edited by a moderator: May 5, 2017