double vs. triple leaf

Posted: Sat Aug 30, 2008 6:15 am

So I'm teaching a course in partial differential equations this year and I'm going to put a lot of music and acoustic problems in it. The point of the course is math, so I can't spend too much time on the physics. But I'm looking for interesting problems that are easy to describe. I'm thinking that comparing the transmission properties of a double vs a triple leaf wall might fit the bill. Does anyone know where I can find a reference for a mathematical analysis of this problem? I know Rod's book has experimental results. Those will be useful, but I'm looking for math.

Posted: Sat Aug 30, 2008 6:53 am

The methods I know of predicting TL are a bit empirical. Search for Ben Sharp or Messneir. A book which has some info is Engineering Noise Control by Bies and Hansen. But only related to double walls.

Posted: Tue Sep 02, 2008 12:04 am

Bob,

For double partitions, like andre recommended I'd go with Bies & Hansen:
Bies, D.A. & Hansen C.H. (2003); Engineering Noise Control. Spon.
It has mostly analytic/empirical stuff but also some numerical analyses.

You might also want to check out:
Sharp, B. (1973); A Study of Techniques to Increase the Sound Insulation of Building Elements. Wyle Report 73-5.
It's quite a long paper (ca 200 pp) but is very thorough and also deals with triple-leaf partitions.

If you want something heavier on the differential math analysis go with:
Sewell, E. C. (1970); Transmission of Reverberant Sound Through a Single-Leaf Partition. J. Sound. Vib 12(1)
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I think a nice problem would be to mathematically show that given two near-identical partitions (same materials, same width) only arranged in different constructions (double-leaf and triple-leaf), below mass law region, the low frequency transmission loss would be higher for a double-leaf system.

Cheers,

Jon.

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