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From: pete@valid.UUCP (Pete Zakel)
Newsgroups: net.audio,net.math
Subject: Number theory and acoustic paneling
Message-ID: <34@valid.UUCP>
Date: Thu, 16-Jan-86 17:45:55 EST
Article-I.D.: valid.34
Posted: Thu Jan 16 17:45:55 1986
Date-Received: Sun, 19-Jan-86 04:35:55 EST
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Organization: Valid Logic, San Jose, CA
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Xref: watmath net.audio:7195 net.math:2668

The latest Science News (January 4, 1986, Vol. 129, No. 1) has an article
"Acoustic Residues" which describes a new type of acoustic paneling based
on quadratic-residue sequences.  The example in the article uses the prime
number 17 for designing a reflection phase grating that gives proper
diffusion for making music sound better in poor listening environments.
Basically, the panels consist of a sequence of "wells" whose depth
corresponds to the remainder of the well number squared divided by the
prime number used.  In the example the number 17 is used which gives depths
of 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, ...

The gratings can be used around speakers to minimize early reflections,
behind performers during recording sessions, on ceilings to "expand" the size
of the room, etc., etc.  I won't try to repeat the entire article here, but
I'll mention that panels are being manufactured by RPG Diffusor Systems, Inc.
in Largo, MD.  The scientist who pioneered the ideas is Manfred R. Schroeder
of the Drittes Physikalisches Institut at the University of Goettingen in
West Germany.  He's also associated with AT&T Bell Labs in Murray Hill, NJ.
The title of his recent address to the Acoustical Society of America was:
"The unreasonable effectiveness of number theory in acoustics."

-Pete Zakel (..!{hplabs,amd,pyramid,ihnp4}!pesnta!valid!pete)