Xref: utzoo sci.physics:6321 sci.math:6090 sci.electronics:5594
Path: utzoo!attcan!uunet!wucs1!kumar
From: kumar@wucs1.wustl.edu (Arun Kumar)
Newsgroups: sci.physics,sci.math,sci.electronics
Subject: Re: noise cancellation(long)
Keywords: anti-noise
Message-ID: <739@wucs1.wustl.edu>
Date: 19 Mar 89 22:03:19 GMT
References: <723@wucs1.wustl.edu> <7260@fluke.COM> <453@corpane.UUCP>
Reply-To: kumar@wucs1.UUCP (Arun Kumar)
Organization: Washington University, St. Louis, MO
Lines: 45

In article <453@corpane.UUCP> sparks@corpane.UUCP (John Sparks) writes:
>Hmm, In theory you can try taking two speakers from a stereo system and
>wire one of them opposite polarity from the other. Then when one cone
>is extending the other is retracting. The two sound sources will be
>180 degrees out of phase with one another. Make sure you feed the same sound
>into both speakers.
>
>But in reality this won't work. Since each sound source is the center of
>a 3 dimensional spheroid of sound waves, They would have to both be located
>in the exact same space in order to cancel out each other. 

There is a troublesome "near-field effect" just as in optics. If the
speakers are reasonably close together, and if you listen to the
arrangement from a little distance ("little" = function of frequency)
certainly the sound would be attenuated.

I think it is possible to determine the characteristics (position and
frequencies) of all sound sources (including secondary sources:
walls and other reflectors) using some space-frequency transform
implemented in hardware. If we (roughly) collocate the primary
sorces of noise and the sources of anti-noise, the far-field approximations
should hold beyond a distance of about 3ft from the noise-antinoise pairs
(approx (2 or 3) * diameter of the hi-fi woofers).

It is possible, I think, to solve the wave-equations for multiple primary-
noise and antinoise sources in hardware, using finite-element analysis
(whether or not the noise-antinoise sources are collocated).
There should be enough time to do all this since we are not dealing with
frequencies above 20K. One problem is how do we treat secondary sources
when solving the wave-equations? Another problem that I see at this stage is a
model that would allow us to determine what antinoise to produce. It
should all reduce to a simple approximation problem I think. Something like:
given a vector x in some vector (or Hilbert) space V, find a vector y
in some subspace W such that ||x-y|| is a minimum. Is there someone who
has some ideas about such a formulation?

Danny Cameron of Intergraph Corp called me to say that a NY
company manufactures an active noise cancellation system. I have written
to the company asking for a brochure, and for info about any installations
in the St Louis area, at the adress provided by Danny. I will post
soon as I have a response.

Arun Kumar (wucs1.wustl.edu)
Box 1045, Computer Science Dept, Washington University, St Louis MO 63130
314-726-4464