Chris Hornbeck wrote:

On Wed, 01 Sep 2004 13:56:57 -0700, Bob Cain
Did you see my proof of why a piston in a tube will evidence
no such behavior with any signal including constant
translation of the piston? I believe it is a refutation of
that (unless, of course either I still don't understand what
you are saying or someone can refute my proof.)


Isn't this (and the case of coupled infinitely extended
planes) just a special case with no relative motion?
Chris Hornbeck

Relative motion as we usually think of it is just the DC
component of the soundfield created by the Tx. That it is
fully coupled in the tube (or infinite plane) means it is
received as is by the Rx without giving rise to any Doppler
effect. Art's step function derivation shows that. That it
is not coupled at all to an Rx in the far, free field is
what allows simplification to the standard Doppler equation
(which is only valid for a constant v and a single frequency
in the Tx spectrum.)


Bob
--

"Things should be described as simply as possible, but no
simpler."

A. Einstein