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Chris Hornbeck
 
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On Wed, 01 Sep 2004 16:40:43 -0700, Bob Cain
wrote:

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


Relative motion as we usually think of it is just the DC
component of the soundfield created by the Tx.


But for our purposes wouldn't it be a better model to
think of the relative motion as a separate thing, and
outside of the Tx and Rx soundfields?

Within those soundfields, especially if they're rigidly
coupled, nothing interesting happens.


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.)


Yeah, this is the part that Scott calls reciprocity failure.
It's a photographer's pun, but it works.

Chris Hornbeck