On Tue, 20 Nov 2007 00:59:34 -0500, "soundhaspriority"
wrote:
The individual modes manifest as
simple oscillators, but to derive an impulse response function from first
principles is nontrivial. It's actually a field theory type problem. The
master equation for acoustics is the Navier-Stokes, and it is very analogous
to Maxwell's for electrodynamics. The difference is, Maxwells are actually
linear partial differential, while Navier-Stokes is nonlinear!
Yeahbut, of course the real world is really-truly-if-you-ask
non-linear, but why isn't a (wrong-ish but believable) linear
intuitive model out there?
Dick Pierce posting here once got at the model in a way I could
almost absorb as intuitive, but I couldn't follow through. My
only real intuitive path is to think in impulses and additions,
solely linear. My bad, but there it is.
Since it is a field, there is a PDE that is obeyed for every point in the
field. If only Navier were linear, there would be an "integral form", just
as there is for Maxells. Once you have an integral form, you can isolate the
"Greens function" from under the integral. The Greens function is a
semimagical expression that when integrated over the entire volume AND the
boundary of the enclosure, gives the field value at a point, which is what
you want.
But Navier-Stokes is more devilish, because unlike Maxells, it is not
invariant under a coordinate transformation. IOW, if you are moving in the
fluid (air) there is no way in hell you can make the equation look as if you
are not moving. The only way the equation can be solved exactly is by
perturbation expansion, ie., Feynman diagrams. And you would not believe the
strange currents that flux back and forth between the infinitesmal volumes:
it isn't isothermal.
There are corners of acoustic theory that were first solved by Gerzon, and
some riddles that have never been solved. So don't beat yourself up 
Acoustics at the field level has bedeviled the best minds.
Certainly doesn't include me. This stuff is way, way over my head.
But I still have my peasant upbringing's belief that an explanation
within my knowledge system is possible. Often wrong, but sometimes
ultimately true.
But I really would like to know why I should hang a baffle on my 8 foot
ceiling. I would have to drill into it, and that ain't theoretical 
Now this I *can* answer. It's because an 8 foot ceiling is too ****ing
low. Start at twice that. Next question.
But seriously, much thanks, as always,
Chris Hornbeck