I want a simple 1-D, numerical solution of the wave equation for a
loudspeaker diaphragm (or a flat plate in 1-D) as it moves thru the
air. I want to be able to printout and/or plot the pressure on the
diaphragm/plate, and anywhere within 2 wavelengths of the
diaphragm/plate, as the diaphragm/plate moves. A simple solution like
the last example at "http://www.ma.umist.ac.uk/kd/comp/node14.html"
(which uses a finite difference approximation?) would be fine. I would
like the following properties, if used, to be variables (not
hard-coded values): initial pressure and density, longitudinal
amplitude and frequency of the diaphragm/plate. All I need is the code
algorithm (in C, Java, Pascal, etc) for the solution; I don't need any
output statements (ie: the 'fprintf' statements in the example link
are not needed).

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Request for Question Clarification by rbnn-ga on 05 Nov 2002 07:19 PST

So we are assuming a circular plate? Isn't there a closed solution for this though?

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Request for Question Clarification by rbnn-ga on 05 Nov 2002 07:40 PST

Also I'm not sure what kind of detail you are looking for - once you
start modeling turbulence, for instance, things get more complicated.

Is there a specific differential equation whose numerical solution you
need implemented? Also, I presume you don't want Fortran (?)

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Clarification of Question by kenmc-ga on 05 Nov 2002 08:00 PST

I was thinking that a simple 1-D solution would be easier to get than
a 2-D (I'm assuming a circular plate is a 2-D model). If a cirular
plate solution is 2-D, I would like to work with a solution that is
less complicated to start with. If I could get 1 or both solutions
(1-D and 2-D) in programming code form, that would be good.

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Clarification of Question by kenmc-ga on 05 Nov 2002 08:03 PST

The most specific I get in regrads to the differential equation is the
wave equation PDE for acoutic waves. And, FORTRAN would be fine.

Sorry, I personally could not find anything useful. Perhaps another
researcher will have more luck!

You may want to take a look at these two programs:
http://gspeakers.sourceforge.net/
http://kfilter.sourceforge.net/

You might also find this page useful:
http://www.ramsete.com/aurora/

I suspect this is "overkill", but there's a dissertation by Gavin
Putland on:

"Modeling of Horns and Enclosures for Loudspeakers"

http://www.users.bigpond.com/putland/phd/thes.pdf

which develops a mathematical model for evaluating frequency response
and pressure in 2-D and 3-D geometries.  Two applications are
discussed in Chapters 10 and 11 and the SPICE code for these is
included in the appendix.

regards, mathtalk-ga

mathtalk-ga that is a good link. I also found some links on heavy-duty
simulation programs, but they mostly assumed that the user was already
familiar with simpler things (which I am definitely not).

I think the best thing might be for someone to write custom code to
solve the problem (?) . I would volunteer for this, but it turns out
that my memory of the required physics (and even differential
equations) is so faded that it would be about a full day project (kind
of embarrassed to admit it actually).

Hopefully someone who knows the physics can bang out a solution
faster, or a better searcher than I can find the right link on the
web...

Oh, the Fortran code for 2-D was here: http://www.soundsoft.demon.co.uk/rimcode.htm