This is a question for the physicists, engineers and mathematicians amongst us.
I am looking for a concise description of harmonica physics. This description
should include the differential equations which describe the dynamics of the
system. My understanding is that harmonicas are classified as free- reed
instruments so any concise description of free-reed physics would probably
do nicely as well. My initial interest is not does not include the dynamics
of bending notes on diatonic harps - single free-reed bending would be
sufficient.
My suspicion is that an adequate description of the free-reed dynamics
would be described by coupled ordinary differential equations with
constant coefficients. One equation would Newtons Second Law applied to
the reed and the second equation would be the Second Law applied to the
air column which is forced through the slot.
I have texts which give non-concise and unnecessarily complicated descriptions. I'm looking for something better.
Any help is appreciated.
Cheers!