Here's something that' been bugging me and I hope that someone on this list
will be able to help me out...
Imagine a sound wave traveling inside a tube (treat it as a plane wave).
When the wave reaches an open end of the tube, part of the wave propagates
into the the room and part of the wave reflects back into the pipe. One
simple way to explain this phenomena is to cite that the acoustic impedance
changed at the opening. (Acoustic impedance, Z, of a pipe is given by Z =
pv/A, where p is the density of air, v is the speed of sound, and A is the
cross-sectional area of the pipe) When the wave reaches a boundary with a
different impedance it generally is partially reflected at that boundary.
This is all fine and dandy; however, I'm looking for a more physical
argument, one based on what is going on with the air molecules (or better
yet, small packets of air). How does the longitudinal wave "know" when it
has reached the end of the tube. I feel that a full explanation would
describe the diffraction of the wave at the tube opening, as well. But
perhaps this is reaching too far.
All of this leads to answering a, perhaps, more interesting question: "Why
does a trumpet, which seems like a closed pipe, produce a nearly harmonic
set of overtones, without any missing harmonics?" The hip-shot response is
because it has a bell (and a mouthpiece), which changes the "effective
length" of the instrument for different frequencies. I'd like to understand
this better.
I've gone through the mathematical derivation in Rossing's book "The
Physics of Musical Instruments" (a text I highly recommend) and it's quite
straightforward, but it doesn't seem to provide me with a lot of physical
insight - which is unusual for Rossing.