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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.
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.
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.