As a retired electronic engineer with radio communication experience I realized that the trumpet has similar characteristics as a radio frequency transmission line.
Regardless of buzzing or or just blowing air through a trumpet mouthpiece the resultant sound waveform as seen by an audio spectrum analyzer contains a whole mix of frequencies in the audible range. Applying this to the trumpet we have this mix traveling forward through the length at the speed of sound ~ 1200 ft/second. Some of this wave traveling forward will be reflected from the change in impedance of the tube in the region of the bell and will interfere with the forward traveling wave creating a new standing wave the frequency of which will depend on the length of tube and energy level of the reflected wave,
When a peak of the reflected wave reaches the lips coinciding with a trough in the forward wave the lips will close momentarily and then reopen by the air flow, according to Benade this takes around 3 cycles for the standing wave to stabilize.
An easy demonstration is to just blow air into the trumpet with the mouthpiece attached with relaxed lips and open aperture, while keeping the air flowing slowly close the aperture, a point will be reached when the standing wave will develop and the trumpet will sound.
References,
A Textbook of Sound Edwin H. Barton
Fundamentals of Musical Acoustics Arthur H. Benade
Music, Physics and Engineering Harry F Olson
Basic Physics Vol 3 Sound and Light Martin and Connor.
Regards, Stuart.
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