Here's what one of the greats, Renold O. Schilke, wrote about trumpets
physics and resonance.
http://www.dallasmusic.org/schilke/Brass%20Clinic.html
One of my favorite stories he gives is this one and the misconception about
bells 'ringing' and projection:
Quote:
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Many people test a bell by tapping it with their finger or knuckle and in tapping the steel bell, it would emit a very ringing sound, truly like a bell. However, when we played this instrument, the quality of sound was extremely dead. On searching for the reason for this, we looked at the oscilloscope when the performer played on the instrument and found the sine pattern very faint but the distortion pattern, coming from the vibration of the bell itself, going through at a very jagged and rapid rate, killing the brilliance of sound of the true tone. At the other extreme was the lead bell. This bell, if rapped with your knuckle, emitted an extremely dead sound like rapping on a piece of wood. However the sound that emanated when it was blown was extremely brilliant, brilliant to the point of being mechanical. This showed up on the oscilloscope as a perfectly true sine pattern, there being no distortions in the harmonics either above or below, and, as a result, the sound was absolutely pure but not usable musically, except for a general effect such as a percussion instrument would give. The voice, you know, registering on an oscilloscope, gives harmonics both above and below the note. These distortions, if we may call them such, give warmth to the tone. We have to have that "distortion" in order to have the sound acceptable to our ears as a musical sound.
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Reading this paper corrected some of the nonsense that I believed early on in my trumpet playing.
Greg