Quote:
If one brass mouthpiece cup is 50 percent the depth of another cup, then it is half the distance from rim to throat and so it reinforces frequencies that are an octave higher.
That is why people who use extra-deep mouthpieces like the Curry TF or the Yamaha 13E4 find that their range has dropped an octave; the cup is twice as deep and so resonates an octave lower.
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Lets see, for the bottle physics, f = v/4L where f is frequency, v is speed of sound, L is length of column of air. Assuming a deep mouthpiece, rim to throat distance approx. 0.75 inches, this gives a fundamental frequency of 4464 Hz. Shallow, 50% depth 0.375 inch gives a fundamental frequency of 8928 Hz. I will remind the readers that double C on a Bb has a frequency of 1865 Hz. The bottle analogy does not hold here...simple reason...we are not trying to drive a column of air the length of the mouthpiece depth, we are trying to drive a resonant column of air that is the total length of the horn, about 4 1/2 feet for a Bb trumpet. I'll return to this thread later to add more insights, as I have to run to pick up the kids.
For the advanced readers
, you may want to bone up on Helmholtz resonators...
Chris