Posted by Chuck(G) on March 01, 2004 at 12:26:21:
In Reply to: Re: Physics of Tubas posted by Cook on March 01, 2004 at 12:05:11:
The effect of the bell is twofold--first of all, it raises the lower resonances of the horn without as strongly affecting the high resonances. It's what makes your horn different from a clarinet--which overblows at the twelfth instead of the octave.
The bell flare also serves as a radiator of high frequencies, which gives the wide-flare instruments their particular "bloom" and warmth.
The bell also makes pedal tones possible.
In deference to Sam's mention of the Golden Section, I'd suggest that instrument designers who would like to get a mathematical bearing on tuba physics study a far-less-romantic mathematical subject--the Bessel function, which does seem to have a direct bearing on conical bore acoustics.
Our own Dr. Fred Young has published several papers on this subject.