Posted by AW on March 01, 2004 at 13:33:45:
In Reply to: Physics of Tubas posted by Cook on March 01, 2004 at 09:53:15:
I'm an engineer too. Thus, I understand the importance of using the correct theory when attempting to understand a phenomenon.
First of all, the resonance series one gets from a closed tube is the odd harmonic series. That means that octaves are not included!
The conical taper and mainly the flare of the bell have the effect of compressing upward the lower frequency parts of the resonance series. The mouthpiece, with its complex shape and its venturi has the effect of compressing downward the higher frequency parts of the resonance series. Thus, what started out as an odd harmonic only resonance series can approximate a series that includes all harmonice -- both even and odd. Since the resonance series of any tapered brass instrument (every one in modern use) is the result of various tweaks and compromises, there is no intrinsic reason why the instrument should have a resonance series that coincides with the harmonic series. It is an art, making the open tones of a brass instrument be "in tune."
Of course, I haven't even started commenting on the relationship between natural harmonic series and the equally-tempered scale we use. For more information on that, see Art Hovey's excellent Tuba Logic Web Site. Also, you can check some of the references Rick Denney mentions. If you want to make some analogies with radio antennas, you should look up some of the more clever (and complex) multi-resonant designs, not simple linear antennas.
Allen Walker