Posted by Rick Denney on March 01, 2004 at 12:02:39:
In Reply to: Physics of Tubas posted by Cook on March 01, 2004 at 09:53:15:
Most of the theories we borrow from are based on parallels to things like vibrating strings or cylindrical organ pipes. With a tapered conical tube, all those rules go out the window. It turns out that the alignment of the overtone series on a tuba is anything but fixed. The impedance of the instrument is closely related to the shape of the conic.
A good book for you is Fletcher and Rossing, The Physics of Musical Instruments, and another one is Benade's Fundamentals of Musical Acoustics. The first is readable by engineers who don't mind a little math, and the second is a little less so.
Rick "disabused of the notion that in-tune harmonics are easy" Denney