Posted by Gerald J. on July 15, 1999 at 11:20:08:
In Reply to: Re: Re: Re: possible easy solution 2 Jay's pet peeve posted by Jay Bertolet on July 15, 1999 at 08:58:16:
The problem is one of scale. Any time an acoustic path changes diameter, it adds a lumped element to the distributed path. Electrically the abrupt change in diameter looks like a capacitor, a low pass element. So a step change in diameter can make high pitches harder to play or harder to get in tune. In the extreme a pair of abrupt changes in diameter with a fatter section can make a resonator that would act as a muffler for the frequencies where its resonant. The gap at the back end of a mouthpiece in a receiver probably wouldn't affect any fundamental frequency, but could affect a high harmonic and thus affect the color of the horn. E.g. A more pronounced gap would make for a darker sound.
Abrupt changes in diameter also act as flow restrictors. Try this on your shop vac. There are two adapters available for converting from 2" to 1-1/4" hoses. One is smoothly tapered, the other is abruptly tapered. You'll find the smoothly tapered one moves more air than the square one. The pressure drop from the square shoulder is significant and that restricts flow.
Its interesting to me (an electrical engineer) that the mathematical formulas for the solutions of acoustic flow are of the exact same form as for radio waves in a wave guide. Which means a lot of the exact same effects occur and the same electrical analogies can be used. I had a professor once (unqualified for the graduate course he was trying to teach) who spent a week of lectures deriving the effects of a step in wave guide height. Then one of the students asked him what it was good for what was it used for? He didn't know. He hadn't read beyond the next page in the book. I wasn't taking notes because I had read the book and was able to point out a couple hundred pages where there were several applications. A step in wave guide height makes a good piece of a filter. But where filtering is not desired its something to avoid because it upsets the propagation of waves. That same thing is true in an acoustics pipe.
Last time I tried playing a french horn it felt to me as if there was a cork in the bore, the back pressure from the horn was so high, I wouldn't have noticed a little more back pressure from a badly fitting mouthpiece. But a good tuba has very little back pressure so the mouthpiece transition might make a detectable difference.
Gerald J.