Posted by Don Shirer on June 07, 2003 at 21:34:21:
In Reply to: Placement of tuning slides on horn posted by Thomas on June 06, 2003 at 22:51:39:
Getting back to the original question...
If the slides are placed on cylindrical portions of the horn of any diameter (and it is difficult to see how they could be otherwise) the exact placement should make little or no difference. (For a chicken/egg question, ask yourself if a trombone slide adds length closer to the mouthpiece or the bell!)
However, the wave velocity (and hence the wavelength) of the sound in the flaring portion of a horn is greater than in the cylindrical part so adding an inch on the bell (keeping the same flare) should lower the pitch less than an inch longer leadpipe since it is increasing the length by a smaller fraction of a wavelength. The difference might well be too small to be noticeable except by golden ears.
Now the caveat: this is what I remember from an acoustics class many (many) years ago. Looking in five texts I had on hand was not much help: they mostly treat loudspeaker horns, not resonators. The closest I could find was in Art Benade's "Fundamentals of Musical Acoustics" (section 20.5). Any volunteers for an experiment?