At 9:16 PM on Sat 11/26/2005 Brian Whatcott wrote:
"If a transverse excitation can lead to longitudinal vibrations,
why couldn't a longitudinal stimulus give rise to transverse vibrations?"
I think this is precisely what happens in the discussed experiment. Rubbing a rod along its length produces longitudinal waves propagating along the symmetry axis, but it also gives rise to transverse wave propagating along the radial directions, that is perpendicular to the symmetry axis. As a result we actually have a system of longitudinal and transverse standing waves. Of course the fundamental frequency of the transverse wave would be much higher (even though it propagates slower than the longitudinal wave) due to the geometry of the rod, and its coupling with surrounding air is generaly weaker, so the dominating contribution to the audible sound would come from the longitudinal wave. But this situation can be reversed, for instance, by changing geometry, - say by increasing the thickness of the rod and dicreasing its length so it becomes a disk. If its center is fixed and we rub as before (which now is rubbing against the edges along the symmetry axis), then, I think t
he transverse wave will be overw
Another aspect of this trickiness involves allowed propagation modes. Even if we separate (or consider only) one of the states, say, pure longitudinal vibrations in the rod, they will not be longitudinal as one might think due to loose use of the language. That is, they are longitudinal with respect to local direction of propagation of the corresponding momentum eigenstate in Cartesian coordinates, but the momentum itself, due to diffraction, will not be along the rod, and so the vibrations will not generally be along the rod, either. So when I said in the beginning "longitudinal waves propagating along the symmetry axis", I was not exactly accurate. It is only the net momentum resulting from the superposition of all allowed plane waves, that will be parallel to the rod, but even so the local "vibrations" may generally be elliptical.