Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

[Phys-L] Re: Singing Rod Demo....



Moses is a theoretician, I take it. The transverse mode to which the
experimentalists are referring is not a radial mode with cylindrical
symmetry but rather a flexural mode. The rod's axis is bent
transversely from its equilibrium position while being supported at
one or two nodes, in its lowest frequency mode.

Leigh

On 28-Nov-05 Moses Fayngold wrote:

From: "Fayngold, Moses" <fayngold@ADM.NJIT.EDU>
Date: November 27, 2005 6:56:44 AM PST (CA)
Subject: Re: Singing Rod Demo....


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 the 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.

Moses Fayngold,
NJIT
_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu
https://www.physics.buffalo.edu/mailman/listinfo/phys-l