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von Philp wrote:_______________________________________________
Some other physics teacher and I were recently debating the singing rod demo
where an aluminum rod resonates after stroking it with fingers rubbed in
rosin.
The debate was about whether the standing waves created were transverse or
longitudinal. My gut feeling is the waves are longitudinal based on the
manner in which the metal rod is stroked. Another teacher strongly believed
that the waves must be transverse because the impressive volume of the sound
is too great to be achieved longitudinally.
What do the rest of you think? Is there a compelling test or evidence to
prove what type of wave it is?
There's a compelling theoretical argument. You know the length of the rod,
and you know the speed of sound in steel. That tells you something about
the frequencies of the longitudinal modes.
The transverse frequencies will be lower by a factor involving the cross-
sectional size of the rod divided by the wavelength (to the 3/2 power I
believe) ... i.e. the mass is the same but the restoring force is much
floppier. Also the transverse dispersion relation will be dramatically
dispersive.
How big is a tuning fork tuned to A440? Not very big, is it? It uses
transverse vibrations of the tines. Compare that to the size of a rod
tuned to A440. Vastly longer, isn't it? It's longitudinal.
Secondly, you can always make something louder by increasing the amplitude.
With a high-Q system such as this one, you can set up an impressively
large amplitude, i.e. lots of stored energy. To the extent that you can
neglect non-acoustic forms of damping, all the energy you put in by hand
via the rosin comes out as sound, and that's a lot of energy.
On the other side of the same coin, there's no particular reason why a
transverse mode should couple particularly well from steel to air. A
piano is made with a huge sounding board for a reason: if you built
one with just strings, it wouldn't be loud enough.
I've never tried it, but I imagine you could get a clean experimental
test by holding the rod almost horizontal and letting one end touch
the surface of a tub of water. Look at the pattern of ripples that
is radiated.