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

[John Denker <jsd@AV8N.COM>]

Spagna Jr., George wrote:
> The waves giving rise to the "singing" are longitudinal.  You can set=
>  up transverse waves by holding the rod in the middle and hitting it.=
>   The frequency is below the audible range, but easily felt with the =
> hand holding the rod.

That's all true, and reflects a solid understanding of the physics, but
I'm not sure it answers the original question.

Let's remember that the OP asked for an argument to convince a skeptic.

    My nephew is taking HS geometry.  I have to keep reminding him of the
    difference between what you know and what you can _prove_.  Yeah,
    I know those triangles are congruent, and I know you know they are
    congruent ... but you haven't _proved_ they are congruent.

a) Yes, there is an easily-perceptible transverse mode at a very low
  frequency.

b) That does not suffice to _prove_ that the singing mode is not also
transverse.

Yeah, we enlightened persons know that the singing mode is longitudinal,
and fact (a) is consistent with what we know, but it is not a proof, and
will not convince a skeptic.

c) Actually FWIW it is easy to prove that there _are_ transverse modes at
roughly the same frequency as the "singing" mode.  Lots of them.

BTW I think Carl Preske gave the best answer to the original question:
Pay attention to the polarization of the _excitation_.  Forget about the
rosin, just smack the end of the rod against a hard floor or other hard
surface ... or smack it end-wise with a hammer.  Geometrically this *has*
to couple to the longitudinal mode(s) and not to any transverse modes.

==========

The physics of bending modes in a rod is interesting.  It's kinda tricky.
I don't know of a way of explaining it to an introductory-level audience.
I saw it in second-year college physics (Feynman volume II chapter 38).

Some of the basic scaling notions -- like the idea that making a beam
twice as thick makes it *eight* times stiffer -- are so simple and so
very useful that they ought to be taught to a wider audience.  As an
application:  3/4" plywood is a *lot* stiffer than 1/2" plywood, more
so than one might naively expect.  Similarly there's the idea that
hollow tubes have a high stiffness-to-weight ratio.  This is fun stuff,
the sort of stuff that makes physics interesting and useful.  Alas I
don't know of any good introductory-level references.  Any suggestions?

(At the non-introductory level, beam-bending is a veritable poster
child for demonstrating what Green functions are good for.)
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