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[Phys-L] Re: PHYS-L Digest - 25 Nov 2005 to 26 Nov 2005 (#2005-420)



The singing rod is one of my favorites. As you deduced, the
vibrations are indeed longitudinal. This can be demonstrated easily
in several ways, but my favorites are:

1. Dangle a key on a keychain so the it just touches the end of the
rod while it is ringing. The key will bounce with great amplitude,
adding its own contribution to the sound.

2. Take an ordinary styrofoam cup and touch the bottom of the cup to
the end of the rod. You should get another 20 dB out of it. What you
are doing in this case is coupling the vibration to the air with an
impedance matching device. The reason the rod sings for so long, of
course, is because it is coupled only weakly to the air, and of
course the rod won't ring nearly as long with the cup touching it.

You should also demonstrate the overtones of the longitudinal mode.
This can be done by suspending (or holding) the rod at different
nodal points, the first of which is located at the L/4 points from
the end of a rod of length L. It is easy to demonstrate the lowest
transverse mode of the rod as well, but you should find and mark the
nodal points on the rod for that mode before doing it (I think they
are .2242 L from the ends, but my memory is not great - look it up),
and of course you have to excite the mode by striking the rod
sideways at it center. The sound produced is very feeble. It is also
poorly coupled to the air, but nondissipative suspension of the rod
is more difficult than it is in the compressive mode of the
longitudinal oscillation. It can be accomplished by drilling the rod
and suspending it vertically from rubber bands or threads through the
holes.

I was once called upon by the Vancouver Opera Company to produce a
large, cylindrical tubular chime with a low F pitch for use in a
production of I Puritani. Such a chime exists, and it is used for
just one note in the opera, but its whereabouts could not be
determined. It travels around the world, since I Puritani is not
produced nearly so frequently as , say, Don Giovanni, and one chime
is enough. A chime of this sort is easy to construct; it's nodal
point are at the same positions as those of the rod's transverse
modes. The Q of the chime is high because it is suspended as I
indicate above. The overtones of the chime are not harmonic, and some
tuning can be done, though I have not attempted this myself. I do
know how to do it, but the VOC located the canonical chime in Florida
before I even bought the tube. They did give me a couple of free
tickets to the production, and a nice conducted backstage tour. My
wife, Evelyn, was thrilled. I'm not a Bellini fan, but I was
thrilled, too. (I have more common tastes - I would very much have
preferred Don Giovanni.)

There is a lot of neat physics in musical instruments I have done
experimental work on tympani, a relatively simple instrument. It is a
real thrill when one figures out how a tymp "works".

Leigh

On 26-Nov-05 Ralph 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?

Thanks,
Ralph von Philp
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