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Re: Beats

At 11:08 AM 9/30/96 -0400, Nick Guilbert wrote:

At a retreat over the weekend, I came across a device (which may have
once served as the cabin's dinner bell) that really has me puzzled. It
consists of what looks to be a solid aluminum rod, about 20 cm in length
and 1 cm diameter, suspended by a pair of fine strings (looped around the
rod) at about the 5 cm and 15 cm points from one end. When struck with the
supplied rubber-headed mallet, the rod emitted a nice high-pitched tone -
and beats! The beat frequency was in the 1-2 Hz range and was both clear
and reproduceable. In fact, the beats were considerably more noticeable
than the ones I *try* to produce in class with a pair of few-Hz-apart
tuning forks.

I can't for the life of me figure out why a single rod would produce
two strong tones a Hertz or two apart in frequency when the dominant tone
was in the 800-900 Hz range. Do the strings introduce some weird boundary
conditions? Is there a plausible explanation if the rod were, in fact,
non-uniform? Could temperature differentials across the rod (in a
non-uniformly-heated cabin - but it's a short rod compared to the length
scale of the temperature differences) have anything to do with it? I
didn't have the opportunity to do extensive tests on the device, but this
really has me bothered.

Any insights? Or am I missing something completely obvious?

If the rod is swinging or rotating after you hit it, you may be hearing
beats due to the doppler shifted frequencies. I do this in class with a
longer (~1.6 m) "singing rod".

George Spagna **********************************************
Department of Physics * "The purpose of science is to get paid *
Randolph-Macon College * for doing fun stuff if you're not a *
P.O. Box 5005 * good enough programmer to write *
Ashland, VA 23005-5505 * computer games for a living." *
* - E. Robert Schulman *
phone: (804) 752-7344 * Ann. Improb. Research, *
FAX: (804) 752-4724 * Vol 2, No. 5, p. 8 *
e-mail: **********************************************