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Re: Beats

The longitudinal mode is usually much higher in frequency. The
transverse mode for a rectangular bar depends on the width and
thickness to different powers (I seem to remember it depends on
thickness to the first power, width to the third). Therefore if the
bar is not totally round and you hit it at an angle with respect to
the "thin" direction, you could excite both longitudinal modes.

The strings should be at the two nodal points on the bar, which
aren't really 1/3 and 2/3.


Perhaps the longitudinal and transverse vibrational modes are very close
in frequency???

cheers

On Mon, 30 Sep 1996, NGUILBER wrote:


This may be serving only to expose my own ignorance, but ...

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?


Nick

Nick Guilbert
The Peddie School
Hightstown, NJ

nguilber@peddie.k12.nj.us