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

[Leigh Palmer <palmer@SFU.CA>]

I want to correct one misimpression that Carl leaves me with here.
When the transverse normal mode of the rod is excited, there will
usually be longitudinal modes excited too. You can see this effect is
relatively greater when the striker used to excite the transverse
mode is hard, like a screwdriver handle, rather than soft, like a
sausage link. The transverse mode is just highly damped, so it dies
away faster than the very high Q longitudinal modes. I doubt that
there is very much "mode conversion"*, since the normal modes of the
bar are just those we are talking about here, and of course they are
very nearly orthogonal, and the way we excite them tends to
preferentially excite just one normal mode.

One can hear evolution of the timbre of a ringing sound in a system
if it has many normal modes with similar frequencies, and one excites
several to appreciable amplitudes at the same time. A simple example
of such a system is the strings responsible for a mid to higher
pitched note on a piano. Three strings, all tuned to nearly the same
frequency, may be struck at once. The decay of this sound is not
simply exponential in time because the normal modes of the system
beat against one another, and the modes have different decay times
(or alternatively put, different Q's).

A much more complex ringing system in which the sound evolves is the
tam-tam, or oriental gong. Struck with a soft mallet near its center,
the gong rings at first with a mellow, lower pitched** sound which
then evolves over a second or so into brighter, higher pitched,
longer lasting overtones. The making of such instruments is a high
art in the orient. Avedis Zildjian, an Armenian in 17th c.
Constantinople, started a company that persists today carrying on its
family secret processes to make the most prized cymbals today.

Vibrating bodies are neat! I go around exciting oscillations in
railings, light standards, and other structures around me. I once
made people on the stairway up inside the Statue of Liberty nervous
by exciting that structure, which has a higher Q than it ought to
have for safety reasons.

Leigh

*Mode conversion, the exchange of energy (sorry Jim) from one normal
mode to another, does occur in nonlinear systems, and of course
everything real is, to some degree, nonlinear. In what I write above
I describe a system in terms of a strictly linear model - Hookeish
springs, etc.

**The tam-tam doesn't have a distinct pitch, of course.

On 27-Nov-05 Carl Preske wrote:

> I used to have students determine the frequency of vibration by
> whatever
> method the wanted to use than have then determine the speed of the
> wave.  A
> quick look in the CRC Handbook and they could determine the type of
> wave and
> their accuracy.  The CRC lists three wave speeds for Al but they
> are widely
> separated so it is easy to choose.  Just for fun note that were you
> strike
> the side of the rod you generate a wave which degenerates quickly,
> relatively speaking, into the wave that is generated by striking
> the end of
> the rod.
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