Re: Waves

[Leigh Palmer <palmer@SFU.CA>]

> Am I correct in explaining string instruments, to say that a string
> actually vibrates in many modes simultaneously when bowed or plucked?
> That is, is it producing its fundamental along with several harmonics
> all at the same time?

Yes, you are correct. For a plucked string, the initial (rest) profile
can be Fourier decomposed into its elements by assuming it is periodic
in space with constrained nodes at its ends. That constraint can be
lifted for a string because the wave velocity is constant.

> Is it possible to show this behavior (if the notion is correct) with a
> string vibrator or other equipment, rather than just postulating to
> students that this does in fact occur?

You can demonstrate this effect with a real-time spectral analyzer.
Alternatively you could record it and analyze it with any of the
freeware spectral analyzers available in software archives. I used
a Tektronix scope plugin for this purpose when I taught the course
in the physics of music.

Leigh