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Re: Waves



David Abineri <dabineri@CHOICE.NET>@lists.nau.edu: Forum for Physics
Educators" <PHYS-L on 07/03/2000 08:16:03 AM

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Subject: Waves

Dave,

There are a couple of ways to demonstrate the fact that several modes can
be excited at the same time.

First, pluck a string near the center and then near the end. This will
produce two noticeably different sounds. Both are the same pitch, but the
one plucked near the end will have a "harsher" timbre, while the one
plucked near the center will sound "hollower". The reason is that
plucking near the center excites primarily the fundamental, with small
amounts of just the odd harmonics. Plucking near the end allows nearly all
harmonics to occur. (If you know Fourier analysis this isn't too hard to
show.)

To build on this, it you have one of the computer based data collections,
most of them have FFT capabilities to analyze waves and show the
contributions of different frequencies to the overall waveform. This will
clearly show that frequencies at multiples of the fundamental are present.


A second approach would be to lightly touch the string at different
locations while plucking. If you touch it right at the center, it will
vibrate freely at a frequency 2 f, but not at f (i.e. 1 octave higher).
Touch it 1/3 of the way and it will vibrate at 3f (octave & fifth).... It
is not completely obvious that the string originally is vibrating at all
these frequencies at once, but it is plausible that it at least can.


Tim Folkerts