Fourier Series Applet of 1D wave Motion, Vibrating String 2.

Cuthbert Nyack

The applet below the string is plucked at 2 points x1 with amplitude a1 and x2 with amplitude a2. (Red) shows how the deflection of the string changes with time. The points at which it is plucked can be changed by changing x1 and x2 and the initial amplitudes can be changed by changing a1 and a2. The frequency of the fundamental tone is T. Time t is given in terms of T.

eg parameters:-
(0.25, 1.0, 0.75, 1.0, 0.0) As t is changed from 0 to 1 the string goes through one vibration. The fundamental frequency is n = 1 with harmonics at n = 3, 5 etc.
(0.25, 1.0, 0.75, -1.0, 0.0) As t is changed from 0 to 0.25 the string goes through half a vibration. The vibration is completed when t = 0.5. In this case the "fundamental" is the "second harmonic" n = 2 with harmonics at n = 6, 10 etc.
(0.1, 1.0, 0.2, 0.0, 0.0) Here the initial displacement is in the shape of a pulse. t = 0.1 shows the wave which travels down the string.
t = 0.25 shows the wave half way down the string.
t = 0.5 shows the wave just after reflection at the end of the string.
t = 0.75 shows the wave half way back up the string.
t = 1.0 shows the string returning to its original shape. In this case the spectrum is broad with maximum ~ n = 5 (nb x2 = 1/5).
(0.25, 1.0, 0.46, -0.4, 0.0) In this case the initial displacement is asymmetrical. Changing t from 0 to 1.0 shows one period of the vibration.

When activated the following gif image show how one of the applets should appear.

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