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Normal modes of a string thought experiment

  1. Oct 14, 2013 #1
    Hey! So If I have a stretched string of length L fastened at one end, and I am moving the other end sinusoidally, will a standing wave appear ONLY if I move the other end with one of the normal-mode frequencies of the string? If not, will the resulting wave be a moving wave which is a superposition of the string's normal modes?
    Last edited: Oct 14, 2013
  2. jcsd
  3. Oct 15, 2013 #2

    Simon Bridge

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    Do it and see :)

    Shaking the string from one end is a bit different from plucking it.
    You get a node a little distance x from your fingers - and you will have excited a normal mode of a string length L-x which is fixed at both ends. Otherwise you have to move your hand with the frequency of the normal modes of your string (work them out for a string length L with one end free).

    When you drive a string like that - the system is a "driven harmonic oscillator" and the solutions can get quite complicated. You can represent the result as a superposition of normal modes - just as the normal modes can be represented as a superposition of travelling waves.

    Real strings can get more complicated still.
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