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Wave equation for a standing wave - clarification needed

  1. Apr 24, 2013 #1
    ImageUploadedByPhysics Forums1366794366.871437.jpg

    Both of the highlighted equations deal with a standing wave. However, they are slightly different in the sense that the latter has a phase shift in it.

    Why ?

    Also, how does one go from the latter equation for a standing wave to :

    2A*sinkx*sinwt. For a string with both ends fixed


    2A*sinkx*coswt. For one end fixed and the other free


    2A*coskx*coswt. For both free.
  2. jcsd
  3. Apr 24, 2013 #2

    Simon Bridge

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    eq. 4.4.2 deals with the specific situation where the amplitude of the wave is zero everywhere at t=0, and the point x=0 is always a node.

    However, t=0 is just when we happen to press the button on the stopwatch and x=0 is just where we happen to put the ruler at the time. These are arbitrary: the wave in front of you could be at any stage in it's motion at t=0 for eg. and the ruler may not start at a node.

    The phase term is needed to account for the possibility that at t=0, and x=0, the wave is not in such a tidy state.

    The other possibilities come from the phase terms ... you change from a sine to a cosine by changing phase by ##\pi/2##.
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