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Homework Help: Waves on a string and motion

  1. Jun 15, 2010 #1
    1. The problem statement, all variables and given/known data
    The displacement y of a long string at position x and time t is given by

    y(x,t) = cos (kx-wt) + sin (kx-wt)

    Show that the motion of the string at any point is SHM.


    3. The attempt at a solution

    As far as i know this is something to do with adding 2 waves together and in this case we have a sinusoidal wave and a cosine wave. If one wave is the reflection of the other then a standing wave will develop, and i think that in this case a standing wave will develop and that would mean that the motion of the string is SHM.

    Is that correct? Would there be a better explanation as to why the motion is in SHM.

    p.s not homework, just past exam question.
     
  2. jcsd
  3. Jun 15, 2010 #2
    To prove the motion a SHM, just transform the displacement into the form of cosine or sine. In this problem, I think it's completely about mathematics.
    How would you prove that this is standing wave by the way?
     
  4. Jun 15, 2010 #3

    Redbelly98

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    Staff Emeritus
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    Homework Helper

    For a standing wave, you must have two waves traveling in opposite directions -- not the case here, since both waves travel in the +x direction.

    You could try the angle-addition formulas for sine and cosine, and work through the algebra.

    Hope that helps.
     
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