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Wave superposition

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data
    What is the equation for the superposition of 2 waves?
    2. Relevant equations



    3. The attempt at a solution
    Displacement of the first wave is D1 = Asin(k1x - ω1t)

    Displacement of second wave is D2= Asin(k2x - ω2t)

    Add together: D1 + D2 = 2Acos[(k1-k2)x/2 - (ω1 - ω2)t/2]*sin[(k1 + k2)x/2 - (ω1 + ω2)t/2]

    But this isn't in terms of what the problem is asking! Help, can the form be changed somehow?

    Is there a way to reduce the k1 and k2 so that it is in that form?
     
    Last edited: Apr 5, 2010
  2. jcsd
  3. Apr 4, 2010 #2

    ideasrule

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    Homework Helper

    But it IS in terms of w1-w2 and w1+w2! Maybe the question meant that you could use y=Asin(w*t) instead of y=Asin(kx-wt), but otherwise, your work is correct.
     
  4. Apr 4, 2010 #3
    Good point. But if the waves have different angular frequencies, wouldn't k be different? I don't see how you can just leave it out.

    When a question asks for something in terms of w1 and w2, doesn't that mean I shouldn't have anything else in there?
     
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