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Waves on a cylinder

  1. Apr 9, 2013 #1
    1. The problem statement, all variables and given/known data

    2rcmm94.png

    2. Relevant equations



    3. The attempt at a solution

    k9x8h1.png

    Not sure what they mean by general superposition of solutions...Do i use D'alembert's solution whereby I assume initial velocity = 0, and therefore:

    z = z(θ-ct) + z(θ+ct)
     
  2. jcsd
  3. Apr 10, 2013 #2
  4. Apr 10, 2013 #3

    TSny

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    Why are you restricting k to positive integers only?


    I don't understand the assumption of zero initial velocity.
    You want to construct a specific superposition of solutions for ω2 that will create a "node" at θ = π/3.
     
  5. Apr 10, 2013 #4
    i'm not sure how to create that superposition do i use A1*exp(kθ-ωt) + A2*exp(k+ωt) or something?
     
  6. Apr 10, 2013 #5

    TSny

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    What are the two values of k corresponding to ω2?

    Superimpose two waves with those values of k. Note that you do not want to change the sign of the ωt term in the exponential. After forming the superposition, you will be able to factor out a common factor of e-iωt.

    You might want to review the concept of "standing waves"on a string.
     
  7. Apr 11, 2013 #6
    The '-ωt' term involves the velocity of the wave, so you must superimpose:

    A1*ei(-kx-ωt) + A2*ei(kx-ωt)

    so that the waves destructively superimpose.
     
  8. Apr 11, 2013 #7
    v60z9e.png

    Is this correct??
     
  9. Apr 11, 2013 #8

    TSny

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    That looks good to me. You want to limit the value of n such that you don't repeat the same positions on the cylinder.
     
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