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Waves in dispersive medium

  1. Apr 9, 2013 #1
    1. The problem statement, all variables and given/known data
    s656v8.png


    2. Relevant equations



    3. The attempt at a solution
    2uzf5dz.png

    i have no clue about the second part..
     
  2. jcsd
  3. Apr 10, 2013 #2
  4. Apr 12, 2013 #3
    Am I suppose to superimpose the following waves:

    exp i(kx - wt) + exp i((k+Δk)x - w't)

    whereby the other wave has a different wavelength such that k becomes k+Δk and w becomes w' (with k+Δk) ?

    op66g.png

    So I found that at h >> 1/k or h >> λ/2∏

    vg = (1/2) vg

    And at h << 1/k or h << λ/2∏

    vg ≈ vp


    I first assume that h >> 1/k or h >> λ/(2∏): But how do i prove this? I can't seem to solve the tanh function to find the value of k..

    I got:
    0.16≈k*tanh(1000k)

    If i assume k≈0.16 since tanh(160) ≈ 1..
    i get vp = 7.9m/s
    Time taken = 35 hours..
     
    Last edited: Apr 12, 2013
  5. Apr 15, 2013 #4
  6. Apr 17, 2013 #5
    bumpp anyone?
     
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