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Verification of of Phase vs. Group Velocity

  1. Oct 10, 2004 #1
    How do i go about verifying this statement: If the phase velocity is the same for all wavelenghts of a certain wave phenomenon (no dispersion), the group and phase velocities are equal. Do i just put the two formulas equal to each other and solve for something or what?
     
  2. jcsd
  3. Oct 10, 2004 #2
    any ideas on how to even start?
     
  4. Oct 10, 2004 #3

    Claude Bile

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    Phase Velocity = w/k

    Group Velocity = dw/dk

    If w/k is constant, it really is not that hard to show that the phase and group velocities are equal.

    Claude.
     
  5. Oct 10, 2004 #4
    Explain please.
     
  6. Oct 11, 2004 #5

    Claude Bile

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    Look at the dispersion relation (w vs k). If w/k is constant, the dispersion relation is just a straight line with gradient w/k.

    Since the group velocity is the gradient, dw/dk, if the dispersion relation is a straight line, then the group velocity will be w/k for all w.

    Claude.
     
  7. Oct 12, 2004 #6
    I think he be suggesting that the local slope of a curve is be equal to the slope of the line joining any two points on it, if the curve is a straight line.
     
  8. Oct 12, 2004 #7

    Claude Bile

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    Spot on. Graphing w vs k may make it less confusing.

    Claude.
     
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