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Homework Help: Finding Group Velocity and Phase Velocity

  1. Mar 20, 2013 #1
    The phase velocity of ocean waves is (gλ/2∏)1/2,where g is the acceleration of gravity.Find the group velocity of ocean waves.

    Relevant equations: λ=h/γmv phase velocity= c2/v(velocity of particle) group velocity=v (velocity of particle).
    thnxx in advance
     
  2. jcsd
  3. Mar 20, 2013 #2
    The wavenumber k:

    [itex]k = \frac{2\pi}{\lambda} [/itex]

    The wavenumber k is the angular frequency in space. The higher k is, the closer the wave peaks are together in space.

    The phase velocity is

    [itex]v_{phase} = \omega / k[/itex]

    where ω is the angular frequency in time

    the group velocity is

    [itex]v_{group} = \frac{ \partial \omega}{ \partial k}[/itex]

    I would express ω in terms of k, using the expression given for phase velocity. Then I would take the derivative of ω with respect to k.
     
  4. Mar 24, 2013 #3
    Thanks alot X
     
  5. Aug 9, 2015 #4
    Thank you so much :)
     
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