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Wave vs. Group Velocity

  1. Apr 28, 2005 #1
    Problem 9.22 from Griffiths:

    Show that in deep water (where the depth is greater than the wavelength) the wave velocity is twice that of the group velocity. where Vw = w/k and Vg = dw/dk

    where w is the angular frequency, and k is the wave number.

    I'm really not certain how to proceed. Can someone give me a hint?
     
  2. jcsd
  3. Apr 28, 2005 #2

    OlderDan

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    This is pretty cool. Check this out for starters

    http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.html

    I think you need a functional relationship between [itex]\omega[/itex] and k to do this. That relationship for deep water is known, so I assume you can find it in Griffiths.
     
    Last edited: Apr 28, 2005
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