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Calculating kinetic energy density of wavepacket in deep water waves

  1. Aug 21, 2012 #1
    1. The problem statement, all variables and given/known data

    Assume that an orca can generate a wavepacket which is half a sine wave. Show that the kinetic energy density in this wave can be written

    U= ρgAλ/(32(π^2))

    2. Relevant equations

    mass per unit length=∫ρ dxdy
    KE=1/2mv^2

    3. The attempt at a solution

    I'm confused on what to use for dx and dy. Would dx and dy be the displacements :

    displacement in x = Ae^ky sin(wt-kx)
    displacement in y = Ae^ky cos(wt-kx)

    This however gives me complicated answers so I think my integral is completely wrong. Also for the velocity which they have given as vp= √gk/2 and vg=1/2vp which one do i use?
     
  2. jcsd
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