# Homework Help: Calculating kinetic energy density of wavepacket in deep water waves

1. Aug 21, 2012

### twinklestar28

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?