# Homework Help: Finding Group Velocity and Phase Velocity

1. Mar 20, 2013

### physycho

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).

2. Mar 20, 2013

### MisterX

The wavenumber k:

$k = \frac{2\pi}{\lambda}$

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

$v_{phase} = \omega / k$

where ω is the angular frequency in time

the group velocity is

$v_{group} = \frac{ \partial \omega}{ \partial k}$

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.

3. Mar 24, 2013

### physycho

Thanks alot X

4. Aug 9, 2015

### Spencer Schimdt

Thank you so much :)