Finding Group Velocity and Phase Velocity

[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).
thnxx in advance

 

[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.

 

[physycho]

Thanks a lot X

 

[Spencer Schimdt]

Thank you so much :)