How Do You Calculate Group Velocity from Phase Velocity?

[lockedup]

Homework Statement

The phase velocity of ocean waves is $$\sqrt{\frac{g\lambda}{2\pi}}$$ , where g is 9.8 m/s2. What is the group velocity?2. Homework Equations
$$v_{p} = \omega/k$$
$$v_{g} = \partial\omega/\partial k$$

The Attempt at a Solution

So I've been trying to find omega and k from the equation in the problem statement. I've tried isolating different variables and plugging back in. I've been at this for a while now. I don't know how many google searches I've done. The only place I can find the given equation is on wiki and they don't derive it. It's for my modern physics class and the book I'm using doesn't explain any of this...

I don't want the answer. I just want a hint to get me started.

 

[ehild]

Look at this place:

http://oceanworld.tamu.edu/resources/ocng_textbook/chapter16/chapter16_01.htm

ehild

 

[vela]

What you need is the dispersion relation $\omega=\omega(k)$. You need to express $\omega$ as a function of k, which you can do if you know the phase velocity in terms of k, not solve for particular values of the variables. Once you have that, you differentiate it to find the group velocity.