# Wave vs. Group Velocity

1. Apr 28, 2005

### pt176900

Problem 9.22 from Griffiths:

Show that in deep water (where the depth is greater than the wavelength) the wave velocity is twice that of the group velocity. where Vw = w/k and Vg = dw/dk

where w is the angular frequency, and k is the wave number.

I'm really not certain how to proceed. Can someone give me a hint?

2. Apr 28, 2005

### OlderDan

This is pretty cool. Check this out for starters

http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/sines/GroupVelocity.html

I think you need a functional relationship between $\omega$ and k to do this. That relationship for deep water is known, so I assume you can find it in Griffiths.

Last edited: Apr 28, 2005