Phase velocity, Group velocity

[Theoretician]

Would someone be kind enough to please give physical meanings to these two terms? I have never fully understood their meaning and difference (although I know how to express them mathematically).

If, say, I have a Gaussian-shaped signal in the frequency domain that I am sending through a medium (such as a crystal) in the direction z say and I want to specify where the maximum intensity is as a function of t (it is at z=0 when t=0), am I right in saying that I would use:

t= z/(group velocity)

where the group velocity is obviously evaluated at the frequency of largest intensity.

Any help on this fairly basic matter would be much appreciated.

 

[Doc Al]

This discussion might help: https://www.physicsforums.com/showthread.php?t=96835

 

[Theoretician]

Thank you, I shall have a look but I actually think that I have a good enough understanding now having read a few relevant sections in the Feynman Lectures (sorry, this is what I should have done first).