Phase and group velocity

[bluesky]

I do not know if it is a homework problem or not.The moderators will determine that.However,I read in acoustics books that it is a standard practice to use superposition of harmonic functions to denote a finite wave train, which cannot be given by a sine/cosine functions(because they are infinitely extended in time and space).This wave tran is known as wave group.

The impression I got is that a wave group is a mathematical concept and have no physical reality.Yet,its velocity, i.e. group velocity is different fro the phase velocity(w/k) of the wave.

So,where we are?It seems that phase velocity (w/k) is the physical reality but the group velocity is a mathematical concept only.However,phase velocity may be >c,whereas group velocity always<c.Please make the misconception clear

[Erasmus00]

Here are some nice demonstrations that should help clear up any confusion

 

Acoustics and Vibration Animations

 

He has some on phase/group velocities. In this case, pictures and demonstrations I think, will be much more helpful than anything I can describe with words.

-Will