Another quick group velocity question

[bon]

Homework Statement

Ok so I'm confused by an apparent inconsistency in my notes..

On the one hand, we are told that in a non-dispersive medium, all frequencies propagate at the same speed, hence phase velocity of individual waves in superposition = group velocity..

so the idea of group velocity is only really important in a dispersive medium - correct?

But then my notes say that: if the velocity of the wave is frequency dependent, then the shape of the wave packed will change over time, because the individual components move with different speeds..so the idea of group velocity (i.e. velocity of the envelope) doesn't really have much meaning. It then goes on to say that in practice in the wave packet it long, there are a small range of frequencies, so ambiguity in group velocity is small...

So I don't think I am really understanding group velocity! On the one hand, I thought it was meant to measure the speed of an envelope in a superposition with different frequency waves...but then my notes say that if the velocity of the waves depends on freq., then the shape of the envelope changes, so the idea doesn't really apply..

any clarification would be great :)

 

[bon]

anyone? :S

 

[bon]

? :(

 

[bon]

can someone clever help me please? :(

 

[bon]

anyone??

 

[bon]

sorry to bump again..but surely someone must be able to help?

 

[nickjer]

The shape of the envelope may be changed, but the envelope as a whole is still moving with a group velocity. Group velocity is important since in some cases it tells you the speed at which the information (or energy) is travelling, but this isn't always true.