Wave questions and Čerenkov radiation

[esvion]

I have a couple questions about waves and Čerenkov radiation:

1. I know in all acoustic waves, rarefaction occurs after a wave passes through a medium. On paper, is the trough of a wave its rarefaction? What is the force that causes rarefaction? I've heard the "atoms are like springs" explanation, but I don't quite understand it. I am trying to understand why the air particles in this http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/monopolfinalptpt.gif" rush towards the center. Why doesn't rarefaction occur in explosions (which have just one gigantic wave followed by much smaller ones) or in light waves? (or does it?)

EDIT: Explanation of picture can be found http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-basics-pointsources.htm" , but it doesn't explain why rarefaction occurs.

2. In Čerenkov radiation, I understand that the phase velocity in a charged particle exceeds the speed of light (in that medium). I also understand that it is possible for lasers to have a higher group velocity than light. How can phase and group velocities (or even frequencies in some cases I believe) be faster than the signal (speed) velocity of a wave? Does the group/phase velocity dissipate when it gets to the end of a signal?

Thanks!

 

[esvion]

Anybody? Should I post this in another part of a messageboard, or is my question not clear?

Help!

 

[Andy Resnick]

I admit an initial reluctance to respond. Your original questions are not very clear to me- for example, question #1 indicates some conceptual confusion between pressure (extrapolated to a discrete, particle model) and force, and question #2 seems like a 'word salad'. For example, I don't know what you mean by 'I also understand that it is possible for lasers to have a higher group velocity than light.'.

Maybe framing the questions with a coherent framework would help: Is there a particular physical phenomena you are thinking about?

 

[esvion]

In question #1 I was asking why rarefaction occurs, if it is represented on a graph by the wave trough, and what other types of waves besides sound waves (explosion, light, ocean etc.) encounter rarefaction.

In question #2 I was asking how group or phase velocity can be faster than the wave signal. I was also asking what would happen if the group/phase velocity (or frequency) was fast enough to get the end of a signal because it was faster than the speed of the signal.

 

[granpa]

rarefaction does occur in explosions. the momentum of the air carries it outward then the pressure drives it back.

phase velocity can exceed c because nothing is actually moving at that speed. its a mathematical artifact. nothing more. group velocity on the other hand is usually descrided as the rate at which energy moves. why it can exceed c is beyond me.

 

[atyy]

http://www.mathpages.com/home/kmath210/kmath210.htm