What is phase velocity?

1. Nov 20, 2012

mycotheology

According to the wiki page, this diagram:

shows the phase velocity and group velocity moving in opposite directions. I think I understand what group velocity is, its the velocity of the overall wavepacket, in the diagram I can see a Gaussian wavepacket moving to the right so I'm guessing thats the group velocity. I can't see the phase velocity. I don't know what I'm looking for because I don't really know what phase means. I understand the concept of constructive and destructive interference and how 2 waves can be in or out of phase but I don't understand what phase means with respect to an individual wave. Does the word phase mean where the waveform is on the y axis, at a particular point on the x axis? Thats the idea I have of phase and with that in mind, I can't understand how phase can have a velocity.

Last edited: Nov 20, 2012
2. Nov 20, 2012

Staff: Mentor

Correct!

The phase velocity refers to the individual waves "inside" the wave packet, which are moving to the left in your example. Actually, what you're seeing is the average phase velocity of the individual waves that combine to produce the wave packet.

Last edited by a moderator: Apr 16, 2017
3. Nov 20, 2012

Simon Bridge

I think the way to see the phase motion is to pick an individual peak and keep your finger on it.

4. Nov 21, 2012

mycotheology

So if I did a Fourier transform on the wavepacket and broke it down into its constituent sine waves, they'd be moving to the left. Still can't see it though. Are you able to see the individual waves inside the packet in that diagram?

Whats confusing me is the way each individual ripple is growing and shrinking as it moves from left to right. In other words, each peak is moving up and down the y axis as it traverses the x axis. I thought that phase depended on the position on the y axis. If I follow an individual peak, I do see it moving from right to left though, should I just forget about the y axis?

5. Nov 21, 2012

arildno

Group velocity is, essentially, the velocity by which ENERGY propagates. Energy is what effectively determines the actual AMPLITUDE of a given peak, whereas the peak itself moves with a different velocity. THAT velocity is what we call phase velocity.

6. Nov 21, 2012

mycotheology

Ah right, that clears it up, thanks a lot.

7. Nov 22, 2012

Simon Bridge

That's it :)
The phase is the angle that the phasor makes with the horizontal axis.
If the length of the phasor is constant, then that corresponds to the y-coordinate.
But if the length of the phasor is a function of time, then the same phase points may have different y-positions. All the peaks have the same phase - and they are easy to see - so...

http://en.wikipedia.org/wiki/Phasor (second diagram)