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I am trying to understand the difference between 'wave velocity' and 'phase velocity'. I know that generally they are equal, but when is that not the case?

I, of course, tried to google it, and didn't come up with anything useful. So, any help I would get will be highly appreciated. Thanks in advance.

P.S. I am not talking about group velocity.

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Wave velocity, when not otherwise specified, usually means the phase velocity: the rate at which the phase travels in space.

This site animates the differences between phase and group velocities. The group velocity is the speed at which energy is transported.

So if the context implies that the wave is carrying energy, the wave velocity is also the group velocity.

In a dispersionless media group and phase velocity are the same. Special treatment is required for strongly absorbing regions near a resonance.

A detailed treatment of phase, group, and signal velocity can be found here.

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  • $\begingroup$ Thank you. When would the wave velocity NOT equal the phase velocity? I haven't encountered any cases so far in which they are not the same thing. That is what I'm asking. $\endgroup$ – Victor Apr 23 '16 at 20:51
  • $\begingroup$ @Victor: See additional link added at the bottom of the answer. It is too long for me to summarize; it cover's all of the main points quite well. $\endgroup$ – Peter Diehr Apr 23 '16 at 23:42

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