Andrew- That's a nice question whose answer is a little tricky. When we
try to describe wave speeds carefully we use two different definitions,
which generally give different values. That's ok because they mean
different things.
The 'phase velocity' fits your definition. If you have a nicely
repeating wave pattern, it describes how rapidly the crests and troughs
(or regions of positive and negative field, or whatever is appropriate
for the particular wave) move through space. That might sound like all
you need, but it does not really give the rate at which energy is
flowing in the wave.
We also define a 'group velocity'. That's the rate at which a
little wave packet moves forward. The individual crests within the
packet can slip forward or backward with respect to the packet, with
new ones arising at the front or back of the packet, so their speed
doesn't have to be the same as the packet speed if different
wavelengths travel at different speeds. The group velocity gives a
better measure of how fast energy (and also information) move in the
wave.
There are cases where the phase velocity is bigger than the speed
of light in a vacuum, but the group velocity still obeys that speed
limit.
Mike W.
(published on 10/22/2007)
