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Q & A: wave speed

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Most recent answer: 10/22/2007
Q:
What is really meant by the speed of a wave? Is it how fast the energy is moving, or is it how fast it gets from one point to another? I know that wavelength x frequency = speed, but I’m having trouble picturing what that means.
- Andrew (age 12)
Colorado
A:
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)

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