malcolm@alice.marlow.reuters.co.uk (Malcolm Melville) (02/20/88)
Just read the stuff on the difference between sound and light waves and it reminded me that I was always confused by this concept of wave and group velocities. It was explained to me one time using the model of a pair of scissors closing. The intersection point of the blades moves rapidly and is like the group velocity. The points of the blades are real physical points and move slower abd are like the wave velocity. (I told you I didn't ever unerstand this stuff.) Does this mean that the group velocity is always larger than the wave velocity? Is it true that the group velocity can be greater than the speed of light?? How does this affect me?? All explainations welcome!! Malcolm -- The views expressed are my own rather than my employers. Mind you lots of other guys round here feel the same way. Malcolm Melville
hdunne@amethyst.ma.arizona.edu (|-|ugh) (02/24/88)
I don't think the scissors analogy is particularly helpful. Basicly, the group
velocity is the velocity at which information propagates. It can be slower or
faster than the wave velocity, and need not go in the same direction. It can't
be faster than light.
Suppose for example you drop a rock into a lake. A series of waves will spread
out in a circle from the point where the rock entered the water. You will get
a sharp leading edge to the wave packet and a gradual trailing edge. The wave
packet travels at the group velocity, which in this example happens to be half
the wave velocity (assuming the lake is deep). Thus individual ripples will
appear at the trailing edge and move to the front (since they're travelling
faster than the group velocity) where they disappear. A person on the opposite
shore doesn't know you threw a rock in the water until the wave packet reaches
him, since it is the wave packet that carries information, not the individual
ripples.
Hugh Dunne | UUCP: ..{cmcl2,ihnp4,seismo!noao}!arizona!amethyst!hdunne
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