Path: utzoo!mnetor!uunet!lll-winken!lll-lcc!lll-tis!ames!hao!noao!amethyst!hdunne
From: hdunne@amethyst.ma.arizona.edu (|-|ugh)
Newsgroups: sci.misc
Subject: Re: Wave and Group Velocity
Message-ID: <411@amethyst.UUCP>
Date: 24 Feb 88 04:01:36 GMT
References: <251@alice.marlow.reuters.co.uk>
Sender: uucp@amethyst.UUCP
Organization: Dept. of Math., Univ. of Arizona at Tucson
Lines: 19

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
Dept. of Math.    |     Phone:      | ARPA:     hdunne@amethyst.ma.arizona.edu
Univ. of Arizona  | +1 602 621 4766 | Bitnet:   hdunne@arizrvax
Tucson AZ  85721  | +1 602 621 6893 | Internet: hdunne@rvax.ccit.arizona.edu