Re: wave packet in a string (2D wave packet?)

From: idyllic (idyllic.math_at_gmail.com)
Date: 10/04/04 

Date: 4 Oct 2004 04:49:49 -0700

First, Thanks for your help very much, I so wandered about this
problem.
The text book is:
   Quantum Mechanics concepts and applications by Nouredine Zettili
(2001)
   at page 44 the upmost paragraph.
Here I type all the original words from the text:
  A vibrating string provides a clear qualitative illustration of the
difference between Vph and Vg. The velocity of the wave travelling
along the string must certainly be distinguished from the velocity of
a point on the string itself. Suppose the string were stretched
horizontally along the x-axis, Vph would represent the velocity at
which the wave travels along the x-axis(i.e., the wave moving along
the string); Vg would represent the velocity at which a particle, or a
mass element, of the cord oscillates up and down about an equilibrium
position in a direction perpendicular to the string. The group
velocity is thus directed along a direction perpendicular to the
string, while the phase velocity is directed along the string itself.

jtbellj3p@presby.edu (Jon Bell) wrote in message news:<cjqq9n$5bt$1@jtbell.presby.edu>...
> In article <f9b8e54f.0410032038.3fc35702@posting.google.com>,
> idyllic <idyllic.math@gmail.com> wrote:
> > In my text book of quantum mechanics, it says, in a vibrating
> >string(the string lies in the x-direction), the phase velocity
> >represents the velocity at which the wave travels along the string;
>
> OK
>
> >while the group velocity represents the velocity at which a particle
> >of the cord oscillates up and down about an equilibrium position.
>
> That is completely wrong. Either you have misread the book, or else the
> book's author has made such a serious mistake that I would be suspicious
> of anything else he writes.
>
> The easiest way to picture group velocity on a vibrating string is to
> imagine making two waves with wavelengths and frequencies that are nearly
> equal, travel along the string. The two waves interfere and produce
> "beats" (which are more familiar in sound waves). The velocity of the
> beat pattern along the string is the group velocity in this case. It is
> *not* the transverse velocity of a particle in the string.

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