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Velocity of Wave Packets

by Hyperreality
Tags: packets, velocity, wave
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Hyperreality
#1
Jan17-05, 07:23 PM
P: 203
Wave packets has a group velocity of

[tex]v_{group}=\frac{d\omega}{dk}[/tex]

and its phase velocity is

[tex]v_{phase}=\frac{\omega}{k}[/tex]

Show that the group velocity and the phase velocity are related by:

[tex]v_{group} = v_{phase} - \lambda\frac{dv_{phase}}{d\lambda}[/tex]

Can someone please tell me where to start on this problem?
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dextercioby
#2
Jan17-05, 07:52 PM
Sci Advisor
HW Helper
P: 11,948
All u need to know besides the rules of differentiation is
[tex] k=:\frac{2\pi}{\lambda} [/tex]

Daniel.

PS.Compute the RHS of your equality and show it matches the LHS.


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