A. John Mallinckrodt   Professor of Physics, Cal Poly Pomona
Wave
Packets
Phase and Group Velocities of Wave Packets
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The following movies show wave packets with various combinations of phase and group velocity. Each waveform is the sum of five sinusoids with the general format

which yields

Each movie is set up for seamless looping, but you may have to download and play them outside your browser to enable the loop feature.

Phase Velocity = Group Velocity [179K]
A=0.7, wo = ko = 1, Dw = Dk = 0.05
The entire waveform—the component waves and their envelope—moves as one. Kind'a boring.

Phase Velocity > Group Velocity [179K]
A=0.7, wo = ko = 1, Dw = 0.025, Dk = 0.05
The component waves move more quickly than the envelope.

Phase Velocity < Group Velocity
[179K]
A=0.7, wo = ko = 1, Dw = 0.1, Dk = 0.05
The component waves move more slowly than the envelope.

Group Velocity = 0
[18K]
A=0.7, wo = ko = 1, Dw = 0, Dk = 0.05
The envelope is stationary while the component waves move underneath.

Phase Velocity = 0
[178K]
A=0.7, wo = 0, ko = 1, Dw = Dk = 0.05
Now only the envelope moves over stationary component waves.

Phase Velocity = -Group Velocity
[179K]
A=0.7, wo = ko = 1, Dw = -0.05, Dk = 0.05
Finally, the envelope moves in the opposite direction of the component waves.
 ©2001 by A. John Mallinckrodt ajm at csupomona.edu http://www.csupomona.edu/~ajm Many documents are provided in ".pdf" format. Click here to get the free Acrobat Reader application. The space for this page is provided by Cal Poly Pomona and is subject to its policies. Nevertheless, the opinions expressed here are my own and do not necessarily represent official policy of the University. I take full responsibility for the information presented and will appreciate being informed of errors or inaccuracies. Last modified on 25 March, 2004