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, w_o = k_o = 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, w_o = k_o = 1, Dw = 0.025, Dk = 0.05
The component waves move more quickly than the envelope.

Phase Velocity < Group Velocity [179K]

A=0.7, w_o = k_o = 1, Dw = 0.1, Dk = 0.05
The component waves move more slowly than the envelope.

Group Velocity = 0 [18K]

A=0.7, w_o = k_o = 1, Dw = 0, Dk = 0.05
The envelope is stationary while the component waves move underneath.

Phase Velocity = 0 [178K]

A=0.7, w_o = 0, k_o = 1, Dw = Dk = 0.05
Now only the envelope moves over stationary component waves.

Phase Velocity = -Group Velocity [179K]

A=0.7, w_o = k_o = 1, Dw = -0.05, Dk = 0.05
Finally, the envelope moves in the opposite direction of the component waves.