Group Velocity!

It is not unusual for the phase speed of a wave to depend on the frequency or wavelength of the wave, in certain media. In these media, the function ω(k) is called a “dispersion relation,” and the medium is called dispersive. In such a material, information and energy are usually transported at the group velocity, whose magnitude is given by

vg = dω/dk.

It is also not unusual for the group velocity to be in the opposite direction to the phase velocity of the individual waves:

Wave Applets

Types of Wave

Fathers of the Wave!