Group and Phase Velocity
The group velocity is the speed of the overall shape of a modulated wave (called the envelope). This is defined by (chosen here to equal 1), where is the angular velocity and is the wave number. The phase velocity of a wave is the speed at which a given phase of a wave travels through space, equal to .
The wave shown here is a sum of two waves that differ by a small phase (called a beat) of the form .