Phase and group velocity

Demonstration of phase and group velocity on the composition of two harmonic progressive waves.

We have four cases here: 1.) v_g < v_φ, 2.) v_g = v_φ, 3.) v_g > v_φ and 4.) v_g < 0.

First watch the movement of the modulating wave (indicated by dashed lines), then watch the movement of the carrier wave relative to the modulating wave, and finally focus on the movement of the carrier wave relative to the "background" (represented by the stationary vertical line).