TRAVELLING WAVE ANIMATIONS

PHASE VELOCITY AND GROUP VELOCITY

A plane harmonic wave propagating along the +Z axis is described by the equation

wavefunction

A amplitude

k wavenumber

angular velocity

wavelength

period

frequency

The phase velocity v_p of the wave is

The group velocity describes the speed of propagation of a pulse in a medium. To see this fact, consider propagation of two plane waves with different parameters but equal amplitudes

The superposition of the two waves gives a resultant complex wave

The envelop of the complex wave moves at the group velocity

Figures 1 and 2 show animations of the waves as they travel in a non-dispersive and dispersive medium. In a non-dispersive medium all frequencies travel with the same phase velocity and the phase and group velocities are identical. In a dispersive medium, waves with different frequencies have different phase velocities and the envelop propagates at the group velocity .

Fig. 1. Non-dispersive medium:

Fig. 2. Dispersive medium:

Any comments, suggestions or corrections please email Ian Cooper

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