Phase velocity

File:Wave group.gif

Gravity waves on the ocean surface over deep water. The red dot moves with the phase velocity. The green dots propagate with the group velocity. The phase velocity here is twice the group velocity.

The phase velocity of a wave is the rate at which the phase of any one frequency component of the wave travels.

Any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength λ (lambda) and wave period

Phase Velocity Media

• Wave packet propagation (phase faster than group, nondispersive).gif

  Propagation of a wave packet demonstrating a phase velocity greater than the group velocity.

• Wave opposite-group-phase-velocity.gif

  This shows a wave with the group velocity and phase velocity going in different directions. The group velocity is positive (i.e., the envelope of the wave moves rightward), while the phase velocity is negative (i.e., the peaks and troughs move leftward).

• Wavepacket1.gif

  A superposition of 1D plane waves (blue) each traveling at a different phase velocity (traced by blue dots) results in a Gaussian wave packet (red) that propagates at the group velocity (traced by the red line).

T as

[math]\displaystyle{ v_\mathrm{p} = \frac{\lambda}{T}. }[/math]