Phase velocity
The speed v_p = ω/k at which an individual crest of a sinusoidal wave moves. Can exceed c; carries no information.
Definition
For a plane wave of the form cos(kx − ωt), the phase velocity is the speed at which a point of constant phase — a crest or a trough — travels: v_p = ω/k. It is the speed you would measure by watching one specific crest and timing its progress.
Phase velocity is, perhaps counter-intuitively, not bounded by the speed of light. X-rays in glass, radio waves in an ionosphere, and microwaves in a waveguide all have v_p greater than c. Relativity is not violated because a pure sine wave, being infinite in extent and time, carries no information. Information requires modulation, and modulation builds a wave packet, which travels at the group velocity.
History
The phase-versus-group distinction was crystallised by William Rowan Hamilton in 1839 and given its modern treatment by Lord Rayleigh in the Theory of Sound (1877).