Wiktionary
n. (context physics English) The velocity of propagation of a pure sine wave of infinite extent and infinitesimal amplitude.
Wikipedia
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, 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 (lambda) and period as
$$v_\mathrm{p} = \frac{\lambda}{T}.$$
Equivalently, in terms of the wave's angular frequency , which specifies angular change per unit of time, and wavenumber (or angular wave number) , which represents the proportionality between the angular frequency and the linear speed (speed of propagation) ν,
$$v_\mathrm{p} = \frac{\omega}{k}.$$
To understand where this equation comes from, consider a basic sine wave, . After time , the source has produced oscillations. After the same time, the initial wave front has propagated away from the source through space to the distance to fit the same number of oscillations, .
Thus the propagation velocity v is . The wave propagates faster when higher frequency oscillations are distributed less densely in space. Formally, is the phase. Since and , the wave velocity is .
Usage examples of "phase velocity".
In fact, the group velocity for water waves is exactly half the phase velocity.
The way we hype up ultrawave is to use an old application of wave-guide theory, whereby the real transmission of energy is at light speed, but a quasi-imaginary thing called phase velocity is going faster.
That's because the phase velocity of the wave crests is greater than the speed of a group of waves.
Their leaden masses magnified by velocity, the huge slugs skipped through existence like stones across water, passing like phantoms through the fleet of life, emerging fully into normal space only as they approached their target, traveling then like De Broglie wavicles, their matter churning internally with a phase velocity greater than that of light.