Phase velocity

Phase velocity is the speed at which a point of constant phase travels through a wave. For a sinusoidal wave, it equals angular frequency divided by wavenumber.

Angular frequency: Angular frequency is the rate of change of a wave's phase, measured in radians per unit time. It supplies the time rate in the ratio that defines phase velocity.
Refractive index: Refractive index is the ratio of light's speed in vacuum to its phase velocity in a material. It expresses optical phase velocity as a material property.
Phase (waves): Phase is the position within a cycle of an oscillation, usually expressed as an angle. Phase velocity tracks how a chosen phase value moves across space.
Signal velocity: Signal velocity is the speed at which a detectable change or message propagates. It concerns information transfer, unlike the motion of a constant-phase point.
Wavenumber: Wavenumber is the spatial rate of change of phase, commonly expressed in radians per unit length. It supplies the spatial rate in the defining frequency-to-wavenumber ratio.
Cherenkov radiation: Cherenkov radiation is emitted when a charged particle travels through a medium faster than light's phase velocity there. The relevant threshold compares particle speed with phase speed, not vacuum light speed.
Wave: A wave is a propagating disturbance or oscillation that transfers energy or information through space or a medium. Phase velocity is one way to quantify a wave's propagation.
Energy velocity: Energy velocity is the speed at which energy is transported by a wave or wave packet. It can differ from phase velocity in dispersive or absorbing media.
Dispersion relation: A dispersion relation specifies how a wave's angular frequency depends on its wavenumber. Its slope from the origin gives phase velocity at each wavenumber.
Water wave: A water wave is a disturbance that propagates across or through a body of water. Surface-wave dispersion makes the phase speed depend on wavelength and water depth.

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