Phase velocity
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 will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength
λ and period
T as Or, equivalently, in terms of the wave's angular frequency
ω, which specifies angular change per unit of time, and wavenumber
k, which represents the proportionality between the angular frequency ω and the linear speed νp: To understand where this equation comes from, imagine a basic sine wave,
A cos . Given time
t, the source produces
ωt/2π = ft oscillations. At the same time, the initial wave front propagates away from the source through the space to the distance
x to fit the same amount of oscillations,
kx =
ωt. So that the propagation velocity
v is
v =
x/
t =
ω/
k.