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The phase velocity of a wave is the rate at which the wave propagates in any medium. 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 time period T as
Equivalently, in terms of the wave's angular frequency ω, which specifies angular change per unit of time, and wavenumber k, which represent the angular change per unit of space,
v p = ω k . {\displaystyle v_{\mathrm {p} }={\frac {\omega }{k}}.}
To understand where this equation comes from, consider a basic cosine wave, A cos. After time t, the source has produced ωt/2π = ft oscillations. After the same time, the initial wave front has propagated away from the source through space to the distance x to fit the same number of oscillations, kx = ωt. Thus the propagation velocity v is v = x/t = ω/k.