Phase velocity (redirected from Phase velocity vector)

Phase velocity

The velocity of propagation of a pure sine wave of infinite extent. In one dimension, for example, the form of the disturbance for such a wave is given by y(x, t) = A sin [2π(x/λ - t/T)]. Here x is the position at which the disturbance y(x, t) exists at time t, λ is the wavelength, T is the period which is related to the wave frequency by T = 1/f, and A is the disturbance amplitude. The argument of the sine function is called the phase. The phase velocity is the speed with which a point of constant phase can be said to move. Thus x/λ - ft = constant, so the phase velocity v_p is given by dx/dt = v_p = λf. This is the basic relationship connecting phase velocity, wavelength, and frequency. See Phase (periodic phenomena), Sine wave, Wave motion

The phase velocity for waves in a medium is determined in part by intrinsic properties of the medium. For all mechanical waves in elastic media, the square of the phase velocity is proportional to the ratio of the appropriate elastic property of the medium to the appropriate inertia property. The phase velocity of electromagnetic waves depends upon the medium as well. In vacuum, the phase velocity c is given by c² = l/ε₀μ₀ ≈ 9 × 10¹⁶ m²/s², where ε₀ and μ₀ are respectively the permittivity and permeability of the vacuum. Phase velocity may also depend upon the mode of wave propagation—in general, upon the frequency of the wave. Waves of different frequencies will travel at different speeds, resulting in a phenomenon called dispersion. See Electromagnetic radiation, Light, Wave equation