Slovník pojmů

Wave vector, wave-number

In a lossless medium, wave number specifies the phase change [radians] of a propagating wave on the one-meter long trajectory in a given direction. Therefore, wave number is given in radians per meter. Wave number is associated with the wavelength k = 2π/λ and with the phase velocity of propagation k = ω/v_f. If wave-number k is associated with the direction of wave propagation, then both the wavelength and the phase velocity are associated with the direction of wave propagation. If another direction is considered, the above-given relations stay valid, but all the three quantities are associated with the given direction. In the direction of propagation, wave number is of the highest value, wavelength and phase velocity are of the lowest one.

In a lossy medium, wave number is complex. Its real part k' gives the phase change of wave on the one-meter long trajectory as already explained. Imaginary part (when sign is changed) k'' gives the specific wave attenuation. The wave amplitude decreases on the trajectory of the length r for

where k'' is imaginary part of wave-number in the direction r.

Magnitude of the wave vector is identical with the magnitude of wave number. Direction of the wave vector is identical with the direction of wave propagation. If projections of wave vector to various directions are computed, then wavelength and phase velocity for those directions can be determined.