# Dictionary:Wavenumber (k)

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1. The number of waves per unit distance perpendicular to a wavefront, that is, the reciprocal of the wavelength. It equals ${\frac {\kappa }{2\pi }}$ , that is, wavenumber k is to $\kappa$ as frequency f is to angular frequency $\omega$ . (Some authors define $\kappa$ as the wavenumber.)

2. Spatial frequency, the number of wave cycles per unit of distance in a given direction (direction of the spread); apparent wavenumber. Specifically, the reciprocal of the apparent wavelength $\lambda _{a}$ along the spread direction:

${\frac {1}{\lambda _{a}}}={\frac {f}{V_{a}}}=k_{a}={\frac {\kappa _{a}}{2\pi }}$ ,

where f=frequency and Va is apparent velocity. If a wavefront makes the angle $\omega$ with the given direction,

$\kappa ={\frac {2\pi fsin{\theta }}{V}}$ .

where V is the actual velocity of the wavefront. A wavenumber of zero indicates a wavefront striking a line of detectors simultaneously. See f-k plot.

3. See propagation constant.