# 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 ${\displaystyle {\frac {\kappa }{2\pi }}}$, that is, wavenumber k is to ${\displaystyle \kappa }$ as frequency f is to angular frequency ${\displaystyle \omega }$. (Some authors define ${\displaystyle \kappa }$ 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 ${\displaystyle \lambda _{a}}$ along the spread direction:

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

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

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

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.