Wavenumber

The wavenumber of a wave is its spatial frequency. It can be seen as the number of peaks (or valleys) the wave has per unit distance. It is the spatial equivalent of temporal frequency. It can be given in two different forms:

• the ordinary wavenumber is measured in $\text{cycles}/\text{m}$ (or other unit of distance) and is denoted $\tilde{\nu}$ or $h$;
• the angular wavenumber is measured in $\text{rad}/\text{m}$ (or other unit of distance) and is denoted $k$. This is the form that is always used in physics.

The two are related by $k=\tilde{\nu}/2\pi$. It is typical in physics to always refer to angular wavenumber, even without specifically mentioning "angular". They are related to the wavelength by $\lambda=1/\tilde{\nu}$ and $\lambda=2\pi/k$.

For waves in more than one dimension, the wavevector $\mathbf{k}$ is a vector that describes the direction of propagation of the wave. The modulo of the wavevector is the wavenumber, $\lvert \mathbf{k} \rvert=k$.