Wavelength - Knowlpedia

For a plane wave with nonzero angular wavevector $k$ , its wavelength in the direction $k/|k|$ is

\lambda=\frac{2\pi}{|k|}.

Advancing by this distance changes $k\cdot x$ by $2\pi$ , leaving the exponential unchanged. The wavenumber is the reciprocal length with the angular factor included.

Variable phase

Where $\nabla\Psi\ne0$ , $2\pi/|\nabla\Psi|$ is a local wavelength from linearizing the phase. For a nonlinear phase it need not be an exact distance between successive crests over a finite interval. If the Fourier convention uses cycles per length $|\xi|$ , the corresponding wavelength is $1/|\xi|$ .