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In physics, a wave vector (also spelled wavevector) is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important. Its magnitude is either the wavenumber or angular wavenumber of the wave (inversely proportional to the wavelength), and its direction is ordinarily the direction of wave propagation (but not always, see below).

In the context of special relativity the wave vector can also be defined as a four-vector.

## Definitions

Wavelength of a sine wave, λ, can be measured between any two consecutive points with the same phase, such as between adjacent crests, or troughs, or adjacent zero crossings with the same direction of transit, as shown.

There are two common definitions of wave vector, which differ by a factor of 2π in their magnitudes. One definition is preferred in physics and related fields, while the other definition is preferred in crystallography and related fields.[1] For this article, they will be called the "physics definition" and the "crystallography definition", respectively.

In both definitions below, the magnitude of the wave vector is represented by ${\displaystyle k}$; the direction of the wave vector is discussed in the following section.

### Physics definition

A perfect one-dimensional traveling wave follows the equation:

${\displaystyle \psi (x,t)=A\cos(kx-\omega t+\varphi )}$

where:

• x is position,
• t is time,
• ${\displaystyle \psi }$ (a function of x and t) is the disturbance describing the wave (for example, for an ocean wave, ${\displaystyle \psi }$${\displaystyle k}$; the direction of the wave vector is discussed in the following section.

A perfect one-dimensional traveling wave follows the equation: