**Wave vector** A wave vector

**k** is a vector representation of a wave.

__Magnitude:__ The wave vector

**k** has magnitude indicating wavenumber.

k = |

**k**| = 2π/λ

__Direction:__ The direction of the wave vector

**k** indicates the direction of wave propagation.

__Common representation of a single wave:__ At a single point in space: ψ(t) = A cos(φ + ωt )

For a wave that is travelling along an axis z, the phase at any point along the axis will be shifted from what it is at the origin. This is accounted for by an additional phase offset term:

ψ(t,z) = A cos(φ + kz + ωt )

For a wave that is travelling in any particular direction:

ψ(t,

**r**) = A cos(φ +

**k**.

**r** + ωt )

A is the amplitude

ω is the angular frequency

φ is the starting phase of the wave

t is time

__Reference:__ Wave vector

http://en.wikipedia.org/wiki/Wave_vector