Editing Wave vector (section)

==Definition==
{{See also|Traveling wave}}
[[File:Sine wavelength.svg|thumb|right|Wavelength of a [[sine wave]], {{mvar|λ}}, can be measured between any two consecutive points with the same [[phase (waves)|phase]], such as between adjacent crests, or troughs, or adjacent [[zero crossing]]s with the same direction of transit, as shown.]] 

The terms ''wave vector'' and ''angular wave vector'' have distinct meanings.  Here, the wave vector is denoted by <math> \tilde{\boldsymbol{\nu}}  </math> and the wavenumber by <math>\tilde{\nu} = \left| \tilde{\boldsymbol{\nu}} \right|</math>.  The angular wave vector is denoted by {{math|'''k'''}} and the angular wavenumber by {{math|1=''k'' = {{abs|'''k'''}}}}.  These are related by <math>\mathbf k = 2\pi \tilde{\boldsymbol{\nu}}</math>.

A sinusoidal [[traveling wave]] follows the equation
:<math>\psi(\mathbf{r},t) = A \cos (\mathbf{k} \cdot \mathbf{r} - \omega t + \varphi) ,</math>
where:
* {{math|'''r'''}} is position,
* {{mvar|t}} is time,
* {{mvar|&psi;}} is a function of {{math|'''r'''}} and {{mvar|t}} describing the disturbance describing the wave (for example, for an [[ocean wave]], {{mvar|&psi;}} would be the excess height of the water, or for a [[sound wave]], {{mvar|&psi;}} would be the excess [[air pressure]]).
* {{mvar|A}} is the [[amplitude]] of the wave (the peak magnitude of the oscillation),
* {{mvar|&phi;}} is a [[phase offset]],
* {{mvar|&omega;}} is the (temporal) [[angular frequency]] of the wave, describing how many radians it traverses per unit of time, and related to the [[Period (physics)|period]] {{mvar|T}} by the equation <math>\omega= \tfrac{2\pi}{T},</math>
* {{math|'''k'''}} is the angular wave vector of the wave, describing how many radians it traverses per unit of distance, and related to the [[wavelength]] by the equation <math>|\mathbf{k}|= \tfrac{2\pi}{\lambda}.</math>

The equivalent equation using the wave vector and frequency is<ref>{{cite book |url=https://books.google.com/books?id=xjIGV_hPiysC&pg=PA259|title= Modern Crystallography| page=259 |isbn=978-3-540-56558-1 |last=Vaĭnshteĭn|first=Boris Konstantinovich |year=1994}}</ref>
:<math> \psi \left( \mathbf{r}, t \right) = A \cos \left(2\pi \left( \tilde{\boldsymbol{\nu}} \cdot {\mathbf r} - f t \right) + \varphi \right) ,</math>
where:
* <math> f </math> is the frequency
* <math> \tilde{\boldsymbol{\nu}}  </math> is the wave vector