View source for Wavenumber–frequency diagram

{{Short description|Diagrams representing dispersion in atmospheric waves}}
A '''wavenumber–frequency diagram''' is a [[plot (graphics)|plot]] displaying the relationship between the [[wavenumber]] (spatial frequency) and the [[frequency]] (temporal frequency) of certain phenomena. Usually frequencies are placed on the vertical axis, while wavenumbers are placed on the horizontal axis.<ref name="fleagle">{{cite book| author1 = R.G. Fleagle | author2= J.A. Businger |author-link2=Joost Businger | title = An introduction to atmospheric physics| url = https://books.google.com/books?id=u7YItwAACAAJ| year = 1990| publisher = [[Academic Press]]| isbn = 978-0-12-260355-6| pages = 183–198 }}</ref><ref name="pedlosky">{{cite book| author = J. Pedlosky| title = Geophysical fluid dynamics| url = https://books.google.com/books?id=FXs-uRSDBFYC| edition = 2nd| year = 1998| publisher = [[Springer (publisher)|Springer]]| isbn = 978-0-387-96387-7| pages = 676–678 }}</ref>

In the [[atmospheric science]]s, these plots are a common way to visualize [[atmospheric wave]]s.

In the [[geoscience]]s, especially seismic data analysis, these plots also called ''f''–''k'' plot, in which energy density within a given time interval is contoured on a frequency-versus-wavenumber basis.  They are used to examine the direction and apparent velocity of seismic waves and in [[velocity filter]] design.

==Origins==

In general, the relationship between [[wavelength]] <math>\lambda</math>, [[frequency]] <math>\nu</math>, and the [[phase velocity]] <math>v_{p}</math> of a sinusoidal wave is:

:<math>v_\text{p} = \lambda \nu </math>

Using the [[wavenumber]] (<math>k=2\pi/\lambda</math>) and [[angular frequency]] (<math>\omega=2\pi\nu</math>) notation, the previous equation can be rewritten as

:<math>v_\text{p} = \frac{\omega}{k}</math>

On the other hand, the [[group velocity]] is equal to the [[slope (mathematics)|slope]] of the wavenumber–frequency diagram:

:<math>v_\text{g} = \frac{\partial\omega}{\partial k} </math>

Analyzing such relationships in detail often yields information on the [[physical property|physical properties]] of the [[transmission medium|medium]], such as [[density]], [[wikt:composition|composition]], etc.

==See also==

* [[Dispersion relation]]

==References==

{{reflist}}

{{DEFAULTSORT:Wavenumber-frequency diagram}}
[[Category:Wave mechanics]]
[[Category:Diagrams]]