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| 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| author = R.G. Fleagle, J.A. Businger| title = An introduction to atmospheric physics| url = http://books.google.com/?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 = http://books.google.com/?id=FXs-uRSDBFYC| edition = 2nd| year = 1998| publisher = [[Springer (publisher)|Springer]]| isbn = 978-0-387-96387-7| pages = 676–678 }}</ref>
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| In the [[atmospheric science]]s, these plots are a common way to visualize [[atmospheric wave]]s.
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| 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.
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| ==Origins==
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| In general, the relationship between [[wavelength]] ''λ'', [[frequency]] ''ν'', and the [[phase velocity]] ''v''<sub>p</sub> of a sinusoidal wave is:
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| :<math>v_\text{p} = \lambda \nu </math>
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| Since the [[wavenumber]] ''k'', is the inverse of wavelength (''k'' = 1/''λ'') the previous equation can be rewritten as
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| :<math>v_\text{p} = \frac{\nu}{k}</math> | |
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| On the other hand, the [[group velocity]] is equal to the [[slope (mathematics)|slope]] of the wavenumber–frequency diagram:
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| :<math>v_\text{g} = \frac{\partial\nu}{\partial k} </math>
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| 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.
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| ==See also==
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| * [[Dispersion relation]]
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Wavenumber-frequency diagram}}
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| [[Category:Wave mechanics]]
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| [[Category:Diagrams]]
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