Editing Wavelength (section)

==== Nonuniform media ====
[[File:Local wavelength.svg|thumb|Various local wavelengths on a crest-to-crest basis in an ocean wave approaching shore<ref name=Pinet2/>]]
Wavelength can be a useful concept even if the wave is not [[periodic function|periodic]] in space. For example, in an ocean wave approaching shore, shown in the figure, the incoming wave undulates with a varying ''local'' wavelength that depends in part on the depth of the sea floor compared to the wave height. The analysis of the wave can be based upon comparison of the local wavelength with the local water depth.<ref name=Pinet2>
{{cite book |title=op. cit
 |author = Paul R Pinet
 |url = https://books.google.com/books?id=6TCm8Xy-sLUC&pg=PA242
 |page = 242
 |isbn = 978-0-7637-5993-3
 |year = 2009
 |publisher = Jones & Bartlett Learning
 }}</ref>

[[File:Cochlea wave animated.gif|right|thumb|A sinusoidal wave travelling in a nonuniform medium, with loss]]
Waves that are sinusoidal in time but propagate through a medium whose properties vary with position (an ''inhomogeneous'' medium) may propagate at a velocity that varies with position, and as a result may not be sinusoidal in space. The figure at right shows an example. As the wave slows down, the wavelength gets shorter and the amplitude increases; after a place of maximum response, the short wavelength is associated with a high loss and the wave dies out.

The analysis of [[differential equation]]s of such systems is often done approximately, using the ''[[WKB approximation|WKB method]]'' (also known as the ''Liouville–Green method''). The method integrates phase through space using a local [[wavenumber]], which can be interpreted as indicating a "local wavelength" of the solution as a function of time and space.<ref>
{{cite book
 | title = Principles of Plasma Mechanics
 | author = Bishwanath Chakraborty
 | publisher = New Age International
 | isbn = 978-81-224-1446-2
 | page = 454
 | url = https://books.google.com/books?id=_MIdEiKqdawC&q=wkb+local-wavelength&pg=PA454
 | year = 2007
 }}</ref><ref>
{{cite book
 | title = Time-frequency and time-scale methods: adaptive decompositions, uncertainty principles, and sampling
 | author1=Jeffrey A. Hogan
 | author2=Joseph D. Lakey
 | name-list-style=amp | publisher = Birkhäuser
 | year = 2005
 | isbn = 978-0-8176-4276-1
 | page = 348
 | url = https://books.google.com/books?id=YOf0SRzxz3gC&q=wkb+local-wavelength&pg=PA348
 }}</ref>
This method treats the system locally as if it were uniform with the local properties; in particular, the local wave velocity associated with a frequency is the only thing needed to estimate the corresponding local wavenumber or wavelength. In addition, the method computes a slowly changing amplitude to satisfy other constraints of the equations or of the physical system, such as for [[conservation of energy]] in the wave.