Editing Standing wave (section)

== Examples ==
One easy example to understand standing waves is two people shaking either end of a [[jump rope]].  If they shake in sync the rope can form a regular pattern of waves oscillating up and down, with stationary points along the rope where the rope is almost still (nodes) and points where the arc of the rope is maximum (antinodes).

=== Acoustic resonance ===
{{Main|Acoustic resonance}}

[[File:Rotatingsaturnhexagon gif.ogv|frame|right|[[Saturn's hexagon|The hexagonal cloud feature]] at the north pole of Saturn was initially thought to be standing [[Rossby wave]]s.<ref>[http://pubs.giss.nasa.gov/docs/1990/1990_Allison_etal.pdf A Wave Dynamical Interpretation of Saturn's Polar Region] {{webarchive|url=https://web.archive.org/web/20111021145109/http://pubs.giss.nasa.gov/docs/1990/1990_Allison_etal.pdf |date=2011-10-21 }}, M. Allison, D. A. Godfrey, R. F. Beebe, Science vol. 247, pg. 1061 (1990)</ref> However, this explanation has recently been disputed.<ref>{{cite journal | doi = 10.1016/j.icarus.2009.10.022 | bibcode=2010Icar..206..755B | volume=206 | issue=2 | title=A laboratory model of Saturn's North Polar Hexagon | year=2010 | journal=Icarus | pages=755–763 | last1 = Barbosa Aguiar | first1 = Ana C.}}</ref>]]
Standing waves are also observed in physical media such as strings and columns of air. Any waves traveling along the medium will reflect back when they reach the end. This effect is most noticeable in musical instruments where, at various multiples of a [[vibrating string]] or [[air column]]'s [[natural frequency]], a standing wave is created, allowing [[harmonics]] to be identified. Nodes occur at fixed ends and anti-nodes at open ends. If fixed at only one end, only odd-numbered harmonics are available. At the open end of a pipe the anti-node will not be exactly at the end as it is altered by its contact with the air and so [[end correction]] is used to place it exactly. The density of a string will affect the frequency at which harmonics will be produced; the greater the density the lower the frequency needs to be to produce a standing wave of the same harmonic.

=== Visible light ===
Standing waves are also observed in optical media such as [[Waveguide (optics)|optical waveguides]] and [[optical cavity|optical cavities]]. [[Laser]]s use optical cavities in the form of a pair of facing mirrors, which constitute a [[Fabry–Pérot interferometer]]. The [[Active laser medium|gain medium]] in the cavity (such as a [[crystal]]) emits light [[Coherence (physics)|coherently]], exciting standing waves of light in the cavity.<ref>{{cite book |first1=Rayf |last1=Shiell |first2=Iain |last2=McNab |date=2024 |title= Pedrottis' Introduction to Optics |publisher=[[Cambridge University Press]] |edition=4 |isbn= 9781316518625}}</ref> The wavelength of light is very short (in the range of [[nanometer]]s, 10<sup>−9</sup> m) so the standing waves are microscopic in size. One use for standing light waves is to measure small distances, using [[optical flat]]s.

=== X-rays ===
Interference between [[X-ray]] beams can form an [[X-ray standing wave]] (XSW) field.<ref name="batterman_1964">{{cite journal | doi = 10.1103/RevModPhys.36.681 | bibcode=1964RvMP...36..681B | volume=36 | issue=3 | title=Dynamical Diffraction of X Rays by Perfect Crystals | year=1964 | journal=Reviews of Modern Physics | pages=681–717 | last1 = Batterman | first1 = Boris W. | last2 = Cole | first2 = Henderson}}</ref> Because of the short wavelength of X-rays (less than 1 nanometer), this phenomenon can be exploited for measuring atomic-scale events at material [[Surface science|surfaces]]. The XSW is generated in the region where an X-ray beam interferes with a [[Bragg diffraction|diffracted]] beam from a nearly perfect [[single crystal]] surface or a reflection from an [[X-ray reflectivity|X-ray mirror]]. By tuning the crystal geometry or X-ray wavelength, the XSW can be translated in space, causing a shift in the [[X-ray fluorescence]] or [[photoelectron]] yield from the atoms near the surface. This shift can be analyzed to pinpoint the location of a particular atomic species relative to the underlying [[crystal structure]] or mirror surface. The XSW method has been used to clarify the atomic-scale details of [[Semiconductor doping|dopants]] in semiconductors,<ref>{{cite journal | doi = 10.1103/PhysRevLett.22.703 | bibcode=1969PhRvL..22..703B | volume=22 | issue=14 | title=Detection of Foreign Atom Sites by Their X-Ray Fluorescence Scattering | year=1969 | journal=Physical Review Letters | pages=703–705 | last1 = Batterman | first1 = Boris W.}}</ref> atomic and molecular [[adsorption]] on surfaces,<ref>{{cite journal | doi = 10.1103/PhysRevLett.49.560 | bibcode=1982PhRvL..49..560G | volume=49 | issue=8 | title=Solution to the Surface Registration Problem Using X-Ray Standing Waves | year=1982 | journal=Physical Review Letters | pages=560–563 | last1 = Golovchenko | first1 = J. A. | last2 = Patel | first2 = J. R. | last3 = Kaplan | first3 = D. R. | last4 = Cowan | first4 = P. L. |author5-link=Michael Bedzyk | last5 = Bedzyk | first5 = M. J.| url=https://dash.harvard.edu/bitstream/handle/1/29407052/SolutionToTheSurfaceRegistrationProblem.pdf?sequence=1 }}</ref> and chemical transformations involved in [[Heterogeneous catalysis|catalysis]].<ref>{{cite journal | last1 = Feng | first1 = Z. | last2 = Kim | first2 = C.-Y. | last3 = Elam | first3 = J.W. | last4 = Ma | first4 = Q. | last5 = Zhang | first5 = Z. | last6 = Bedzyk | first6 = M.J. | year = 2009 | title = Direct Atomic-Scale Observation of Redox-Induced Cation Dynamics in an Oxide-Supported Monolayer Catalyst: WO<sub>''x''</sub>/α-Fe<sub>2</sub>O<sub>3</sub>(0001) | journal = J. Am. Chem. Soc. | volume = 131 | issue = 51| pages = 18200–18201 | doi = 10.1021/ja906816y | pmid = 20028144 }}</ref>

=== Mechanical waves ===
Standing waves can be mechanically induced into a solid medium using resonance.  One easy to understand example is two people shaking either end of a jump rope.  If they shake in sync, the rope will form a regular pattern with nodes and antinodes and appear to be stationary, hence the name standing wave.  Similarly a cantilever beam can have a standing wave imposed on it by applying a base excitation. In this case the free end moves the greatest distance laterally compared to any location along the beam.  Such a device can be used as a [[sensor]] to track changes in [[natural frequency|frequency]] or [[phase shift|phase]] of the resonance of the fiber. One application is as a measurement device for [[dimensional metrology]].<ref>{{Cite journal | doi=10.1063/1.2052027|title = Development of a virtual probe tip with an application to high aspect ratio microscale features| journal=Review of Scientific Instruments| volume=76| issue=9| pages=095112–095112–8|year = 2005|last1 = Bauza|first1 = Marcin B.| last2=Hocken| first2=Robert J.| last3=Smith| first3=Stuart T.| last4=Woody| first4=Shane C.| bibcode=2005RScI...76i5112B}}</ref><ref>{{cite web|url=http://www.insitutec.com|title=Precision Engineering and Manufacturing Solutions – IST Precision|website=www.insitutec.com|access-date=28 April 2018|url-status=live|archive-url=https://web.archive.org/web/20160731063517/http://www.insitutec.com/|archive-date=31 July 2016}}</ref>

=== Seismic waves ===
Standing surface waves on the Earth are observed as [[seismic wave#Normal modes|free oscillations of the Earth]].

=== Faraday waves ===
The [[Faraday wave]] is a non-linear standing wave at the air-liquid interface induced by hydrodynamic instability. It can be used as a liquid-based template to assemble microscale materials.<ref>{{cite journal | doi = 10.1002/adma.201402079 | pmid=24956442 | volume=26 | issue=34 | title=Microscale Assembly Directed by Liquid-Based Template | year=2014 | journal=Advanced Materials | pages=5936–5941 | last1 = Chen | first1 = Pu| pmc=4159433 | bibcode=2014AdM....26.5936C }}</ref>

=== Seiches ===
A [[seiche]] is an example of a standing wave in an enclosed body of water. It is characterised by the oscillatory behaviour of the water level at either end of the body and typically has a nodal point near the middle of the body where very little change in water level is observed. It should be distinguished from a simple [[storm surge]] where no oscillation is present. In sizeable lakes, the period of such oscillations may be between minutes and hours, for example [[Lake Geneva]]'s longitudinal period is 73 minutes and its transversal seiche has a period of around 10 minutes,<ref>{{Citation|last=Lemmin|first=Ulrich|chapter=Surface Seiches|date=2012|encyclopedia=Encyclopedia of Lakes and Reservoirs|pages=751–753|editor-last=Bengtsson|editor-first=Lars|publisher=Springer Netherlands|language=en|doi=10.1007/978-1-4020-4410-6_226|isbn=978-1-4020-4410-6|editor2-last=Herschy|editor2-first=Reginald W.|editor3-last=Fairbridge|editor3-first=Rhodes W.|series=Encyclopedia of Earth Sciences Series}}</ref> while Lake Huron can be seen to have resonances with periods between 1 and 2 hours.<ref>{{cite web|url=http://www.glerl.noaa.gov/seagrant/glwlphotos/Seiche/13July1995/13July1995Storm.html|title=Lake Huron Storm Surge July 13, 1995 |publisher=NOAA |access-date=2023-01-01 |archive-date=2008-09-16 |archive-url=https://web.archive.org/web/20080916230039/http://www.glerl.noaa.gov/seagrant/glwlphotos/Seiche/13July1995/13July1995Storm.html |url-status=dead}}</ref> See [[seiche#Lake seiches|Lake seiches]].<ref name="2000-02--umn">{{cite web |first=Ben |last=Korgen |url=http://www.seagrant.umn.edu/newsletter/2000/02/bonanza_for_lake_superior_seiches_do_more_than_move_water.html |title=Bonanza for Lake Superior: Seiches Do More Than Move Water |publisher=[[University of Minnesota Duluth]] |website=seagrant.umn.edu |date=February 2000 |archive-url=https://web.archive.org/web/20071227044356/http://www.seagrant.umn.edu/newsletter/2000/02/bonanza_for_lake_superior_seiches_do_more_than_move_water.html |archive-date=2007-12-27 |url-status=dead}}
</ref><ref>{{cite web |url=https://www.soest.hawaii.edu/GG/ASK/seiche.html |title=Seiche |website=www.soest.hawaii.edu |access-date=2023-01-01 |archive-date=2019-01-26 |archive-url=https://web.archive.org/web/20190126040622/http://www.soest.hawaii.edu/GG/ASK/seiche.html |url-status=live}}</ref><ref>{{cite web |url=https://arstechnica.com/science/2013/06/japanese-earthquake-literally-made-waves-in-norway/ |title=Japanese earthquake literally made waves in Norway |first=Scott K. |last=Johnson |date=30 June 2013 |website=Ars Technica |access-date=2023-01-01 |archive-date=30 July 2022 |archive-url=https://web.archive.org/web/20220730162534/https://arstechnica.com/science/2013/06/japanese-earthquake-literally-made-waves-in-norway/ |url-status=live}}</ref>