Editing Speed of light (section)

=== Cavity resonance ===
[[File:Waves in Box.svg|thumb|right|Electromagnetic [[standing waves]] in a cavity|alt=A box with three waves in it; there are one and a half wavelength of the top wave, one of the middle one, and a half of the bottom one.]]

Another way to measure the speed of light is to independently measure the frequency ''f'' and wavelength ''λ'' of an electromagnetic wave in vacuum. The value of ''c'' can then be found by using the relation ''c''&nbsp;=&nbsp;''fλ''. One option is to measure the resonance frequency of a [[cavity resonator]]. If the dimensions of the resonance cavity are also known, these can be used to determine the wavelength of the wave. In 1946, [[Louis Essen]] and A.C. Gordon-Smith established the frequency for a variety of [[normal mode]]s of microwaves of a [[microwave cavity]] of precisely known dimensions. The dimensions were established to an accuracy of about ±0.8&nbsp;μm using gauges calibrated by interferometry.<ref name="Essen1948"/> As the wavelength of the modes was known from the geometry of the cavity and from [[electromagnetic theory]], knowledge of the associated frequencies enabled a calculation of the speed of light.<ref name="Essen1948">
{{Cite journal
 |last1=Essen |first1=L.
 |last2=Gordon-Smith |first2=A. C.
 |year=1948
 |title=The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator
 |journal=[[Proceedings of the Royal Society of London A]]
 |volume=194 |issue=1038 |pages=348–361
 |doi=10.1098/rspa.1948.0085
 |bibcode=1948RSPSA.194..348E
 |jstor=98293
 |doi-access=free
}}</ref><ref>
{{Cite journal
 |last=Essen |first=L.
 |year=1947
 |title=Velocity of Electromagnetic Waves
 |journal=Nature
 |volume=159 |issue=4044 |pages=611–612
 |doi=10.1038/159611a0
 |bibcode=1947Natur.159..611E
 |s2cid=4101717
}}</ref>

The Essen–Gordon-Smith result, {{val|299792|9|u=km/s}}, was substantially more precise than those found by optical techniques.<ref name="Essen1948" /> By 1950, repeated measurements by Essen established a result of {{val|299792.5|3.0|u=km/s}}.<ref name="Essen1950">
{{Cite journal
 |last=Essen |first=L.
 |year=1950
 |title=The Velocity of Propagation of Electromagnetic Waves Derived from the Resonant Frequencies of a Cylindrical Cavity Resonator
 |journal=[[Proceedings of the Royal Society of London A]]
 |volume=204 |issue=1077 |pages=260–277
 |doi=10.1098/rspa.1950.0172
 |bibcode=1950RSPSA.204..260E
 |jstor=98433
 |s2cid=121261770
}}</ref>

A household demonstration of this technique is possible, using a [[microwave oven]] and food such as marshmallows or margarine: if the turntable is removed so that the food does not move, it will cook the fastest at the [[antinode]]s (the points at which the wave amplitude is the greatest), where it will begin to melt. The distance between two such spots is half the wavelength of the microwaves; by measuring this distance and multiplying the wavelength by the microwave frequency (usually displayed on the back of the oven, typically 2450&nbsp;MHz), the value of ''c'' can be calculated, "often with less than 5% error".<ref>
{{Cite journal
 |last = Stauffer | first = R. H.
 |date=April 1997
 |title = Finding the Speed of Light with Marshmallows
 |journal = [[The Physics Teacher]]
 |volume = 35
 |issue = 4 
 |page = 231
 |url = https://www.physics.umd.edu/icpe/newsletters/n34/marshmal.htm
 |access-date = 15 February 2010
 |bibcode = 1997PhTea..35..231S |doi = 10.1119/1.2344657
}}</ref><ref>
{{Cite web
 |url =http://www.bbc.co.uk/norfolk/features/ba_festival/bafestival_speedoflight_experiment_feature.shtml
 |title = BBC Look East at the speed of light
 |work = BBC Norfolk website
 |access-date = 15 February 2010
}}</ref>