Doppler effect: Difference between revisions

]]The '''Doppler effect''' (also '''Doppler shift''') is the change in the [[frequency]] of a [[wave]] in relation to an observer who is moving relative to the source of the wave.<ref>{{cite book | author=United States. Navy Department | title=Principles and Applications of Underwater Sound, Originally Issued as Summary Technical Report of Division 6, NDRC, Vol. 7, 1946, Reprinted...1968 | year=1969 | url=https://books.google.com/books?id=gjYGC_sc6lcC&pg=PA194 | access-date=2021-03-29 | page=194}}</ref><ref>{{cite book | last=Joseph | first=A. | title=Measuring Ocean Currents: Tools, Technologies, and Data | publisher=Elsevier Science | year=2013 | isbn=978-0-12-391428-6 | url=https://books.google.com/books?id=FRVaNZEQCa4C&pg=PA164 | access-date=2021-03-30 | page=164}}</ref><ref name="Giordano">{{cite book

  | isbn  = 978-0534424718

  }}</ref> The ''Doppler effect'' is named after the physicist [[Christian Doppler]], who described the phenomenon in 1842. A common example of Doppler shift is the change of [[pitch (music)|pitch]] heard when a [[vehicle]] sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.<ref name="Possel">{{cite web

   | access-date = September 4, 2017}}</ref> Hence, from the observer's perspective, the time between cycles is reduced, meaning the frequency is increased. Conversely, if the source of the sound wave is moving away from the observer, each cycle of the wave is emitted from a position farther from the observer than the previous cycle, so the arrival time between successive cycles is increased, thus reducing the frequency.

For waves that propagate in a [[transmission medium|medium]], such as [[sound]] waves, the [[velocity]] of the observer and of the source are relative to the medium in which the waves are transmitted.<ref name="Giordano" /> The total Doppler effect in such cases may therefore result from motion of the source, motion of the observer, motion of the medium, or any combination thereof. For waves propagating in [[vacuum]], as is possible for [[electromagnetic waves]] or [[gravitational wave]]s, only the difference in velocity between the observer and the source needs to be considered.

Doppler first proposed this effect in 1842 in his treatise "''[[Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels]]''" (On the coloured light of the [[binary stars]] and some other stars of the heavens).<ref name="AlecEden">Alec Eden ''The search for Christian Doppler'', Springer-Verlag, Wien 1992. Contains a facsimile edition with an [[English language|English]] translation.</ref> The hypothesis was tested for sound waves by [[C. H. D. Buys Ballot|Buys Ballot]] in 1845.<ref group=p>{{cite journal | last=Buys Ballot | title=Akustische Versuche auf der Niederländischen Eisenbahn, nebst gelegentlichen Bemerkungen zur Theorie des Hrn. Prof. Doppler (in German) | journal=Annalen der Physik und Chemie |year=1845 | volume=142 | issue=11 | pages=321–351 | doi=10.1002/andp.18451421102|bibcode = 1845AnP...142..321B | url=https://zenodo.org/record/1423606 }}</ref> He confirmed that the sound's [[Pitch (music)#Pitch and frequency|pitch]] was higher than the emitted frequency when the sound source approached him, and lower than the emitted frequency when the sound source receded from him. [[Hippolyte Fizeau]] discovered independently the same phenomenon on [[electromagnetic wave]]s in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau" but that name was not adopted by the rest of the world as Fizeau's discovery was six years after Doppler's proposal).<ref group=p>Fizeau: "Acoustique et optique". ''Lecture, [[Philomatic Society|Société Philomathique]] de Paris'', 29 December 1848. According to Becker(pg. 109), this was never published, but recounted by M. Moigno(1850): "Répertoire d'optique moderne" (in French), vol 3. pp 1165–1203 and later in full by Fizeau, "Des effets du mouvement sur le ton des vibrations sonores et sur la longeur d'onde des rayons de lumière"; [Paris, 1870]. ''Annales de Chimie et de Physique'', 19, 211–221.</ref><ref>Becker (2011). Barbara J. Becker, ''Unravelling Starlight: William and Margaret Huggins and the Rise of the New Astronomy'', illustrated Edition, [[Cambridge University Press]], 2011; {{ISBN|110700229X}}, 9781107002296.</ref> In Britain, [[John Scott Russell]] made an experimental study of the Doppler effect (1848).<ref group=p>{{cite journal | last=Scott Russell | first=John | url=http://www.ma.hw.ac.uk/~chris/doppler.html | title=On certain effects produced on sound by the rapid motion of the observer | journal=Report of the Eighteenth Meeting of the British Association for the Advancement of Science |year=1848 | volume=18 | issue=7 | pages=37–38 | access-date=2008-07-08 }}</ref>

In [[classical physics]], where the speeds of the source and the receiver relative to the medium are lower than the speed of waves in the medium, the relationship between observed frequency <math>f</math> and emitted frequency <math>f_\text{0}</math> is given by:<ref name=halliday>{{cite book |last1=Walker |first1=Jearl |last2=Resnick |first2=Robert |authorlink2=Robert Resnick |last3=Halliday |first3=David |authorlink3=David Halliday (physicist) |title=Halliday & Resnick Fundamentals of Physics |date=2007 |publisher=Wiley |isbn=9781118233764 |oclc=436030602 |edition=8th}}</ref>

<math display="block">f = \left( \frac{c \pm v_\text{r}}{c \mp v_\text{s}} \right) f_0 </math>

* <math>c </math> is the propagation speed of waves in the medium;

* <math>v_\text{r} </math> is the speed of the receiver relative to the medium. In the formula, <math>v_\text{r} </math> is added to <math>c</math> if the receiver is moving towards the source, subtracted if the receiver is moving away from the source;

* <math>v_\text{s} </math> is the speed of the source relative to the medium. <math>v_\text{s} </math> is subtracted from <math>c</math> if the source is moving towards the receiver, added if the source is moving away from the receiver.

 

<math display="block">\frac{f}{v_{wr}} = \frac{f_0}{v_{ws}} = \frac{1}{\lambda}</math>

* <math>v_{wr}</math> is the wave's speed relative to the receiver;

* <math>v_{ws}</math> is the wave's speed relative to the source;

* <math>\lambda</math> is the wavelength.

[[John William Strutt, 3rd Baron Rayleigh|Lord Rayleigh]] predicted the following effect in his classic book on sound: if the observer were moving from the (stationary) source at twice the speed of sound, a musical piece ''previously'' emitted by that source would be heard in correct tempo and pitch, but as if played ''backwards''.<ref>{{cite book|last=Strutt (Lord Rayleigh)| first=John William|title=The Theory of Sound|editor=MacMillan & Co|date=1896| edition=2|volume=2| pages=154| url=https://archive.org/stream/theorysound02raylgoog#page/n176/mode/2up|publisher=Macmillan}}</ref>

The relationship between the [[Redshift#Expansion of space|expansion of the universe]] and the Doppler effect is not simple matter of the source moving away from the observer.<ref name="Peacock">{{cite arXiv|eprint=0809.4573|class=astro-ph|author=JA Peacock|title=A diatribe on expanding space|date=2008}}</ref><ref name="Hogg">{{cite journal |author=Bunn |first1=E. F. |last2=Hogg |first2=D. W. |year=2009 |title=The kinematic origin of the cosmological redshift |journal=American Journal of Physics |volume=77 |issue=8 |pages=688–694 |arxiv=0808.1081 |bibcode=2009AmJPh..77..688B |doi=10.1119/1.3129103 |s2cid=1365918}}</ref> In cosmology, the redshift of expansion is considered separate from redshifts due to gravity or Doppler motion.<ref>{{cite book |last=Harrison |first=Edward Robert  |date= 2000 |title=Cosmology: The Science of the Universe |publisher=Cambridge University Press |edition=2nd |url=https://books.google.com/books?id=-8PJbcA2lLoC&pg=PA315|pages=306''ff'' |isbn=978-0-521-66148-5 }}</ref>

The Doppler effect is used in some types of [[radar]], to measure the velocity of detected objects. A radar beam is fired at a moving target – e.g. a motor car, as police use radar to detect speeding motorists – as it approaches or recedes from the radar source. Each successive radar wave has to travel farther to reach the car, before being reflected and re-detected near the source. As each wave has to move farther, the gap between each wave increases, increasing the wavelength. In some situations, the radar beam is fired at the moving car as it approaches, in which case each successive wave travels a lesser distance, decreasing the wavelength. In either situation, calculations from the Doppler effect accurately determine the car's speed. Moreover, the [[proximity fuze]], developed during [[World War II]], relies upon Doppler radar to detonate explosives at the correct time, height, distance, etc.{{Citation needed|date=December 2009}}

Because the Doppler shift affects the wave incident upon the target as well as the wave reflected back to the radar, the change in frequency observed by a radar due to a target moving at relative speed <math>\Delta v</math> is twice that from the same target emitting a wave:<ref>{{cite web|url=http://www.radartutorial.eu/11.coherent/co06.en.html| title=Radar Basics|first=Dipl.-Ing. (FH) Christian|last=Wolff|website=radartutorial.eu|access-date=14 April 2018}}</ref>

<math display="block">\Delta f=\frac{2\Delta v}{c}f_0.</math>

Doppler also needs to be compensated in [[satellite communication]].

Fast moving satellites can have a Doppler shift of dozens of kilohertz relative to a ground station. The speed, thus magnitude of Doppler effect, changes due to earth curvature. Dynamic Doppler compensation, where the frequency of a signal is changed progressively during transmission, is used so the satellite receives a constant frequency signal.<ref>{{Cite book|last=Qingchong |first=Liu |title=MILCOM 1999. IEEE Military Communications. Conference Proceedings (Cat. No.99CH36341) |chapter=Doppler measurement and compensation in mobile satellite communications systems |volume=1 |year=1999 |pages=316–320 |doi=10.1109/milcom.1999.822695|isbn=978-0-7803-5538-5 |citeseerx=10.1.1.674.3987 |s2cid=12586746 }}</ref> After realizing that the Doppler shift had not been considered before launch of the [[Huygens (spacecraft)#Critical design flaw partially resolved|Huygens probe]] of the 2005 [[Cassini–Huygens]] mission, the probe trajectory was altered to approach [[Titan (moon)|Titan]] in such a way that its transmissions traveled perpendicular to its direction of motion relative to Cassini, greatly reducing the Doppler shift.<ref name="TitanCalling">{{cite news|title=Titan Calling |first=James |last=Oberg |publisher=[[IEEE Spectrum]] |url=https://spectrum.ieee.org/aerospace/space-flight/titan-calling |archive-url=https://archive.today/20120914080503/http://spectrum.ieee.org/aerospace/space-flight/titan-calling |url-status=dead |archive-date=September 14, 2012 |date=October 4, 2004 }} (offline as of 2006-10-14, see [https://web.archive.org/web/20041010192803/http://www.spectrum.ieee.org/WEBONLY/publicfeature/oct04/1004titan.html Internet Archive version])</ref>

Since 1968 scientists such as [[Victor Veselago]] have speculated about the possibility of an inverse Doppler effect. The size of the Doppler shift depends on the [[refractive index]] of the medium a wave is traveling through. Some materials are capable of [[negative refraction]], which should lead to a Doppler shift that works in a direction opposite that of a conventional Doppler shift.<ref>{{cite web|url=https://physicsworld.com/a/doppler-shift-is-seen-in-reverse/|title=Doppler shift is seen in reverse|date=10 March 2011|website=Physics World}}</ref> The first experiment that detected this effect was conducted by Nigel Seddon and Trevor Bearpark in [[Bristol]], [[United Kingdom]] in 2003.<ref group=p>{{cite journal |last1=Kozyrev |first1=Alexander B. |last2=van der Weide |first2=Daniel W. |title=Explanation of the Inverse Doppler Effect Observed in Nonlinear Transmission Lines |journal=Physical Review Letters |volume=94 |issue=20 |pages=203902 |year=2005 |pmid=16090248 |doi=10.1103/PhysRevLett.94.203902 |bibcode=2005PhRvL..94t3902K}}</ref> Later, the inverse Doppler effect was observed in some inhomogeneous materials, and predicted inside a [[Vavilov–Cherenkov effect|Vavilov–Cherenkov]] cone.<ref>{{Cite journal| last1=Shi|first1=Xihang | last2=Lin|first2=Xiao| last3=Kaminer|first3=Ido |last4=Gao|first4=Fei |last5=Yang|first5=Zhaoju|last6=Joannopoulos|first6=John D.|last7=Soljačić|first7=Marin| last8=Zhang |first8=Baile |date=October 2018|title=Superlight inverse Doppler effect|journal=Nature Physics|volume=14|issue=10| pages=1001–1005| doi=10.1038/s41567-018-0209-6|issn=1745-2473|arxiv=1805.12427|bibcode=2018NatPh..14.1001S|s2cid=125790662}}</ref>

* [[Doppler cooling]]

* [[Fading]]

* [[Fizeau experiment]]

* [[Rayleigh fading]]

* [[Redshift]]

* [[Laser Doppler imaging]]

* [[Relativistic Doppler effect]]

* {{cite web | url = http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html | title = Doppler Effect | first = Eleni | last = Adrian | publisher = [[National Center for Supercomputing Applications|NCSA]] | date = 24 June 1995 | access-date = 2008-07-13 | archive-url = https://web.archive.org/web/20090512192731/http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html | archive-date = 12 May 2009 | url-status = dead }}