Editing Doppler effect (section)

==Applications==
===Sirens===
[[File:Juli 2016 - Spoedtransport, Huisarts, Brandweer, Politie en Ambulances met spoed in Rotterdam -451.webm|start=7:14|end=8:30|thumb|Sirens on passing emergency vehicles.]]
A [[siren (alarm)|siren]] on a passing [[emergency vehicle]] will start out higher than its stationary pitch, slide down as it passes, and continue lower than its stationary pitch as it recedes from the observer. Astronomer [[John Dobson (astronomer)|John Dobson]] explained the effect thus:

{{Blockquote|The reason the siren slides is because it doesn't hit you.}}

In other words, if the siren approached the observer directly, the pitch would remain constant, at a higher than stationary pitch, until the vehicle hit him, and then immediately jump to a new lower pitch. Because the vehicle passes by the observer, the radial speed does not remain constant, but instead varies as a function of the angle between his line of sight and the siren's velocity:
<math display="block">v_\text{radial} = v_\text{s}  \cos(\theta)</math>
where <math>\theta</math> is the angle between the object's forward velocity and the line of sight from the object to the observer.

===Astronomy===
{{Main|Relativistic Doppler effect}}

[[Image:Redshift.svg|thumb|upright|[[Redshift]] of [[spectral line]]s in the [[optical spectrum]] of a supercluster of distant galaxies (right), as compared to that of the Sun (left)]]

The [[Relativistic Doppler effect|Doppler effect for electromagnetic waves]] such as light is of widespread use in [[astronomy]] to measure the speed at which [[star]]s and [[galaxy|galaxies]] are approaching or receding from us, resulting in so called [[blueshift]] or [[redshift]], respectively. This may be used to detect if an apparently single star is, in reality, a close [[Binary star|binary]], to measure the rotational speed of stars and galaxies, or to [[Doppler spectroscopy|detect exoplanets]]. This effect typically happens on a very small scale; there would not be a noticeable difference in visible light to the unaided eye.<ref>{{cite web |url=http://www.astro.ucla.edu/~wright/doppler.htm|title=Doppler Shift| website=astro.ucla.edu}}</ref>
The use of the Doppler effect in astronomy depends on knowledge of precise frequencies of [[spectral line|discrete lines]] in the [[electromagnetic spectroscopy|spectra]] of stars.

Among the [[List of nearest stars|nearby stars]], the largest [[radial velocities]] with respect to the [[Sun]] are +308&nbsp;km/s ([[BD-15°4041]], also known as LHS 52, 81.7 light-years away) and −260&nbsp;km/s ([[Woolley 9722]], also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial speed means the star is receding from the Sun, negative that it is approaching.

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>

Distant galaxies also exhibit [[peculiar motion]] distinct from their cosmological recession speeds. If redshifts are used to determine distances in accordance with [[Hubble's law]], then these peculiar motions give rise to [[redshift-space distortions]].<ref>An excellent review of the topic in technical detail is given here: {{cite journal|last1=Percival|first1=Will| last2=Samushia|first2=Lado| last3=Ross|first3=Ashley|last4=Shapiro|first4=Charles|last5=Raccanelli|first5=Alvise|year= 2011 |title=Review article: Redshift-space distortions|journal=Philosophical Transactions of the Royal Society|volume=369|issue=1957|pages=5058–67| doi=10.1098/rsta.2011.0370|pmid=22084293|bibcode=2011RSPTA.369.5058P|doi-access=free}}</ref>

===Radar===
{{Main|Doppler radar}}
[[File:radar gun.jpg|thumb|U.S. Military Police using a [[radar gun]], an application of Doppler radar, to catch speeding violators.]]
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>

===Medical===
{{Main|Doppler ultrasonography}}
[[File:CarotidDoppler1.jpg|thumb|upright|Colour flow ultrasonography (Doppler) of a [[carotid artery]] – scanner and screen]]
An [[echocardiogram]] can, within certain limits, produce an accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the [[ultrasound]] beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, abnormal communications between the left and right side of the heart, leaking of blood through the valves (valvular regurgitation), and calculation of the [[cardiac output]]. [[Contrast-enhanced ultrasound]] using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.<ref>{{cite journal| last1=Davies|first1=MJ| last2=Newton|first2=JD|title=Non-invasive imaging in cardiology for the generalist|journal=British Journal of Hospital Medicine| date=2 July 2017|volume=78|issue=7|pages=392–398|doi=10.12968/hmed.2017.78.7.392|pmid=28692375}}</ref><ref>{{cite journal| last1=Appis|first1=AW|last2=Tracy|first2=MJ|last3=Feinstein|first3=SB|title=Update on the safety and efficacy of commercial ultrasound contrast agents in cardiac applications|journal=Echo Research and Practice|date=1 June 2015|volume=2|issue=2| pages=R55–62|doi=10.1530/ERP-15-0018|pmid=26693339|pmc=4676450}}</ref>

Although "Doppler" has become synonymous with "velocity measurement" in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (''when'' the received signal arrives).<ref group=p>{{Cite journal|last=Petrescu|first=Florian Ion T|year=2015|title=Improving Medical Imaging and Blood Flow Measurement by using a New Doppler Effect Relationship|url=https://www.proquest.com/openview/cec7b768b14887621e9494261e122a4c/1?pq-origsite=gscholar&cbl=1226369|journal=American Journal of Engineering and Applied Sciences|volume=8|issue=4 |pages=582–588| via=ProQuest|doi=10.3844/ajeassp.2015.582.588|doi-access=free}}</ref>

Velocity measurements of blood flow are also used in other fields of [[medical ultrasonography]], such as [[obstetric ultrasonography]] and [[neurology]]. Velocity measurement of blood flow in arteries and veins based on Doppler effect is an effective tool for diagnosis of vascular problems like [[stenosis]].<ref>{{cite book |first1=D. H. |last1=Evans |first2=W. N. |last2=McDicken |title=Doppler Ultrasound |edition=2nd |publisher=John Wiley and Sons |location=New York |date=2000 |isbn=978-0-471-97001-9 }}{{page needed|date=June 2015}}</ref>

===Flow measurement===
Instruments such as the [[laser Doppler velocimetry|laser Doppler velocimeter]] (LDV), and [[acoustic Doppler velocimetry|acoustic Doppler velocimeter]] (ADV) have been developed to measure velocities in a fluid flow. The LDV emits a light beam and the ADV emits an ultrasonic acoustic burst, and measure the Doppler shift in wavelengths of reflections from particles moving with the flow. The actual flow is computed as a function of the water velocity and phase. This technique allows non-intrusive flow measurements, at high precision and high frequency.

===Velocity profile measurement===
Developed originally for velocity measurements in medical applications (blood flow), Ultrasonic Doppler Velocimetry (UDV) can measure in real time complete velocity profile in almost any liquids containing particles in suspension such as dust, gas bubbles, emulsions. Flows can be pulsating, oscillating, laminar or turbulent, stationary or transient. This technique is fully non-invasive.

===Satellites===
{|style="margin: 0 auto;"
| [[File:SatDoppler.png|thumb|300px|upright|Possible Doppler shifts in dependence of the elevation angle ([[Low Earth orbit|LEO]]: orbit altitude <math>h</math> = 750&nbsp;km). Fixed ground station.<ref>Otilia Popescuy, Jason S. Harrisz and Dimitrie C. Popescuz, Designing the Communica- tion Sub-System for Nanosatellite CubeSat Missions: Operational and Implementation Perspectives, 2016, IEEE</ref>]]
| [[File:DopplerSatScheme.png|thumb|300px|upright|Geometry for Doppler effects. Variables: <math>\vec{v}_\text{mob}</math> is the velocity of the mobile station, <math>\vec{v}_\text{Sat}</math> is the velocity of the satellite, <math>\vec{v}_\text{rel,sat}</math> is the relative velocity of the satellite, <math>\phi</math> is the elevation angle of the satellite and <math>\theta</math> is the driving direction with respect to the satellite.]]
| [[File:SatDopplerSpectrum.png|thumb|300px|upright|Doppler effect on the mobile channel. Variables: <math>f_c = \frac{c}{\lambda_{\rm c}}</math> is the carrier frequency, <math>f_{\rm D,max}=\frac{v_{\rm mob}}{\lambda_{\rm c}}</math> is the maximum Doppler shift due to the mobile station moving (see [[Rayleigh fading#Doppler power spectral density|Doppler Spread]]) and <math>f_{\rm D,Sat}</math> is the additional Doppler shift due to the satellite moving.]] 
|}

====Satellite navigation====
{{main|Satellite navigation}}
The Doppler shift can be exploited for [[satellite navigation]] such as in [[Transit (satellite)|Transit]] and [[DORIS (satellite system)|DORIS]].

====Satellite communication====
{{main|Satellite communication}}
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>

Doppler shift of the direct path can be estimated by the following formula:<ref>Arndt, D. (2015). On Channel Modelling for Land Mobile Satellite Reception (Doctoral dissertation).</ref>
<math display="block">f_{\rm D, dir} = \frac{v_{\rm mob}}{\lambda_{\rm c}}\cos\phi \cos\theta</math>
where <math>v_\text{mob}</math> is the speed of the mobile station, <math>\lambda_{\rm c}</math> is the wavelength of the carrier, <math>\phi</math> is the elevation angle of the satellite and <math>\theta</math> is the driving direction with respect to the satellite.

The additional Doppler shift due to the satellite moving can be described as:
<math display="block">f_{\rm D,sat} = \frac{v_{\rm rel,sat}}{\lambda_{\rm c}}</math>
where <math>v_{\rm rel,sat}</math> is the relative speed of the satellite.

===Audio===
The [[Leslie speaker]], most commonly associated with and predominantly used with the famous [[Hammond organ]], takes advantage of the Doppler effect by using an electric motor to rotate an acoustic horn around a loudspeaker, sending its sound in a circle. This results at the listener's ear in rapidly fluctuating frequencies of a keyboard note.

===Vibration measurement===
A [[laser Doppler vibrometer]] (LDV) is a non-contact instrument for measuring vibration. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the laser beam frequency due to the motion of the surface.

===Robotics===
Dynamic real-time path planning in robotics to aid the movement of robots in a sophisticated environment with moving obstacles often take help of Doppler effect.<ref>{{Cite book |doi = 10.1007/978-3-030-04239-4_19|chapter = Potential and Sampling Based RRT Star for Real-Time Dynamic Motion Planning Accounting for Momentum in Cost Function|title = Neural Information Processing|volume = 11307|pages = 209–221|series = Lecture Notes in Computer Science|year = 2018|last1 = Agarwal|first1 = Saurabh|last2 = Gaurav| first2 = Ashish Kumar|last3 = Nirala|first3 = Mehul Kumar|last4 = Sinha|first4 = Sayan|isbn = 978-3-030-04238-7}}</ref> Such applications are specially used for competitive robotics where the environment is constantly changing, such as robosoccer.