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<title>Doppler effect</title>

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Doppler effect

</h1>

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</style><div role="note" class="hatnote navigation-not-searchable">For the music project, see <a href="Dopplereffekt" title="Dopplereffekt">Dopplereffekt</a>.</div>

<div role="note" class="hatnote navigation-not-searchable">"Doppler" redirects here. For other uses, see <a href="Doppler_(disambiguation)" class="mw-disambig" title="Doppler (disambiguation)">Doppler (disambiguation)</a>.</div>

The Doppler effect (also Doppler shift) is the change in the <a href="Frequency" title="Frequency">frequency</a> of a <a href="Wave" title="Wave">wave</a> in relation to an observer who is moving relative to the source of the wave.<a href="#cite_note-1">[1]</a><a href="#cite_note-2">[2]</a><a href="#cite_note-Giordano-3">[3]</a> The Doppler effect is named after the physicist <a href="Christian_Doppler" title="Christian Doppler">Christian Doppler</a>, who described the phenomenon in 1842. A common example of Doppler shift is the change of <a href="Pitch_(music)" title="Pitch (music)">pitch</a> heard when a <a href="Vehicle" title="Vehicle">vehicle</a> 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.<a href="#cite_note-Possel-4">[4]</a>

When the source of the sound wave is moving towards the observer, each successive cycle of the wave is emitted from a position closer to the observer than the previous cycle.<a href="#cite_note-Possel-4">[4]</a><a href="#cite_note-Henderson-5">[5]</a> 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 <a href="Transmission_medium" title="Transmission medium">medium</a>, such as <a href="Sound" title="Sound">sound</a> waves, the <a href="Velocity" title="Velocity">velocity</a> of the observer and of the source are relative to the medium in which the waves are transmitted.<a href="#cite_note-Giordano-3">[3]</a> 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 <a href="Vacuum" title="Vacuum">vacuum</a>, as is possible for <a href="Electromagnetic_waves" class="mw-redirect" title="Electromagnetic waves">electromagnetic waves</a> or <a href="Gravitational_wave" title="Gravitational wave">gravitational waves</a>, only the difference in velocity between the observer and the source needs to be considered.

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

Doppler first proposed this effect in 1842 in his treatise "<a href="%C3%9Cber_das_farbige_Licht_der_Doppelsterne_und_einiger_anderer_Gestirne_des_Himmels" class="mw-redirect" title="Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels">Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels</a>" (On the coloured light of the <a href="Binary_stars" class="mw-redirect" title="Binary stars">binary stars</a> and some other stars of the heavens).<a href="#cite_note-AlecEden-6">[6]</a> The hypothesis was tested for sound waves by <a href="C._H._D._Buys_Ballot" title="C. H. D. Buys Ballot">Buys Ballot</a> in 1845.<a href="#cite_note-7">[p 1]</a> He confirmed that the sound's <a href="Pitch_(music)#Pitch_and_frequency" title="Pitch (music)">pitch</a> 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. <a href="Hippolyte_Fizeau" title="Hippolyte Fizeau">Hippolyte Fizeau</a> discovered independently the same phenomenon on <a href="Electromagnetic_wave" class="mw-redirect" title="Electromagnetic wave">electromagnetic waves</a> 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).<a href="#cite_note-8">[p 2]</a><a href="#cite_note-9">[7]</a> In Britain, <a href="John_Scott_Russell" title="John Scott Russell">John Scott Russell</a> made an experimental study of the Doppler effect (1848).<a href="#cite_note-10">[p 3]</a>

<div class="mw-heading mw-heading2"><h2 id="General">General</h2></div>

In <a href="Classical_physics" title="Classical physics">classical physics</a>, 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 xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f}</annotation>

</semantics>

</math><img src="./132e57acb643253e7810ee9702d9581f159a1c61.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" loading="lazy"> and emitted frequency <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\text{0}}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{\text{0}}}</annotation>

</semantics>

</math><img src="./e8b6e44a30a297af5191bb54d912ad346b2734df.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.193ex; height:2.509ex;" alt="{\displaystyle f_{\text{0}}}" loading="lazy"> is given by:<a href="#cite_note-halliday-11">[8]</a>

<mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f=\left({\frac {c\pm v_{\text{r}}}{c\mp v_{\text{s}}}}\right)f_{0}}</annotation>

</semantics>

</math>

where

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle c}</annotation>

</semantics>

</math><img src="./86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" loading="lazy"> is the propagation speed of waves in the medium;</li>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{r}}}</annotation>

</semantics>

</math><img src="./b732ef992c8ed9e1a6176f8f75fb8696df730d95.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.004ex; height:2.009ex;" alt="{\displaystyle v_{\text{r}}}" loading="lazy"> is the speed of the receiver relative to the medium. In the formula, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{r}}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{r}}}</annotation>

</semantics>

</math><img src="./b732ef992c8ed9e1a6176f8f75fb8696df730d95.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.004ex; height:2.009ex;" alt="{\displaystyle v_{\text{r}}}" loading="lazy"> is added to <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle c}</annotation>

</semantics>

</math><img src="./86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" loading="lazy"> if the receiver is moving towards the source, subtracted if the receiver is moving away from the source;</li>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation>

</semantics>

</math><img src="./b967b0fadf0e61501f222904f77e4f0bd87e67b9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}" loading="lazy"> is the speed of the source relative to the medium. <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{s}}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation>

</semantics>

</math><img src="./b967b0fadf0e61501f222904f77e4f0bd87e67b9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}" loading="lazy"> is subtracted from <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle c}</annotation>

</semantics>

</math><img src="./86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" loading="lazy"> if the source is moving towards the receiver, added if the source is moving away from the receiver.</li></ul>

Note this relationship predicts that the frequency will decrease if either source or receiver is moving away from the other.

Equivalently, under the assumption that the source is either directly approaching or receding from the observer:

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mfrac>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mfrac>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {f}{v_{wr}}}={\frac {f_{0}}{v_{ws}}}={\frac {1}{\lambda }}}</annotation>

</semantics>

</math>

where

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{wr}}</annotation>

</semantics>

</math><img src="./e5be0ac8d5796cc3d70eea6d3a578ba7fb2325e1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.278ex; height:2.009ex;" alt="{\displaystyle v_{wr}}" loading="lazy"> is the wave's speed relative to the receiver;</li>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{ws}}</annotation>

</semantics>

</math><img src="./8f804ddccd92171c60bef11146d8872bcce61037.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.308ex; height:2.009ex;" alt="{\displaystyle v_{ws}}" loading="lazy"> is the wave's speed relative to the source;</li>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation>

</semantics>

</math><img src="./b43d0ea3c9c025af1be9128e62a18fa74bedda2a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }" loading="lazy"> is the wavelength.</li></ul>

If the source approaches the observer at an angle (but still with a constant speed), the observed frequency that is first heard is higher than the object's emitted frequency. Thereafter, there is a <a href="Monotonic" class="mw-redirect" title="Monotonic">monotonic</a> decrease in the observed frequency as it gets closer to the observer, through equality when it is coming from a direction perpendicular to the relative motion (and was emitted at the point of closest approach; but when the wave is received, the source and observer will no longer be at their closest), and a continued monotonic decrease as it recedes from the observer. When the observer is very close to the path of the object, the transition from high to low frequency is very abrupt. When the observer is far from the path of the object, the transition from high to low frequency is gradual.

If the speeds <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{s}}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation>

</semantics>

</math><img src="./b967b0fadf0e61501f222904f77e4f0bd87e67b9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}" loading="lazy"> and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{r}}\,}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{r}}\,}</annotation>

</semantics>

</math><img src="./42a3bd83cadb09f9c7b668486adba362d67098a0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.392ex; height:2.009ex;" alt="{\displaystyle v_{\text{r}}\,}" loading="lazy"> are small compared to the speed of the wave, the relationship between observed frequency <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f}</annotation>

</semantics>

</math><img src="./132e57acb643253e7810ee9702d9581f159a1c61.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}" loading="lazy"> and emitted frequency <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\text{0}}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f_{\text{0}}}</annotation>

</semantics>

</math><img src="./e8b6e44a30a297af5191bb54d912ad346b2734df.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.193ex; height:2.509ex;" alt="{\displaystyle f_{\text{0}}}" loading="lazy"> is approximately<a href="#cite_note-halliday-11">[8]</a>

<table>

<th>Observed frequency</th>

<th>Change in frequency

</th></tr>

<tr>

<mrow>

<mrow>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f=\left(1+{\frac {\Delta v}{c}}\right)f_{0}}</annotation>

</semantics>

</math><img src="./40a01dd1044f4fd5da9e006725e25fe2f3eb7f32.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.281ex; height:6.176ex;" alt="{\displaystyle f=\left(1+{\frac {\Delta v}{c}}\right)f_{0}}" loading="lazy"></div></td>

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \Delta f={\frac {\Delta v}{c}}f_{0}}</annotation>

</semantics>

</math><img src="./5c849ba0e7fa8bb8c8239af2a7e5429c25df38e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.406ex; height:5.343ex;" alt="{\displaystyle \Delta f={\frac {\Delta v}{c}}f_{0}}" loading="lazy"></div>

</td></tr></tbody></table>

where

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \Delta f=f-f_{0}}</annotation>

</semantics>

</math><img src="./78f9fc709af6e3c21b614a13482244f5379b0663.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.625ex; height:2.509ex;" alt="{\displaystyle \Delta f=f-f_{0}}" loading="lazy"></li>

<msub>

</mrow>

</msub>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \Delta v=-(v_{\text{r}}-v_{\text{s}})}</annotation>

</semantics>

</math><img src="./af43c7c306a6d443a8c9142ade0a200da8481ed1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.632ex; height:2.843ex;" alt="{\displaystyle \Delta v=-(v_{\text{r}}-v_{\text{s}})}" loading="lazy"> is the opposite of the relative speed of the receiver with respect to the source: it is positive when the source and the receiver are moving towards each other.</li></ul>

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</style><div class="math_proof" style="">Proof

Given <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f=\left({\frac {c+v_{\text{r}}}{c+v_{\text{s}}}}\right)f_{0}}">

<mrow>

<mfrac>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

<mrow>

<msub>

</mrow>

</msub>

</mrow>

</mfrac>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f=\left({\frac {c+v_{\text{r}}}{c+v_{\text{s}}}}\right)f_{0}}</annotation>

</semantics>

</math><img src="./edefa636d4d33ac28088c5548038ed30483590aa.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.07ex; height:6.176ex;" alt="{\displaystyle f=\left({\frac {c+v_{\text{r}}}{c+v_{\text{s}}}}\right)f_{0}}" loading="lazy">

we divide for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle c}</annotation>

</semantics>

</math><img src="./86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" loading="lazy">

<mrow>

<mfrac>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mfrac>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<mrow>

<mfrac>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mfrac>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle f=\left({\frac {1+{\frac {v_{\text{r}}}{c}}}{1+{\frac {v_{\text{s}}}{c}}}}\right)f_{0}=\left(1+{\frac {v_{\text{r}}}{c}}\right)\left({\frac {1}{1+{\frac {v_{\text{s}}}{c}}}}\right)f_{0}}</annotation>

</semantics>

</math>

Since <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {v_{\text{s}}}{c}}\ll 1}">

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {v_{\text{s}}}{c}}\ll 1}</annotation>

</semantics>

</math><img src="./ef70119e7510573d25bdc49f23ee9753aaaeb8fd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.62ex; height:4.676ex;" alt="{\displaystyle {\frac {v_{\text{s}}}{c}}\ll 1}" loading="lazy"> we can substitute using the <a href="Taylor's_series" class="mw-redirect" title="Taylor's series">Taylor's series</a> expansion of <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{1+x}}}">

<mfrac>

<mrow>

</mrow>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {1}{1+x}}}</annotation>

</semantics>

</math><img src="./0e7d2df86c30c3b4ead9fdb615774af8a731a69a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:6.169ex; height:5.343ex;" alt="{\displaystyle {\frac {1}{1+x}}}" loading="lazy"> truncating all <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}}">

<msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle x^{2}}</annotation>

</semantics>

</math><img src="./cf0bf28fd28f45d07e1ceb909ce333c18c558c93.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.384ex; height:2.676ex;" alt="{\displaystyle x^{2}}" loading="lazy"> and higher terms:

<mfrac>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mfrac>

</mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\frac {1}{1+{\frac {v_{\text{s}}}{c}}}}\approx 1-{\frac {v_{\text{s}}}{c}}}</annotation>

</semantics>

</math>

When substituted in the last line, one gets:

<mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

</mrow>

<msub>

</mrow>

</msub>

<mrow>

<mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mfrac>

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<annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {v_{\text{r}}}{c}}\right)\left(1-{\frac {v_{\text{s}}}{c}}\right)f_{0}=\left(1+{\frac {v_{\text{r}}}{c}}-{\frac {v_{\text{s}}}{c}}-{\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}\right)f_{0}}</annotation>

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For small <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{s}}}">

<msub>

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</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation>

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</math><img src="./b967b0fadf0e61501f222904f77e4f0bd87e67b9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}" loading="lazy"> and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{r}}}">

<msub>

</mrow>

</msub>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\text{r}}}</annotation>

</semantics>

</math><img src="./b732ef992c8ed9e1a6176f8f75fb8696df730d95.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.004ex; height:2.009ex;" alt="{\displaystyle v_{\text{r}}}" loading="lazy">, the last term <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}}">

<mfrac>

<mrow>

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<annotation encoding="application/x-tex">{\displaystyle {\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}}</annotation>

</semantics>

</math><img src="./1f310769f794a8d0ef6897663fdff2fac9428833.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:4.848ex; height:5.009ex;" alt="{\displaystyle {\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}}" loading="lazy"> becomes insignificant, hence:

<mrow>

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<annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {v_{\text{r}}-v_{\text{s}}}{c}}\right)f_{0}}</annotation>

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</math>

</div>

<div class="gallerytext">Stationary sound source produces sound waves at a constant frequency f, and the wave-fronts propagate symmetrically away from the source at a constant speed c. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where f = f0.</div>

</li>

<div class="gallerytext">The same sound source is <a href="Radiating" class="mw-redirect" title="Radiating">radiating</a> sound waves at a constant frequency in the same medium. However, now the sound source is moving with a speed υs = 0.7 c. Since the source is moving, the center of each new <a href="Wavefront" title="Wavefront">wavefront</a> is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency f = <style data-mw-deduplicate="TemplateStyles:r1214402035">

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</style>⁠c + 0/c – 0.7c⁠ f0 = 3.33 f0 and an observer behind the source will hear a lower frequency f = ⁠c − 0/c + 0.7c⁠ f0 = 0.59 f0.</div>

</li>

<div class="gallerytext">Now the source is moving at the speed of sound in the medium (υs = c). The wave fronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives and an observer behind the source will hear a lower frequency f = ⁠c – 0/c + c⁠ f0 = 0.5 f0.</div>

</li>

<div class="gallerytext">The sound source has now surpassed the speed of sound in the medium, and is traveling at 1.4 c. Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer hears the sound. As a result, an observer in front of the source will detect nothing and an observer behind the source will hear a lower frequency f = ⁠c – 0/c + 1.4c⁠ f0 = 0.42 f0.</div>

</li>

</ul>

<div class="mw-heading mw-heading2"><h2 id="Consequences">Consequences</h2></div>

Assuming a stationary observer and a wave source moving towards the observer at (or exceeding) the speed of the wave, the Doppler equation predicts an infinite (or negative) frequency as from the observer's perspective. Thus, the Doppler equation is inapplicable for such cases. If the wave is a sound wave and the sound source is moving faster than the speed of sound, the resulting <a href="Shock_wave" title="Shock wave">shock wave</a> creates a <a href="Sonic_boom" title="Sonic boom">sonic boom</a>.

<a href="John_William_Strutt%2C_3rd_Baron_Rayleigh" class="mw-redirect" title="John William Strutt, 3rd Baron Rayleigh">Lord Rayleigh</a> 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.<a href="#cite_note-12">[9]</a>

<div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div>

<div class="mw-heading mw-heading3"><h3 id="Sirens">Sirens</h3></div>

A <a href="Siren_(alarm)" title="Siren (alarm)">siren</a> on a passing <a href="Emergency_vehicle" title="Emergency vehicle">emergency vehicle</a> 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 <a href="John_Dobson_(astronomer)" class="mw-redirect" title="John Dobson (astronomer)">John Dobson</a> explained the effect thus:

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</style><blockquote class="templatequote">The reason the siren slides is because it doesn't hit you.</blockquote>

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:

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<mtext>radial</mtext>

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<annotation encoding="application/x-tex">{\displaystyle v_{\text{radial}}=v_{\text{s}}\cos(\theta )}</annotation>

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where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>

</semantics>

</math><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"> is the angle between the object's forward velocity and the line of sight from the object to the observer.

<div class="mw-heading mw-heading3"><h3 id="Astronomy">Astronomy</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></div>

The <a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">Doppler effect for electromagnetic waves</a> such as light is of widespread use in <a href="Astronomy" title="Astronomy">astronomy</a> to measure the speed at which <a href="Star" title="Star">stars</a> and <a href="Galaxy" title="Galaxy">galaxies</a> are approaching or receding from us, resulting in so called <a href="Blueshift" class="mw-redirect" title="Blueshift">blueshift</a> or <a href="Redshift" title="Redshift">redshift</a>, respectively. This may be used to detect if an apparently single star is, in reality, a close <a href="Binary_star" title="Binary star">binary</a>, to measure the rotational speed of stars and galaxies, or to <a href="Doppler_spectroscopy" title="Doppler spectroscopy">detect exoplanets</a>. This effect typically happens on a very small scale; there would not be a noticeable difference in visible light to the unaided eye.<a href="#cite_note-13">[10]</a>

The use of the Doppler effect in astronomy depends on knowledge of precise frequencies of <a href="Spectral_line" title="Spectral line">discrete lines</a> in the <a href="Electromagnetic_spectroscopy" class="mw-redirect" title="Electromagnetic spectroscopy">spectra</a> of stars.

Among the <a href="List_of_nearest_stars" title="List of nearest stars">nearby stars</a>, the largest <a href="Radial_velocities" class="mw-redirect" title="Radial velocities">radial velocities</a> with respect to the <a href="Sun" title="Sun">Sun</a> are +308 km/s (BD-15°4041, also known as LHS 52, 81.7 light-years away) and −260 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 <a href="Redshift#Expansion_of_space" title="Redshift">expansion of the universe</a> and the Doppler effect is not simple matter of the source moving away from the observer.<a href="#cite_note-Peacock-14">[11]</a><a href="#cite_note-Hogg-15">[12]</a> In cosmology, the redshift of expansion is considered separate from redshifts due to gravity or Doppler motion.<a href="#cite_note-16">[13]</a>

Distant galaxies also exhibit <a href="Peculiar_motion" class="mw-redirect" title="Peculiar motion">peculiar motion</a> distinct from their cosmological recession speeds. If redshifts are used to determine distances in accordance with <a href="Hubble's_law" title="Hubble's law">Hubble's law</a>, then these peculiar motions give rise to <a href="Redshift-space_distortions" title="Redshift-space distortions">redshift-space distortions</a>.<a href="#cite_note-17">[14]</a>

<div class="mw-heading mw-heading3"><h3 id="Radar">Radar</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Doppler_radar" title="Doppler radar">Doppler radar</a></div>

The Doppler effect is used in some types of <a href="Radar" title="Radar">radar</a>, 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 <a href="Proximity_fuze" title="Proximity fuze">proximity fuze</a>, developed during <a href="World_War_II" title="World War II">World War II</a>, relies upon Doppler radar to detonate explosives at the correct time, height, distance, etc.

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 xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta v}">

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle \Delta v}</annotation>

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</math><img src="./e18b43e4225eeaafeeb25aefc4ee90bd86f004dc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.063ex; height:2.176ex;" alt="{\displaystyle \Delta v}" loading="lazy"> is twice that from the same target emitting a wave:<a href="#cite_note-18">[15]</a>

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<annotation encoding="application/x-tex">{\displaystyle \Delta f={\frac {2\Delta v}{c}}f_{0}.}</annotation>

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<div class="mw-heading mw-heading3"><h3 id="Medical">Medical</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Doppler_ultrasonography" title="Doppler ultrasonography">Doppler ultrasonography</a></div>

An <a href="Echocardiogram" class="mw-redirect" title="Echocardiogram">echocardiogram</a> 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 <a href="Ultrasound" title="Ultrasound">ultrasound</a> 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 <a href="Cardiac_output" title="Cardiac output">cardiac output</a>. <a href="Contrast-enhanced_ultrasound" title="Contrast-enhanced ultrasound">Contrast-enhanced ultrasound</a> using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.<a href="#cite_note-19">[16]</a><a href="#cite_note-20">[17]</a>

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).<a href="#cite_note-21">[p 4]</a>

Velocity measurements of blood flow are also used in other fields of <a href="Medical_ultrasonography" class="mw-redirect" title="Medical ultrasonography">medical ultrasonography</a>, such as <a href="Obstetric_ultrasonography" title="Obstetric ultrasonography">obstetric ultrasonography</a> and <a href="Neurology" title="Neurology">neurology</a>. Velocity measurement of blood flow in arteries and veins based on Doppler effect is an effective tool for diagnosis of vascular problems like <a href="Stenosis" title="Stenosis">stenosis</a>.<a href="#cite_note-22">[18]</a>

<div class="mw-heading mw-heading3"><h3 id="Flow_measurement">Flow measurement</h3></div>

Instruments such as the <a href="Laser_Doppler_velocimetry" title="Laser Doppler velocimetry">laser Doppler velocimeter</a> (LDV), <a href="Acoustic_Doppler_current_profiler" title="Acoustic Doppler current profiler">Acoustic Doppler current profiler</a> (ADCP), and <a href="Acoustic_Doppler_velocimetry" title="Acoustic Doppler velocimetry">acoustic Doppler velocimeter</a> (ADV) have been developed to measure velocities in a fluid flow. The LDV emits a <a href="Light_beam" title="Light beam">light beam</a>, and the ADCP and 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.

<div class="mw-heading mw-heading3"><h3 id="Velocity_profile_measurement">Velocity profile measurement</h3></div>

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.

<div class="mw-heading mw-heading3"><h3 id="Satellites">Satellites</h3></div>

<td>

</td>

<td>

</td>

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</td></tr></tbody></table>

<div class="mw-heading mw-heading4"><h4 id="Satellite_navigation">Satellite navigation</h4></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Satellite_navigation" title="Satellite navigation">Satellite navigation</a></div>

The Doppler shift can be exploited for <a href="Satellite_navigation" title="Satellite navigation">satellite navigation</a> such as in <a href="Transit_(satellite)" title="Transit (satellite)">Transit</a> and <a href="DORIS_(satellite_system)" title="DORIS (satellite system)">DORIS</a>.

<div class="mw-heading mw-heading4"><h4 id="Satellite_communication">Satellite communication</h4></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Satellite_communication" class="mw-redirect" title="Satellite communication">Satellite communication</a></div>

Doppler also needs to be compensated in <a href="Satellite_communication" class="mw-redirect" title="Satellite communication">satellite communication</a>.

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.<a href="#cite_note-24">[20]</a> After realizing that the Doppler shift had not been considered before launch of the <a href="Huygens_(spacecraft)#Critical_design_flaw_partially_resolved" title="Huygens (spacecraft)">Huygens probe</a> of the 2005 <a href="Cassini%E2%80%93Huygens" title="Cassini–Huygens">Cassini–Huygens</a> mission, the probe trajectory was altered to approach <a href="Titan_(moon)" title="Titan (moon)">Titan</a> in such a way that its transmissions traveled perpendicular to its direction of motion relative to Cassini, greatly reducing the Doppler shift.<a href="#cite_note-TitanCalling-25">[21]</a>

Doppler shift of the direct path can be estimated by the following formula:<a href="#cite_note-26">[22]</a>

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<annotation encoding="application/x-tex">{\displaystyle f_{\rm {D,dir}}={\frac {v_{\rm {mob}}}{\lambda _{\rm {c}}}}\cos \phi \cos \theta }</annotation>

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where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{mob}}}">

<msub>

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<annotation encoding="application/x-tex">{\displaystyle v_{\text{mob}}}</annotation>

</semantics>

</math><img src="./a44578cef60aa8926da7097fdb674b21afa9f995.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.465ex; height:2.009ex;" alt="{\displaystyle v_{\text{mob}}}" loading="lazy"> is the speed of the mobile station, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{\rm {c}}}">

<msub>

</mrow>

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<annotation encoding="application/x-tex">{\displaystyle \lambda _{\rm {c}}}</annotation>

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</math><img src="./4dd534f7f2534d6e22f726e0facac0e7aaacd5e8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.318ex; height:2.509ex;" alt="{\displaystyle \lambda _{\rm {c}}}" loading="lazy"> is the wavelength of the carrier, <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \phi }</annotation>

</semantics>

</math><img src="./72b1f30316670aee6270a28334bdf4f5072cdde4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }" loading="lazy"> is the elevation angle of the satellite and <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>

</semantics>

</math><img src="./6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"> is the driving direction with respect to the satellite.

The additional Doppler shift due to the satellite moving can be described as:

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<annotation encoding="application/x-tex">{\displaystyle f_{\rm {D,sat}}={\frac {v_{\rm {rel,sat}}}{\lambda _{\rm {c}}}}}</annotation>

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where <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\rm {rel,sat}}}">

<msub>

</mrow>

</msub>

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</mrow>

<annotation encoding="application/x-tex">{\displaystyle v_{\rm {rel,sat}}}</annotation>

</semantics>

</math><img src="./22c1700f72e5dad3d5b6059085ea6bdf76341ecc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.759ex; height:2.343ex;" alt="{\displaystyle v_{\rm {rel,sat}}}" loading="lazy"> is the relative speed of the satellite.

<div class="mw-heading mw-heading3"><h3 id="Audio">Audio</h3></div>

The <a href="Leslie_speaker" title="Leslie speaker">Leslie speaker</a>, most commonly associated with and predominantly used with the famous <a href="Hammond_organ" title="Hammond organ">Hammond organ</a>, 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.

<div class="mw-heading mw-heading3"><h3 id="Vibration_measurement">Vibration measurement</h3></div>

A <a href="Laser_Doppler_vibrometer" title="Laser Doppler vibrometer">laser Doppler vibrometer</a> (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.

<div class="mw-heading mw-heading3"><h3 id="Robotics">Robotics</h3></div>

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.<a href="#cite_note-27">[23]</a> Such applications are specially used for competitive robotics where the environment is constantly changing, such as robosoccer.

<div class="mw-heading mw-heading2"><h2 id="Inverse_Doppler_effect">Inverse Doppler effect</h2></div>

Since 1968 scientists such as <a href="Victor_Veselago" title="Victor Veselago">Victor Veselago</a> have speculated about the possibility of an inverse Doppler effect. The size of the Doppler shift depends on the <a href="Refractive_index" title="Refractive index">refractive index</a> of the medium a wave is traveling through. Some materials are capable of <a href="Negative_refraction" title="Negative refraction">negative refraction</a>, which should lead to a Doppler shift that works in a direction opposite that of a conventional Doppler shift.<a href="#cite_note-28">[24]</a> The first experiment that detected this effect was conducted by Nigel Seddon and Trevor Bearpark in <a href="Bristol" title="Bristol">Bristol</a>, <a href="United_Kingdom" title="United Kingdom">United Kingdom</a> in 2003.<a href="#cite_note-29">[p 5]</a> Later, the inverse Doppler effect was observed in some inhomogeneous materials, and predicted inside a <a href="Vavilov%E2%80%93Cherenkov_effect" class="mw-redirect" title="Vavilov–Cherenkov effect">Vavilov–Cherenkov</a> cone.<a href="#cite_note-30">[25]</a>

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</style><div class="div-col" style="column-width: 30em;">

<ul><li><a href="Bistatic_Doppler_shift" class="mw-redirect" title="Bistatic Doppler shift">Bistatic Doppler shift</a></li>

<li><a href="Differential_Doppler_effect" title="Differential Doppler effect">Differential Doppler effect</a></li>

<li><a href="Doppler_cooling" title="Doppler cooling">Doppler cooling</a></li>

<li><a href="Dopplergraph" title="Dopplergraph">Dopplergraph</a></li>

<li><a href="Fading" title="Fading">Fading</a></li>

<li><a href="Fizeau_experiment" title="Fizeau experiment">Fizeau experiment</a></li>

<li><a href="Photoacoustic_Doppler_effect" title="Photoacoustic Doppler effect">Photoacoustic Doppler effect</a></li>

<li><a href="Range_rate" class="mw-redirect" title="Range rate">Range rate</a></li>

<li><a href="Rayleigh_fading" title="Rayleigh fading">Rayleigh fading</a></li>

<li><a href="Redshift" title="Redshift">Redshift</a></li>

<li><a href="Laser_Doppler_imaging" title="Laser Doppler imaging">Laser Doppler imaging</a></li>

<li><a href="Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li></ul>

</div>

<div class="mw-heading mw-heading2"><h2 id="Primary_sources">Primary sources</h2></div>

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</style><cite id="CITEREFBuys_Ballot1845" class="citation journal cs1">Buys Ballot (1845). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1423606">"Akustische Versuche auf der Niederländischen Eisenbahn, nebst gelegentlichen Bemerkungen zur Theorie des Hrn. Prof. Doppler (in German)"</a>. Annalen der Physik und Chemie. 142 (11): 321–351. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1845AnP...142..321B">1845AnP...142..321B</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18451421102">10.1002/andp.18451421102</a>.</cite>

</li>

<li id="cite_note-8"><a href="#cite_ref-8">^</a> Fizeau: "Acoustique et optique". Lecture, <a href="Philomatic_Society" class="mw-redirect" title="Philomatic Society">Société Philomathique</a> 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.

</li>

<li id="cite_note-10"><a href="#cite_ref-10">^</a> <cite id="CITEREFScott_Russell1848" class="citation journal cs1">Scott Russell, John (1848). <a rel="nofollow" class="external text" href="http://www.ma.hw.ac.uk/~chris/doppler.html">"On certain effects produced on sound by the rapid motion of the observer"</a>. Report of the Eighteenth Meeting of the British Association for the Advancement of Science. 18 (7): 37–38. Retrieved 2008-07-08.</cite>

</li>

<li id="cite_note-21"><a href="#cite_ref-21">^</a> <cite id="CITEREFPetrescu2015" class="citation journal cs1">Petrescu, Florian Ion T (2015). <a rel="nofollow" class="external text" href="https://www.proquest.com/openview/cec7b768b14887621e9494261e122a4c/1?pq-origsite=gscholar&cbl=1226369">"Improving Medical Imaging and Blood Flow Measurement by using a New Doppler Effect Relationship"</a>. American Journal of Engineering and Applied Sciences. 8 (4): 582–588. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.3844%2Fajeassp.2015.582.588">10.3844/ajeassp.2015.582.588</a>.</cite>

</li>

<li id="cite_note-29"><a href="#cite_ref-29">^</a> <cite id="CITEREFKozyrevvan_der_Weide2005" class="citation journal cs1">Kozyrev, Alexander B.; van der Weide, Daniel W. (2005). "Explanation of the Inverse Doppler Effect Observed in Nonlinear Transmission Lines". Physical Review Letters. 94 (20): 203902. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005PhRvL..94t3902K">2005PhRvL..94t3902K</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.94.203902">10.1103/PhysRevLett.94.203902</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16090248">16090248</a>.</cite>

</li>

</ol></div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

<li id="cite_note-1"><a href="#cite_ref-1">^</a> <cite id="CITEREFUnited_States._Navy_Department1969" class="citation book cs1">United States. Navy Department (1969). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=gjYGC_sc6lcC&pg=PA194">Principles and Applications of Underwater Sound, Originally Issued as Summary Technical Report of Division 6, NDRC, Vol. 7, 1946, Reprinted...1968</a>. p. 194. Retrieved 2021-03-29.</cite>

</li>

<li id="cite_note-2"><a href="#cite_ref-2">^</a> <cite id="CITEREFJoseph2013" class="citation book cs1">Joseph, A. (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=FRVaNZEQCa4C&pg=PA164">Measuring Ocean Currents: Tools, Technologies, and Data</a>. Elsevier Science. p. 164. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-12-391428-6</bdi>. Retrieved 2021-03-30.</cite>

</li>

<li id="cite_note-Giordano-3">^ <a href="#cite_ref-Giordano_3-0">a</a> <a href="#cite_ref-Giordano_3-1">b</a> <cite id="CITEREFGiordano2009" class="citation book cs1">Giordano, Nicholas (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BwistUlpZ7cC&pg=PA424">College Physics: Reasoning and Relationships</a>. Cengage Learning. pp. 421–424. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0534424718</bdi>.</cite>

</li>

<li id="cite_note-Possel-4">^ <a href="#cite_ref-Possel_4-0">a</a> <a href="#cite_ref-Possel_4-1">b</a> <cite id="CITEREFPossel2017" class="citation web cs1">Possel, Markus (2017). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170914003837/http://www.einstein-online.info/spotlights/doppler">"Waves, motion and frequency: the Doppler effect"</a>. Einstein Online, Vol. 5. Max Planck Institute for Gravitational Physics, Potsdam, Germany. Archived from <a rel="nofollow" class="external text" href="http://www.einstein-online.info/spotlights/doppler">the original</a> on September 14, 2017. Retrieved September 4, 2017.</cite>

</li>

<li id="cite_note-Henderson-5"><a href="#cite_ref-Henderson_5-0">^</a> <cite id="CITEREFHenderson2017" class="citation web cs1">Henderson, Tom (2017). <a rel="nofollow" class="external text" href="http://www.physicsclassroom.com/class/waves/Lesson-3/The-Doppler-Effect">"The Doppler Effect – Lesson 3, Waves"</a>. Physics tutorial. The Physics Classroom. Retrieved September 4, 2017.</cite>

</li>

<li id="cite_note-AlecEden-6"><a href="#cite_ref-AlecEden_6-0">^</a> Alec Eden The search for Christian Doppler, Springer-Verlag, Wien 1992. Contains a facsimile edition with an <a href="English_language" title="English language">English</a> translation.

</li>

<li id="cite_note-9"><a href="#cite_ref-9">^</a> Becker (2011). Barbara J. Becker, Unravelling Starlight: William and Margaret Huggins and the Rise of the New Astronomy, illustrated Edition, <a href="Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, 2011; <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>110700229X</bdi>, 9781107002296.

</li>

<li id="cite_note-halliday-11">^ <a href="#cite_ref-halliday_11-0">a</a> <a href="#cite_ref-halliday_11-1">b</a> <cite id="CITEREFWalkerResnickHalliday2007" class="citation book cs1">Walker, Jearl; <a href="Robert_Resnick" title="Robert Resnick">Resnick, Robert</a>; <a href="David_Halliday_(physicist)" title="David Halliday (physicist)">Halliday, David</a> (2007). Halliday & Resnick Fundamentals of Physics (8th ed.). Wiley. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9781118233764</bdi>. <a href="OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/436030602">436030602</a>.</cite>

</li>

<li id="cite_note-12"><a href="#cite_ref-12">^</a> <cite id="CITEREFStrutt_(Lord_Rayleigh)1896" class="citation book cs1">Strutt (Lord Rayleigh), John William (1896). MacMillan & Co (ed.). <a rel="nofollow" class="external text" href="https://archive.org/stream/theorysound02raylgoog#page/n176/mode/2up">The Theory of Sound</a>. Vol. 2 (2 ed.). Macmillan. p. 154.</cite>

</li>

<li id="cite_note-13"><a href="#cite_ref-13">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.astro.ucla.edu/~wright/doppler.htm">"Doppler Shift"</a>. astro.ucla.edu.</cite>

</li>

<li id="cite_note-Peacock-14"><a href="#cite_ref-Peacock_14-0">^</a> <cite id="CITEREFJA_Peacock2008" class="citation arxiv cs1">JA Peacock (2008). "A diatribe on expanding space". <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/0809.4573">0809.4573</a> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/astro-ph">astro-ph</a>].</cite>

</li>

<li id="cite_note-Hogg-15"><a href="#cite_ref-Hogg_15-0">^</a> <cite id="CITEREFBunnHogg2009" class="citation journal cs1">Bunn, E. F.; Hogg, D. W. (2009). "The kinematic origin of the cosmological redshift". American Journal of Physics. 77 (8): 688–694. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/0808.1081">0808.1081</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009AmJPh..77..688B">2009AmJPh..77..688B</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.3129103">10.1119/1.3129103</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1365918">1365918</a>.</cite>

</li>

<li id="cite_note-16"><a href="#cite_ref-16">^</a> <cite id="CITEREFHarrison2000" class="citation book cs1">Harrison, Edward Robert (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-8PJbcA2lLoC&pg=PA315">Cosmology: The Science of the Universe</a> (2nd ed.). Cambridge University Press. pp. 306ff. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-521-66148-5</bdi>.</cite>

</li>

<li id="cite_note-17"><a href="#cite_ref-17">^</a> An excellent review of the topic in technical detail is given here: <cite id="CITEREFPercivalSamushiaRossShapiro2011" class="citation journal cs1">Percival, Will; Samushia, Lado; Ross, Ashley; Shapiro, Charles; Raccanelli, Alvise (2011). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.2011.0370">"Review article: Redshift-space distortions"</a>. Philosophical Transactions of the Royal Society. 369 (1957): 5058–67. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011RSPTA.369.5058P">2011RSPTA.369.5058P</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.2011.0370">10.1098/rsta.2011.0370</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22084293">22084293</a>.</cite>

</li>

<li id="cite_note-18"><a href="#cite_ref-18">^</a> <cite id="CITEREFWolff" class="citation web cs1">Wolff, Dipl.-Ing. (FH) Christian. <a rel="nofollow" class="external text" href="http://www.radartutorial.eu/11.coherent/co06.en.html">"Radar Basics"</a>. radartutorial.eu. Retrieved 14 April 2018.</cite>

</li>

<li id="cite_note-19"><a href="#cite_ref-19">^</a> <cite id="CITEREFDaviesNewton2017" class="citation journal cs1">Davies, MJ; Newton, JD (2 July 2017). "Non-invasive imaging in cardiology for the generalist". British Journal of Hospital Medicine. 78 (7): 392–398. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.12968%2Fhmed.2017.78.7.392">10.12968/hmed.2017.78.7.392</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28692375">28692375</a>.</cite>

</li>

<li id="cite_note-20"><a href="#cite_ref-20">^</a> <cite id="CITEREFAppisTracyFeinstein2015" class="citation journal cs1">Appis, AW; Tracy, MJ; Feinstein, SB (1 June 2015). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4676450">"Update on the safety and efficacy of commercial ultrasound contrast agents in cardiac applications"</a>. Echo Research and Practice. 2 (2): R55–62. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1530%2FERP-15-0018">10.1530/ERP-15-0018</a>. <a href="PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4676450">4676450</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26693339">26693339</a>.</cite>

</li>

<li id="cite_note-22"><a href="#cite_ref-22">^</a> <cite id="CITEREFEvansMcDicken2000" class="citation book cs1">Evans, D. H.; McDicken, W. N. (2000). Doppler Ultrasound (2nd ed.). New York: John Wiley and Sons. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-471-97001-9</bdi>.</cite>

</li>

<li id="cite_note-23"><a href="#cite_ref-23">^</a> Otilia Popescuy, Jason S. Harrisz and Dimitrie C. Popescuz, "Designing the Communication Sub-System for Nanosatellite CubeSat Missions: Operational and Implementation Perspectives", 2016, IEEE

</li>

<li id="cite_note-24"><a href="#cite_ref-24">^</a> <cite id="CITEREFQingchong1999" class="citation book cs1">Qingchong, Liu (1999). "Doppler measurement and compensation in mobile satellite communications systems". MILCOM 1999. IEEE Military Communications. Conference Proceedings (Cat. No.99CH36341). Vol. 1. pp. 316–320. <a href="CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.674.3987">10.1.1.674.3987</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Fmilcom.1999.822695">10.1109/milcom.1999.822695</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-7803-5538-5</bdi>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:12586746">12586746</a>.</cite>

</li>

<li id="cite_note-TitanCalling-25"><a href="#cite_ref-TitanCalling_25-0">^</a> <cite id="CITEREFOberg2004" class="citation news cs1">Oberg, James (October 4, 2004). <a rel="nofollow" class="external text" href="https://archive.today/20120914080503/http://spectrum.ieee.org/aerospace/space-flight/titan-calling">"Titan Calling"</a>. <a href="IEEE_Spectrum" title="IEEE Spectrum">IEEE Spectrum</a>. Archived from <a rel="nofollow" class="external text" href="https://spectrum.ieee.org/aerospace/space-flight/titan-calling">the original</a> on September 14, 2012.</cite> (offline as of 2006-10-14, see <a rel="nofollow" class="external text" href="https://web.archive.org/web/20041010192803/http://www.spectrum.ieee.org/WEBONLY/publicfeature/oct04/1004titan.html">Internet Archive version</a>)

</li>

<li id="cite_note-26"><a href="#cite_ref-26">^</a> Arndt, D. (2015). On Channel Modelling for Land Mobile Satellite Reception (Doctoral dissertation).

</li>

<li id="cite_note-27"><a href="#cite_ref-27">^</a> <cite id="CITEREFAgarwalGauravNiralaSinha2018" class="citation book cs1">Agarwal, Saurabh; Gaurav, Ashish Kumar; Nirala, Mehul Kumar; Sinha, Sayan (2018). "Potential and Sampling Based RRT Star for Real-Time Dynamic Motion Planning Accounting for Momentum in Cost Function". Neural Information Processing. Lecture Notes in Computer Science. Vol. 11307. pp. 209–221. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-030-04239-4_19">10.1007/978-3-030-04239-4_19</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-030-04238-7</bdi>.</cite>

</li>

<li id="cite_note-28"><a href="#cite_ref-28">^</a> <cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physicsworld.com/a/doppler-shift-is-seen-in-reverse/">"Doppler shift is seen in reverse"</a>. Physics World. 10 March 2011.</cite>

</li>

<li id="cite_note-30"><a href="#cite_ref-30">^</a> <cite id="CITEREFShiLinKaminerGao2018" class="citation journal cs1">Shi, Xihang; Lin, Xiao; Kaminer, Ido; Gao, Fei; Yang, Zhaoju; Joannopoulos, John D.; Soljačić, Marin; Zhang, Baile (October 2018). "Superlight inverse Doppler effect". Nature Physics. 14 (10): 1001–1005. <a href="ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<a rel="nofollow" class="external text" href="https://arxiv.org/abs/1805.12427">1805.12427</a>. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018NatPh..14.1001S">2018NatPh..14.1001S</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41567-018-0209-6">10.1038/s41567-018-0209-6</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1745-2473">1745-2473</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:125790662">125790662</a>.</cite>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li>Doppler, C. (1842). <a href="%C3%9Cber_das_farbige_Licht_der_Doppelsterne_und_einiger_anderer_Gestirne_des_Himmels" class="mw-redirect" title="Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels">Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels (About the coloured light of the binary stars and some other stars of the heavens)</a>. Publisher: Abhandlungen der Königl. Böhm. Gesellschaft der Wissenschaften (V. Folge, Bd. 2, S. 465–482) [Proceedings of the Royal Bohemian Society of Sciences (Part V, Vol 2)]; Prague: 1842 (Reissued 1903). Some sources mention 1843 as year of publication because in that year the article was published in the Proceedings of the Bohemian Society of Sciences. Doppler himself referred to the publication as "Prag 1842 bei Borrosch und André", because in 1842 he had a preliminary edition printed that he distributed independently.</li>

<li>"Doppler and the Doppler effect", E. N. da C. Andrade, Endeavour Vol. XVIII No. 69, January 1959 (published by ICI London). Historical account of Doppler's original paper and subsequent developments.</li>

<li>David Nolte (2020). "The fall and rise of the Doppler effect. Physics Today, v. 73, pp. 31–35. <a rel="nofollow" class="external text" href="https://physicstoday.scitation.org/doi/10.1063/PT.3.4429">DOI: 10.1063/PT.3.4429</a></li>

<li><cite id="CITEREFAdrian1995" class="citation web cs1">Adrian, Eleni (24 June 1995). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090512192731/http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html">"Doppler Effect"</a>. <a href="National_Center_for_Supercomputing_Applications" title="National Center for Supercomputing Applications">NCSA</a>. Archived from <a rel="nofollow" class="external text" href="http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html">the original</a> on 12 May 2009. Retrieved 2008-07-13.</cite></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

<ul><li> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Doppler_effect" class="extiw external" title="commons:Category:Doppler effect">Doppler effect</a> at Wikimedia Commons</li>

<li><a rel="nofollow" class="external text" href="https://www.feynmanlectures.caltech.edu/I_34.html#Ch34-S6">The Doppler effect – The Feynman Lectures on Physics</a></li>

<li><a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/physics/DopplerEffect.html">Doppler Effect</a>, ScienceWorld</li></ul>

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