# Doppler Effect

The Doppler effect, named after Christian Doppler, is the change in frequency and wavelength of a wave as perceived by an observer moving relative to the source of the waves. For waves that propagate in a wave 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. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analysed separately. For waves which do not require a medium, such as light or gravity in special relativity, only the relative difference in velocity between the observer and the source needs to be considered. [pic]

[pic]

A source of waves moving to the left. The frequency is higher on the left, and lower on the right. | |

Doppler first proposed the effect in 1842 in the monograph Über das farbige Licht der Doppelsterne und einige andere Gestirne des Himmels - Versuch einer das Bradleysche Theorem als integrierenden Teil in sich schliessender allgemeiner Theorie (On the coloured light of the binary refracted stars and other celestial bodies - Attempt of a more general theory including Bradley's theorem as an integral part).[1] The hypothesis was tested for sound waves by the Dutch scientist Christoph Hendrik Diederik Buys Ballot in 1845. He confirmed that the sound's pitch was higher as the sound source approached him, and lower as the sound source receded from him. Hippolyte Fizeau discovered independently the same phenomenon on electromagnetic waves in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau"). It is often overlooked that in Doppler's publications (and also Einstein's in his discussion of the Doppler effect) he explicitly acknowledges that his formulae are only approximate since he made several mathematical approximations in his derivation. Doppler's derivation is repeated more or less verbatim in most modern textbooks but often without the warning that the formulas are only valid in some (experimentally often seen) limits. In Britain, John Scott Russell made an experimental study of the Doppler effect. In 1848, Russell reported his study of the Doppler effect. (J.S. Russell, "On certain effects produced on sound by the rapid motion of the observer", Brit. Assn. Rep., vol. 18, p. 37 (1848).) An English translation of Doppler's 1842 monograph can be found in the book by Alec Eden, "The search for Christian Doppler", Springer-Verlag 1992. In this book, Eden felt doubtful regarding Doppler's conclusions on the colour of double stars, but he was convinced regarding Doppler's conclusions on sound. [pic]

[pic]

An illustration of the Doppler effect[2].

The relationship between observed frequency f' and emitted frequency f is given by: [pic]

where

[pic]is the velocity of waves in the medium (in air at T degrees Celsius, this is 332(1 + T/273)1/2 m/s) [pic]is the velocity of the source (the object emitting the sound) Because we are using an inertial reference system, the velocity of an object moving towards the observer is considered as negative, so the detected frequency increases (This is because the source's velocity is in the denominator.) Conversely, detected frequency decreases when the source moves away, and so the source's velocity is added when the motion is away. In the limit where the speed of the wave is much greater than the relative speed of the source and observer (this is often the case with electromagnetic waves, e.g. light), the relationship between observed frequency f′ and emitted frequency f is given by: |Change in frequency |Observed frequency |

|[pic] |[pic] |

where

[pic]is the transmitted frequency

[pic]is the velocity of the transmitter relative to the receiver in meters per second: positive when moving towards one another, negative when moving away [pic]is the...

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