Doppler Effect

The Doppler effect, named after Christian Andreas Doppler , is the apparent change in Frequency or Wavelength of a Wave that is perceived by an observer moving relative to the source of the waves. For waves, such as Sound waves, that propagate in a wave medium, the velocity of the observer and the source are reckoned relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from either motion of the source or motion of the observer. Each of these effects is analyzed 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.

Doppler first proposed the effect in 1842 in the monograph ''Über das farbige Licht der Doppelsterne und einige andere Gestirne des Himmels'' (''On the colored light of the binary star and other stars''). 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 Wave s in 1848 (in France , the effect is sometimes called "effet Doppler-Fizeau").

It is important to realize that the frequency of the sounds that the source ''emits'' does not actually change. To understand what happens, consider the following analogy. Someone throws one ball every second in a man's direction. Assume that balls travel with constant velocity. If the thrower is stationary, the man will receive one ball every second. However, if the thrower is moving towards the man, he will receive balls more frequently because the balls will be less spaced out. The converse is true if the thrower is moving away from the man. So it is actually the ''wavelength'' which is affected; as a consequence, the perceived frequency is also affected.

If the moving source is emitting waves through a medium with an actual frequency ''f''₀, then an observer stationary relative to the medium detects waves with a frequency ''f'' given by:

:

f = f_0 \left ( rac {v}{v + v_{s,r}} 
ight )

where ''v'' is the speed of the waves in the medium and ''v''_{s, r} is the speed of the source with respect to the medium (positive if moving away from the observer, negative if moving towards the observer), radial to the observer.

A similar analysis for a moving observer and a stationary source yields the observed frequency (the observer's velocity being represented as ''v''_o):

:

f = f_0 \left (1 - rac {v_0}{v} 
ight )

where the same convention applies : ''v''_o is positive if the observer is moving away from the source, and negative if the observer is moving towards the source.

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Doppler Effect