The Doppler effect (or Doppler shift), named after Austrian physicist Christian Doppler who proposed it in 1842, is the change in frequency and wavelength of a wave for an observer moving relative to the source of the waves. It is commonly heard when a vehicle sounding a siren approaches, passes and recedes from an observer. The received frequency is increased (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is decreased during the recession.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />
For waves that propagate in a 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 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. The hypothesis was tested for sound waves by Buys Ballot in 1845. He confirmed that the sound's 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 waves in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau"). In Britain, John Scott Russell made an experimental study of the Doppler effect (1848). An English translation of Doppler's 1842 treatise can be found in the book The Search for Christian Doppler by Alec Eden. The relationship between observed frequency f and emitted frequency f0 is given by:
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where
is the velocity of waves in the medium
is the radial component of the velocity of the source (the object emitting the wave) along a line from the source to the observer; positive if moving away from the observer.
The observed frequency is increased if the source is moving towards the observer. It is decreased if the source is moving away.
For all paths of an approaching object, the observed frequency that is first heard is higher than the object's emitted frequency. Thereafter there is a monotonic decrease in the observed frequency as it gets closer to the observer, through equality when it is level with the observer, 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.
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 f0 is given by:
|
Change in frequency |
Observed frequency |
where
is the transmitted frequency
is the velocity of the transmitter relative to the receiver in meters per second: negative when moving towards one another, positive when moving away
is the speed of wave (e.g. 3×108 m/s for electromagnetic waves travelling in a vacuum)
is the wavelength of the transmitted wave subject to change.
These two equations are only accurate to a first order approximation. However, they work reasonably well in the case considered by Doppler: when the speed between the source and receiver is slow relative to the speed of the waves involved and the distance between the source and receiver is large relative to the wavelength of the waves. If either of these two approximations are violated, the formulae are no longer accurate.
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 inverse is true if the thrower is moving away from the man. So it is actually the wavelength which is affected; as a consequence, the received frequency is also affected. It may also be said that the velocity of the wave remains constant whereas wavelength changes; hence frequency also changes.
If the moving source is emitting waves through a medium with an actual frequency f0, then an observer stationary relative to the medium detects waves with a frequency f given by
where v is the speed of the waves in the medium and vs is the speed of the source with respect to the medium (positive if moving away from the observer, negative if moving towards the observer).
A similar analysis for a moving observer and a stationary source yields the observed frequency (the receiver's velocity being represented as vr):
where the same convention applies: vr is positive if the observer is moving away from the source, and negative if the observer is moving towards the source.
These can be generalized into a single equation with both the source and receiver moving.
which can be written as:
Where
vs,r is the source to receiver velocity radial
component.
With a relatively slow moving source, vs,r is
small in comparison to v and the equation approximates
to
.
Craig Bohren pointed out that some physics textbooks erroneously state that the observed frequency increases as the object approaches an observer and then decreases only as the object passes the observer.[3] In fact, the observed frequency of an approaching object declines monotonically from a value above the emitted frequency, through a value equal to the emitted frequency when the object is closest to the observer, and to values increasingly below the emitted frequency as the object recedes from the observer. Bohren proposed that this common misconception might occur because the intensity of the sound increases as an object approaches an observer and decreases once it passes and recedes from the observer.
A stationary microphone records moving police sirens at different pitches depending on their relative direction.
Sirens
The 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 explained the effect thus:
"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 (as vs, r is only the radial component) until the vehicle hit him, and then immediately jump to a new lower pitch. Because the vehicle passes by the observer, the radial velocity does not remain constant, but instead varies as a function of the angle between his line of sight and the siren's velocity:
where vs is the velocity of the object (source of waves) with respect to the medium, and θ is the angle between the object's forward velocity and the line of sight from the object to the observer.
Astronomy
The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blueshift. It has been used to measure the speed at which stars and galaxies are approaching or receding from us, that is, the radial velocity. This is used to detect if an apparently single star is, in reality, a close binary and even to measure the rotational speed of stars and galaxies.
The use of the Doppler effect for light in astronomy depends on our knowledge that the spectra of stars are not continuous. They exhibit absorption lines at well defined frequencies that are correlated with the energies required to excite electrons in various elements from one level to another. The Doppler effect is recognizable in the fact that the absorption lines are not always at the frequencies that are obtained from the spectrum of a stationary light source. Since blue light has a higher frequency than red light, the spectral lines of an approaching astronomical light source exhibit a blueshift and those of a receding astronomical light source exhibit a redshift.
