The Doppler effect (also Doppler shift) is the change in the frequency or, equivalently, the period of a wave in relation to an observer who is moving relative to the source of the wave. It is named after the physicist Christian Doppler, who described the phenomenon in 1842. A common example of a Doppler shift is the change of pitch heard when a vehicle approaches and recedes from an observer. Compared to the emitted sound, the received sound has a higher pitch during the approach, identical at the instant of passing by, and lower pitch during the recession.
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. Hence, from the observer's perspective, the period or 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 period or time between successive cycles is increased, thus reducing the frequency.
For waves propagating in a vacuum, as is possible for electromagnetic waves or gravitational waves, only the relative velocity between the observer and the source needs to be considered. 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 in such cases may therefore result from motion of the source, motion of the observer, motion of the medium, or any combination thereof.
History
Doppler first proposed this effect in 1842 in his treatise "Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels (On the coloured light of the binary stars and some other stars of the heavens).Alec Eden The search for Christian Doppler, Springer-Verlag, Wien 1992. Contains a facsimile edition with an English translation. 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 independently discovered the same phenomenon on electromagnetic waves 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.Fizeau: "Acoustique et optique". Lecture, Société Philomathique 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.Becker (2011). Barbara J. Becker, Unravelling Starlight: William and Margaret Huggins and the Rise of the New Astronomy, illustrated Edition, Cambridge University Press, 2011; , 9781107002296. In Britain, John Scott Russell made an experimental study of the Doppler effect (1848).
General
The relationship between observed frequency and emitting frequency of a wave propagating through a medium is given by:
where is the propagation speed of the wave in the medium; is the speed of the wave receiver relative to the medium. In the formula, is added to if the receiver is moving towards the source, and subtracted if moving away; is the speed of the wave source relative to the medium. In the formula, is subtracted from if the source is moving towards the receiver, and added if moving away.
, , and here are not vectors as velocities, but their magnitudes as speeds. This relationship predicts that the observed frequency by the receiver will decrease if the distance between the source and receiver is increasing. Note that the speed of the wave is determined by the medium, not by the speed of the source.
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 monotonic 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.
Consequences 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 shock wave creates a sonic boom.
Lord Rayleigh 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.
Applications Sirens
A 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:
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 them, 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:
where 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 widespread use in astronomy to measure the speed at which stars and 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, to measure the rotational speed of stars and galaxies, or to 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. The use of the Doppler effect in astronomy depends on knowledge of precise frequencies of discrete lines in the spectra of stars.
Among the nearby stars, the largest radial velocities with respect to the Sun 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 expansion of the universe and the Doppler effect is not simply caused by the source moving away from the observer. In cosmology, the redshift of expansion is considered separate from redshifts due to gravity or Doppler motion.
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.An excellent review of the topic in technical detail is given here:
Radar
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 to or recedes from the radar source. In the case of a car moving away from the 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 gaps between the wave crests increase, increasing the wavelength of the radiation returning to the radar. In the opposite case, when the radar beam is fired at the moving car as it approaches, each successive wave travels a lesser distance, decreasing the wavelength. In either situation, calculations from the Doppler effect accurately determine the car's speed. For instance, a police radar operating at 24.15 GHz (K-band) detecting a vehicle traveling at 30 m/s (108 km/h) will measure a Doppler shift of approximately 4.83 kHz, a change easily detected by modern digital signal processing. Moreover, the proximity fuze, developed during World War II, relies upon Doppler radar to detonate explosives at the correct time, height, distance, etc.
Bats use echolocation in a similar way to locate moths. The Doppler shift affects the frequency of the wave incident upon the target (moth). When the wave is reflected back from the moth to the bat, the moth acts as the wave emitter and the bat as the wave receiver. The frequency of the reflected wave is again Doppler-shifted. A bat, emitting a wave at the frequency and flying at towards a moth flying at will detect a final reflected wave with a frequency:
Medical
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.
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).
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.
Flow measurement Instruments such as the laser Doppler velocimeter (LDV), Acoustic Doppler current profiler (ADCP), and acoustic Doppler velocimeter (ADV) have been developed to measure velocities in a fluid flow. The LDV emits a light beam, 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.
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
Satellite navigation