Doppler effect

Doppler Effect

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Doppler effect

The Doppler effect (or Doppler shift), named after Austria

Austria

Austria , officially the Republic of Austria , is a landlocked country in Central Europe. It borders both Germany and the Czech Republic to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the west....
n physicist Christian Doppler

Christian Doppler

Christian Andreas Doppler was an Austrian mathematician and physicist. He is most famous for what is now called the Doppler effect, which is the apparent change in frequency and wavelength of a wave as perceived by an observer moving relative to the wave's source....
who proposed it in 1842, is the change in frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
and wavelength

Wavelength

In physics, wavelength is the distance between repeating units of a propagating wave of a given frequency. It is commonly designated by the Greek language letter lambda ....
of a wave

Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
for an observer moving relative to the source of the waves. It is commonly heard when a vehicle sounding a siren

Siren (noisemaker)

A siren is a loud noise maker. The original version would yield sounds under water, suggesting a link with the sirens of Greek mythology. Most modern ones are civil defense siren or "air raid" sirens, tornado sirens, or the sirens on emergency service vehicles such as ambulances, police cars and Fire apparatus....
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.

For waves that propagate in a medium, such as sound

Sound

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Development

Doppler first proposed the effect in 1842 in his treatise "Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels

Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels

is a treatise by Christian Doppler in which he postulated his principle that the observed frequency changes if either the source or the observer is moving, which later has been coined the Doppler effect....
" (On the coloured light of the binary stars and some other stars of the heavens). The hypothesis was tested for sound waves by Buys Ballot

C.H.D. Buys Ballot

Christophorus Henricus Diedericus Buys Ballot was a Netherlands chemist and meteorologist after whom Buys-Ballot's law and the Buys Ballot table are named....
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

Hippolyte Fizeau

Armand Hippolyte Louis Fizeau , France physics, was born in Paris. His earliest work was concerned with improvements in photographic processes. Later, in association with Dillon Beaulieu, he engaged in a series of investigations on the interference of light and heat....
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

John Scott Russell

John Scott Russell was a Scotland naval architecture who built the SS Great Eastern in collaboration with Isambard Kingdom Brunel, and made the discovery that gave birth to the modern study of solitons....
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.

General

In classical physics (waves in a medium), the relationship between observed frequency f and emitted frequency f₀ is given by:

where

is the velocity of waves in the medium

is the velocity of the source relative to the medium

is the velocity of the receiver relative to the medium.

Both velocities and are computed so that the observed frequency is increased when either the source is moving towards the observer or the observer is moving towards the source. The frequency is decreased if the either is moving away from the other.

The above formula assumes that the source is either directly approaching or receding from the observer. If the source approaches the observer at an angle (but still with a constant velocity), 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 closest to 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:

Observed frequency	Change in frequency

where

is the velocity of the source relative to the receiver: it is negative when the source is moving towards the receiver, 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 in the reference frame of the source.

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.

Analysis

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 source moving away from the observer 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_s is positive if the source is moving away from the observer, and negative if the source is 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 v_r):

where the similar convention applies: v_r is positive if the observer is moving towards the source, and negative if the observer is moving away from the source.

These can be generalized into a single equation with both the source and receiver moving.

With a relatively slow moving source, v_s,r is small in comparison to v and the equation approximates to where .

However the limitations mentioned above still apply. When the more complicated exact equation is derived without using any approximations (just assuming that everything: source, receiver, and wave or signal are moving linearly) several interesting and perhaps surprising results are found. For example, as Lord Rayleigh noted in his classic book on sound, by properly moving it would be possible to hear a symphony being played backwards. This is the so-called "time reversal effect" of the Doppler effect. Other interesting cases are that the Doppler effect is time dependent in general (thus we need to know not only the source and receivers' velocities, but also their positions at a given time) and also in some circumstances it is possible to receive two signals or waves from a source (or no signal at all). In addition there are more possibilities than just the receiver approaching the signal and the receiver receding from the signal.

All these additional complications are for the classical—i.e., non-relativistic Doppler effect

Relativistic Doppler effect

The relativistic Doppler effect is the change in frequency of light, caused by the relative motion of the source and the observer , when taking into account effects of the special relativity....
. However, all these results also hold for the relativistic Doppler effect as well.

The first attempt to extend Doppler's analysis to light waves was soon made by Fizeau. In fact, light waves do not require a medium to propagate and the correct understanding of the Doppler effect for light requires the use of the Special Theory of Relativity

Special relativity

Relativistic Doppler effect

A common misconception

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. 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 and that this change in intensity is misperceived as a change in frequency.

Applications

Sirens

The siren

Siren (noisemaker)

Emergency vehicle

An emergency vehicle is any vehicle that is designated and authorized to respond to an emergency. These vehicles are usually operated by designated agencies, often part of the government, but also run by charities, non-governmental organizations and some commercial companies....
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

John Dobson (astronomer)

John Lowry Dobson is a highly influential amateur astronomy. He is most well known in astronomy circles because his name is attached to the popular Dobsonian telescope design....
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 v_{s, 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 v_s is the velocity of the object (source of waves) with respect to the medium, and 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

Astronomy

Astronomy is the science of Astronomical object and Phenomenon that originate outside the Earth's atmosphere . It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the physical cosmology....
and results in either a so-called redshift

Redshift

In physics and astronomy, redshift occurs when electromagnetic radiation?usually visible light?emitted or reflected by an object is shifted towards the red end of the electromagnetic spectrum due to the Doppler effect....
or blue shift

Blue Shift

"Blue Shift" is the tenth story chronologically to appear in Stephen Baxter's science fiction anthology novel Vacuum Diagrams. "Blue Shift" was originally published in Writers of the Future volume 5 in 1989....
. It has been used to measure the speed at which star

Star

A star is a massive, luminous ball of Plasma that is held together by its own gravity. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth....
s and galaxies

Galaxy

A galaxy is a massive, gravitation system that consists of stars and stellar remnants, an interstellar medium of gas and cosmic dust, and an important but poorly-understood component tentatively dubbed dark matter....
are approaching or receding from us, that is, the radial velocity
Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
. This is used to detect if an apparently single star is, in reality, a close binary

Binary star

A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star or secondary....
and even to measure the rotational speed of stars and galaxies.

The use of the Doppler effect for light in astronomy

Astronomy

Electromagnetic spectroscopy

Electromagnetic spectroscopy is the spectroscopy of electromagnetic spectrum which arise out of atoms absorbing and emitting quanta of electromagnetic radiation....
of stars are not continuous. They exhibit absorption lines

Spectral line

A spectral line is a dark or bright line in an otherwise uniform and continuous optical spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies....
at well defined frequencies that are correlated with the energies required to excite electron

Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
s in various elements

Chemical element

A chemical element is a type of atom that is distinguished by its atomic number; that is, by the number of protons in its atomic nucleus. The term is also used to refer to a pure chemical Chemical substance composed of atoms with the same number of protons....
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 blue shift and those of a receding astronomical light source exhibit a redshift.

Among the nearby stars

List of nearest stars

This list of stars nearest to the Earth is ordered by increasing distance out to a maximum of 5 parsecs . Including the Solar System, there are currently 50 stellar systems known which may lie within this distance....
, the largest radial velocities with respect to the Sun

Sun

The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....
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 velocity means the star is receding from the Sun, negative that it is approaching.

Temperature measurement

Another use of the Doppler effect, which is found mostly in plasma physics and astronomy, is the estimation of the temperature of a gas (or ion temperature in a plasma) which is emitting a spectral line

Spectral line

A spectral line is a dark or bright line in an otherwise uniform and continuous optical spectrum, resulting from an excess or deficiency of photons in a narrow frequency range, compared with the nearby frequencies....
. Due to the thermal motion of the emitters, the light emitted by each particle can be slightly red- or blue-shifted, and the net effect is a broadening of the line. This line shape is called a Doppler profile

Doppler broadening

In atomic physics, Doppler broadening is the broadening of spectral lines due to the Doppler effect in which the heat movement of atoms or molecules shifts the apparent frequency of each emitter....
and the width of the line is proportional to the square root of the temperature of the emitting species, allowing a spectral line (with the width dominated by the Doppler broadening) to be used to infer the temperature.

Radar

The Doppler effect is used in some types of radar

Radar

Radar is a system that uses electromagnetic radiation waves to identify the range, altitude, direction, or speed of both moving and fixed objects such as aircraft, ships, motor vehicles, weather formations, and terrain....
, 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 velocity. Moreover, the proximity fuze

Proximity fuze

A proximity fuze is a Fuse #Munition_fuses that is designed to detonate an Explosive material device automatically when the distance to target becomes smaller than a predetermined value or when the target passes through a given plane....
, developed during World War II, relies upon Doppler radar to explode at the correct time, height, distance, et cetera.

Medical imaging and blood flow measurement

An echocardiogram can, within certain limits, produce 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

Ultrasound

Ultrasound is cyclic sound pressure with a frequency greater than the upper limit of human hearing . Although this limit varies from person to person, it is approximately 20 Hertz in healthy, young adults and thus, 20 kHz serves as a useful lower limit in describing ultrasound....
beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, any abnormal communications between the left and right side of the heart, any leaking of blood through the valves (valvular regurgitation), and calculation of the cardiac output

Cardiac output

Cardiac output is the volume of blood being pumped by the heart, in particular by a ventricle in a minute. This is measured in dm3 min-1 ....
. 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

Medical ultrasonography

Diagnostic sonography is an ultrasound-based diagnostic medical imaging technique used to visualize subcutaneous body structures including tendons, muscles, joints, vessels and internal organs for possible pathology or lesions....
, such as obstetric ultrasonography

Obstetric ultrasonography

Obstetric sonography is the application of medical ultrasonography to obstetrics, in which ultrasound is used to visualize the embryo or fetus in its mother's uterus ....
and neurology

Neurology

Neurology is a medical specialty dealing with disorders of the nervous system. Specifically, it deals with the diagnosis and treatment of all categories of disease involving the Central nervous system, Peripheral nervous system, and autonomic nervous systems, including their coverings, blood vessels, and...
. 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

Laser Doppler velocimetry

Laser Doppler Velocimetry is a technique for measuring the direction and speed of fluids like Earth's atmosphere and water. In its simplest form, LDV crosses two beams of collimated, monochromatic, and coherent laser light in the flow of the fluid being measured....
(LDV), and Acoustic

Acoustics

Acoustics is the interdisciplinary science that deals with the study of sound, ultrasound and infrasound . A scientist who works in the field of acoustics is an acoustician....
Doppler Velocimeter (ADV) have been developed to measure velocities

Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
in a fluid flow. The LDV emits a light beam and the 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 face. 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 flows), 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.

Underwater acoustics

In military applications the Doppler shift of a target is used to ascertain the speed of a submarine

Submarine

A submarine is a watercraft capable of independent operation below water. It differs from a submersible, which has only limited underwater capability....
using both passive and active sonar

Sonar

Sonar is a technique that uses sound propagation to navigation, communicate with or detect other vessels. There are two kinds of sonar: active and passive....
systems. As a submarine passes by a passive sonobuoy

Sonobuoy

A sonobuoy is a relatively small expendable sonar system that is dropped/ejected from aircraft or ships conducting anti-submarine warfare or underwater acoustics research....
, the stable frequencies undergo a Doppler shift, and the speed and range from the sonobuoy can be calculated. If the sonar system is mounted on a moving ship or another submarine, then the relative velocity

Velocity

In physics, velocity is defined as the Derivative of Position vector. It is a vector physical quantity; both speed and direction are required to define it....
can be calculated.

Audio

The Leslie speaker

Leslie speaker

The Leslie speaker is a specially constructed amplifier/loudspeaker used to create special audio effects utilizing the Doppler effect. Named after its inventor, Donald Leslie, it is particularly associated with the Hammond organ....
, associated with and predominantly used with the Hammond B-3 Organ

Hammond organ

The Hammond organ is an electronic organ which was invented by Laurens Hammond in 1934 and manufactured by the Hammond Organ Company. While the Hammond organ was originally sold to Church as a lower-cost alternative to the wind-driven pipe organ, in the 1960s and 1970s, it became a standard keyboard instrument for jazz, blues, Rock and r...
, takes advantage of the Doppler Effect by using an electric motor

Electric motor

An electric motor uses electrical energy to produce mechanical energy, nearly always by the interaction of magnetic fields and current-carrying conductors....
to rotate a speaker continuously, rapidly alternating the received frequency of a keyboard note.

External links

, ScienceWorld
ScienceWorld

ScienceWorld, also known as Eric Weisstein's World of Science, is a Web site that opened to the general public in January 2002. As of November 2007, ScienceWorld includes more than 4,000 entries in fields of science including astronomy, chemistry, physics, as well as biographies of many scientists....
at MathPages
- Doppler flow meters with engineering examples and applications
from John de Pillis. An animation showing that the speed of a moving wave source does not affect the speed of the wave.
from John de Pillis. How an electromagnetic wave propagates through a vacuum
- Ultrasonic Doppler Velocimeters for real time measurement of velocity profiles in liquids
- Interactive flash simulation for demonstrating Doppler shift.
Excellent interactive applet, go to applet thumbnails>upcoming applets.

Doppler effect

Development

General

Analysis

A common misconception

Applications

Sirens

Astronomy

Temperature measurement

Radar

Medical imaging and blood flow measurement

Flow measurement

Velocity profile measurement

Underwater acoustics

Audio

See also

Further reading

External links