Doppler effect

A change in the observed frequency of a wave, as of sound or light, occurring when the source and observer are in motion relative to each other, with the frequency increasing when the source and observer approach each other and decreasing when they move apart. The motion of the source causes a real shift in frequency of the wave, while the motion of the observer produces only an apparent shift in frequency. Also called Doppler shift.

[After Christian Johann DOPPLER.]

Concept

Almost everyone has experienced the Doppler effect, though perhaps without knowing what causes it. For example, if one is standing on a street corner and an ambulance approaches with its siren blaring, the sound of the siren steadily gains in pitch as it comes closer. Then, as it passes, the pitch suddenly lowers perceptibly. This is an example of the Doppler effect: the change in the observed frequency of a wave when the source of the wave is moving with respect to the observer. The Doppler effect, which occurs both in sound and electromagnetic waves—including light waves—has a number of applications. Astronomers use it, for instance, to gauge the movement of stars relative to Earth. Closer to home, principles relating to the Doppler effect find application in radar technology. Doppler radar provides information concerning weather patterns, but some people experience it in a less pleasant way: when a police officer uses it to measure their driving speed before writing a ticket.

How It Works

Wave Motion and Its Properties

Sound and light are both examples of energy, and both are carried on waves. Wave motion is a type of harmonic motion that carries energy from one place to another without actually moving any matter. It is related to oscillation, a type of harmonic motion in one or more dimensions. Oscillation involves no net movement, only movement in place; yet individual points in the wave medium are oscillating even as the overall wave pattern moves.

The term periodic motion, or movement repeated at regular intervals called periods, describes the behavior of periodic waves—waves in which a uniform series of crests and troughs follow each other in regular succession. A period (represented by the symbol T) is the amount of time required to complete one full cycle of the wave, from trough to crest and back to trough.

Period is mathematically related to several other aspects of wave motion, including wave speed, frequency, and wavelength. Frequency (abbreviated f) is the number of waves passing through a given point during the interval of one second. It is measured in Hertz (Hz), named after nineteenth-century German physicist Heinrich Rudolf Hertz (1857-1894), and a Hertz is equal to one cycle of oscillation per second. Higher frequencies are expressed in terms of kilohertz (kHz; 10³ or 1,000 cycles per second); megahertz (MHz; 10⁶ or 1 million cycles per second); and gigahertz (GHz; 10⁹ or 1 billion cycles per second.) Wavelength (represented by the symbol λ, the Greek letter lambda) is the distance between a crest and the adjacent crest, or a trough and an adjacent trough, of a wave. The higher the frequency, the shorter the wavelength.

Amplitude, though mathematically independent from the parameters discussed, is critical to the understanding of sound. Defined as the maximum displacement of a vibrating material, amplitude is the "size" of a wave. The greater the amplitude, the greater the energy the wave contains: amplitude indicates intensity, which, in the case of sound waves, is manifested as what people commonly call "volume." Similarly, the amplitude of a light wave determines the intensity of the light.

Frame of Reference

A knowledge of the fundamentals involved in wave motion is critical to understanding the Doppler effect; so, too, is an appreciation of another phenomenon, which is as much related to human psychology and perception as it is to physics. Frame of reference is the perspective of an observer with regard to an object or event. Things may look different for one person in one frame of reference than they do to someone in another.

For example, if you are sitting across the table from a friend at lunch, and you see that he has a spot of ketchup to the right of his mouth, the tendency is to say, "You have some ketchup right here"—and then point to the left of your own mouth, since you are directly across the table from his right. Then he will rub the left side of his face with his napkin, missing the spot entirely, unless you say something like, "No—mirror image." The problem is that each of you has a different frame of reference, yet only your friend took this into account.

Relative Motion

Physicists often speak of relative motion, or the motion of one object in relation to another. For instance, the molecules in the human body are in a constant state of motion, but they are not moving relative to the body itself: they are moving relative to one another.

On a larger scale, Earth is rotating at a rate of about 1,000 MPH (1,600 km/h), and orbiting the Sun at 67,000 MPH (107,826 km/h)—almost three times as fast as humans have ever traveled in a powered vehicle. Yet no one senses the speed of Earth's movement in the way that one senses the movement of a car—or, indeed, the way the astronauts aboard Apollo 11 in 1969 perceived that their spacecraft was moving at about 25,000 MPH (40,000 km/h). In the case of the car or the spacecraft, movement can be perceived in relation to other objects: road signs and buildings on the one hand, Earth and the Moon on the other. But humans have no frame of reference from which to perceive the movement of Earth itself.

If one were traveling in a train alongside another train at constant velocity, it would be impossible to perceive that either train was actually moving, unless one looked at a reference point, such as the trees or mountains in the background. Likewise, if two trains were sitting side by side, and one train started to move, the relative motion might cause a passenger in the unmoving train to believe that his or her train was the one moving. In fact, as Albert Einstein (1879-1955) demonstrated with his Theory of Relativity, all motion is relative: when we say that something is moving, we mean that it is moving in relation to something else.

Doppler's Discovery

Long before Einstein was born, Austrian physicist Christian Johann Doppler (1803-1853) made an important discovery regarding the relative motion of sound waves or light waves. While teaching in Prague, now the capital of the Czech Republic, but then a part of the Austro-Hungarian Empire, Doppler became fascinated with a common, but previously unexplained, phenomenon. When an observer is standing beside a railroad track and a train approaches, Doppler noticed, the train's whistle has a high pitch. As it passes by, however, the sound of the train whistle suddenly becomes much lower.

By Doppler's time, physicists had recognized the existence of sound waves, as well as the fact a sound's pitch is a function of frequency—in other words, the closer the waves are to one another, the higher the pitch. Taking this knowledge, he reasoned that if a source of sound is moving toward a listener, the waves in front of the source are compressed, thus creating a higher frequency. On the other hand, the waves behind the moving source are stretched out, resulting in a lower frequency.

After developing a mathematical formula to describe this effect, Doppler presented his findings in 1842. Three years later, he and Dutch meteorologist Christopher Heinrich Buys-Ballot (1817-1890) conducted a highly unusual experiment to demonstrate the theory. Buys-Ballot arranged for a band of trumpet players to perform on an open railroad flatcar, while riding past a platform on which a group of musicians with perfect pitch (that is, a finely tuned sense of hearing) sat listening.

The experiment went on for two days, the flatcar passing by again and again, while the horns blasted and the musicians on the platform recorded their observations. Though Doppler and Buys-Ballot must have seemed like crazy men to those who were not involved in the experiment, the result—as interpreted from the musicians' written impressions of the pitches they heard—confirmed Doppler's theory.

Real-Life Applications

Sound Compression and the Doppler Effect

As stated in the introduction, one can observe the Doppler effect in a number of settings. If a person is standing by the side of a road and a car approaches at a significant rate of speed, the frequency of the sound waves grows until the car passes the observer, then the frequency suddenly drops. But Doppler, of course, never heard the sound of an automobile, or the siren of a motorized ambulance or fire truck.

In his day, the horse-drawn carriage still constituted the principal means of transportation for short distances, and such vehicles did not attain the speeds necessary for the Doppler effect to become noticeable. Only one mode of transportation in the mid-nineteenth century made it possible to observe and record the effect: a steam-powered locomotive. Therefore, let us consider the Doppler effect as Doppler himself did—in terms of a train passing through a s tation.

The Sound of a Train Whistle

When a train is sitting in a station prior to leaving, it blows its whistle, but listeners standing nearby notice nothing unusual. There is no difference—except perhaps in degree of intensity—between the sound heard by someone on the platform, and the sound of the train as heard by someone standing behind the caboose. This is because a stationary train is at the center of the sound waves it produces, which radiate in concentric circles (like a bulls-eye) around it.

As the train begins to move, however, it is no longer at the center of the sound waves emanating from it. Instead, the circle of waves is moving forward, along with the train itself, and, thus, the locomotive compresses waves toward the front. If someone is standing further ahead along the track, that person hears the compressed sound waves. Due to their compression, these have a much higher frequency than the waves produced by a stationary train.

At the same time, someone standing behind the train—a listener on the platform at the station, watching the train recede into the distance—hears the sound waves that emanate from behind the train. It is the same train making the same sound, but because the train has compressed the sound waves in front of it, the waves behind it are spread out, producing a sound of much lower frequency. Thus, the sound of the train, as perceived by two different listeners, varies with frame of reference.

The Sonic Boom: a Related Effect

Some people today have had the experience of hearing a jet fly high overhead, producing a shock wave known as a sonic boom. A sonic boom, needless to say, is certainly not something of which Doppler would have had any knowledge, nor is it an illustration of the Doppler effect, per se. But it is an example of sound compression, and, therefore, it deserves attention here.

The speed of sound, unlike the speed of light, is dependant on the medium through which it travels. Hence, there is no such thing as a fixed "speed of sound"; rather, there is only a speed at which sound waves are transmitted through a given type of material. Its speed through a gas, such as air, is proportional to the square root of the pressure divided by the density. This, in turn, means that the higher the altitude, the slower the speed of sound: for the altitudes at which jets fly, it is about 660 MPH (1,622 km/h).

As a jet moves through the air, it too produces sound waves which compress toward the front, and widen toward the rear. Since sound waves themselves are really just fluctuations in pressure, this means that the faster a jet goes, the greater the pressure of the sound waves bunched up in front of it. Jet pilots speak of "breaking the sound barrier," which is more than just a figure of speech. As the craft approaches the speed of sound, the pilot becomes aware of a wall of high pressure to the front of the plane, and as a result of this high-pressure wall, the jet experiences enormous turbulence.

The speed of sound is referred to as Mach 1, and at a speed of between Mach 1.2 and Mach 1.4, even stranger things begin to happen. Now the jet is moving faster than the sound waves emanating from it, and, therefore, an observer on the ground sees the jet move by well before hearing the sound. Of course, this would happen to some extent anyway, since light travels so much faster than sound; but the difference between the arrival time of the light waves and the sound waves is even more noticeable in this situation.

Meanwhile, up in the air, every protruding surface of the aircraft experiences intense pressure: in particular, sound waves tend to become highly compressed along the aircraft's nose and tail. Eventually these compressed sound waves build up, resulting in a shock wave. Down on the ground, the shock wave manifests as a "sonic boom"—or rather, two sonic booms—one from the nose of the craft, and one from the tail. People in the aircraft do not hear the boom, but the shock waves produced by the compressed sound can cause sudden changes in pressure, density, and temperature that can pose dangers to the operation of the airplane. To overcome this problem, designers of supersonic aircraft have developed planes with wings that are swept back, so they fit within the cone of pressure.

Doppler Radar and Other Sensing Technology

The Doppler effect has a number of applications relating to the sensing of movement. For instance, physicians and medical technicians apply it to measure the rate and direction of blood flow in a patient's body, along with ultra-sound. As blood moves through an artery, its top speed is 0.89 MPH (0.4 m/s)—not very fast, yet fast enough, given the small area in which movement is taking place, for the Doppler effect to be observed. A beam of ultrasound is pointed toward an artery, and the reflected waves exhibit a shift in frequency, because the blood cells are acting as moving sources of sound waves—just like the trains Doppler observed.

Not all applications of the Doppler effect fall under the heading of "technology": some can be found in nature. Bats use the Doppler effect to hunt for prey. As a bat flies, it navigates by emitting whistles and listening for the echoes. When it is chasing down food, its brain detects a change in pitch between the emitted whistle, and the echo it receives. This tells the bat the speed of its quarry, and the bat adjusts its own speed accordingly.

Doppler Radar

Police officers may not enjoy the comparison—given the public's general impression of bats as evil, blood-thirsty creatures—but in using radar as a basis to check for speeding violations, the police are applying a principle similar to that used by bats. Doppler radar, which uses the Doppler effect to calculate the speed of moving objects, is a form of technology used not only by law-enforcement officers, but also by meteorologists.

The change in frequency experienced as a result of the Doppler effect is exactly twice the ratio between the velocity of the target (for instance, a speeding car) and the speed with which the radar pulse is directed toward the target. From this formula, it is possible to determine the velocity of the target when the frequency change and speed of radar propagation are known. The police officer's Doppler radar performs these calculations; then all the officer has to do is pull over the speeder and write a ticket.

Meteorologists use Doppler radar to track the movement of storm systems. By detecting the direction and velocity of raindrops or hail, for instance, Doppler radar can be used to determine the motion of winds and, thus, to predict weather patterns that will follow in the next minutes or hours. But Doppler radar can do more than simply detect a storm in progress: Doppler technology also aids meteorologists by interpreting wind direction, as an indicator of coming storms.

The Doppler Effect in Light Waves

So far the Doppler effect has been discussed purely in terms of sound waves; but Doppler himself maintained that it could be applied to light waves as well, and experimentation conducted in 1901 proved him correct. This was far from an obvious point, since light is quite different from sound.

Not only does light travel much, much faster—186,000 mi (299,339 km) a second—but unlike sound, light does not need to travel through a medium. Whereas sound cannot be transmitted in outer space, light is transmitted by radiation, a form of energy transfer that can be directed as easily through a vacuum as through matter.

The Doppler effect in light can be demonstrated by using a device called a spectroscope, which measures the spectral lines from an object of known chemical composition. These spectral lines are produced either by the absorption or emission of specific frequencies of light by electrons in the source material. If the light waves appear at the blue, or high-frequency end of the visible light spectrum, this means that the object is moving toward the observer. If, on the other hand, the light waves appear at the red, or low-frequency end of the spectrum, the object is moving away.

Hubble and the Red Shift

In 1923, American astronomer Edwin Hubble (1889-1953) observed that the light waves from distant galaxies were shifted so much to the red end of the light spectrum that they must be moving away from the Milky Way, the galaxy in which Earth is located, at a high rate. At the same time, nearer galaxies experienced much less of a red shift, as this phenomenon came to be known, meaning that they were moving away at relatively slower speeds.

Six years later, Hubble and another astronomer, Milton Humason, developed a mathematical formula whereby astronomers could determine the distance to another galaxy by measuring that galaxy's red shifts. The formula came to be known as Hubble's constant, and it established the relationship between red shift and the velocity at which a galaxy or object was receding from Earth. From Hubble's work, it became clear that the universe was expanding, and research by a number of physicists and astronomers led to the development of the "big bang" theory—the idea that the universe emerged almost instantaneously, in some sort of explosion, from a compressed state of matter.

Where to Learn More

Beiser, Arthur. Physics, 5th ed. Reading, MA: Addison-Wesley, 1991.

Bryant-Mole, Karen. Sound and Light. Crystal Lake, IL: Rigby Interactive Library, 1997.

Challoner, Jack. Sound and Light. New York: Kingfisher, 2001.

Dispenzio, Michael A. Awesome Experiments in Light and Sound. Illustrated by Catherine Leary. New York: Sterling Publishing Company, 1999.

"The Doppler Effect." The Physics Classroom (Web site). <http://www.glenbrook.k12.il.us/gbssci/phys/Class/waves/u10l3d.html> (April 29, 2001).

Maton, Anthea. Exploring Physical Science. Upper Saddle River, N.J.: Prentice Hall, 1997.

Russell, David A. "The Doppler Effect and Sonic Booms" Kettering University (Web site). <http://www.kettering.edu/~drussell/Demos/doppler/doppler.html> (April 29, 2001).

Snedden, Robert. Light and Sound. Des Plaines, IL: Heinemann Library, 1999.

"Sound Wave—Doppler Effect" (Web site). <http://csgrad.cs.vt.edu/~chin/doppler.html> (April 29, 2001).

"Wave Motion—Doppler Effect" (Web site). <http://members.aol.com/cepeirce/b21.html> (April 29, 2001).

The change in the frequency of a wave observed at a receiver whenever the source or the receiver of the wave is moving relative to the other or to the carrier of the wave (the medium). The effect was predicted in 1842 by C. Doppler, and first verified for sound waves in 1845 from experiments conducted on a moving train.

The Doppler effect for sound waves is now a commonplace experience: If one is passed by a fast car or a plane, the pitch of its noise is considerably higher in approaching than in parting. The same phenomenon is observed if the source is at rest and the receiver is passing it. The linear optical Doppler effect was first observed in 1905 from a shift of spectral lines emitted by a beam of fast ions (canal rays) emerging from a hole in the cathode of a gas discharge tube run at high voltage. Still, their velocity was several orders of magnitude below that of light in vacuum. The precise interferometric experiments of A. A. Michelson and E. W. Morley (1887) showed clearly that the velocity of light is not bound to any ether, but is measured to be the same in any moving system. This result was a crucial check for A. Einstein's theory of special relativity (1905), which also makes a clear prediction for the optical Doppler effect.

The Doppler effect has important applications in remote-sensing, high-energy physics, astrophysics, and spectroscopy.

Let a wave from a sound source or radar source, or from a laser, be reflected from a moving object back to the source, which may itself move as well. Then a frequency shift is observed by a receiver connected to the source. The measurement provides an excellent means for the remote sensing of velocities of any kind of object, including cars, ships, planes, satellites, flows of fluids, or winds. See also Doppler radar; Remote sensing.

The light from distant stars and galaxies shows a strong Doppler shift to the red, indicating that the universe is rapidly expanding. However, this effect can be mixed up with the gravitational redshift that results from the energy loss which a light quantum suffers when it emerges from a strong gravitational field.

The Doppler width and Doppler shift of spectral lines in sunlight (Fraunhofer lines) are important diagnostic tools for the dynamics of the Sun's atmosphere, indicating its temperature and turbulence. See also Astronomical spectroscopy; Cosmology; Gravitational redshift; Redshift; Sun.

The change in electromagnetic frequency that occurs when the source of the radiation and its observer move toward or away from each other. The faster they come together, the higher the frequency. The faster they move away, the lower the frequency. Discovered by Austrian physicist Christian Doppler (1803-1853), this condition has a great effect on low-earth orbit (LEO) satellites as they weave towards and away from the earth. See Doppler radar.

Download Computer Desktop Encyclopedia to your iPhone/iTouch

The phenomenon evidenced by the change in the observed frequency of a sound or radio wave caused by a time rate of change in the effective length of the path of travel between the source and the point of observation.

See the Introduction, Abbreviations and Pronunciation for further details.

For more information on Doppler effect, visit Britannica.com.

The Austrian physicist Christian Doppler (1803-1853) in 1842 explained the phenomenon of the apparent change in wavelength of radiation-such as sound or light-emitted either by a moving body (source) or by the moving receiver. The frequency of the wavelengths increases and the wavelength becomes shorter as the moving source approaches, producing high-pitched sounds and bluish light (called blue shift). Likewise, as the source recedes from the receiver the frequency of the wavelengths decreases, the sound is pitched lower, and light appears reddish (called red shift). This Doppler effect is commonly demonstrated by the whistle of an approaching train or the roar of a jet aircraft.

There are three differences between acoustical (sound) and optical (light) Doppler effects: The optical frequency change is not dependent on which is moving-the source or observer-nor is it affected by the medium through which the waves are moving, but acoustical frequency is affected by such conditions. Optical frequency changes are affected if the source or observer moves at right angles to the line connecting the source and observer. Observed acoustical changes are not affected in such a situation. Applications of the Doppler phenomenon include the Doppler radar and the measurement by astronomers of the motion and direction of celestial bodies.

A phenomenon observed with waves. The frequency of a wave of light or sound seems higher if the source is moving toward the observer and seems lower if the source is moving away. For example, if an automobile blows its horn as it travels past someone, the apparent pitch of the sound will be higher as it approaches the person and then will grow lower as it passes and moves away.

(DOD, NATO) The phenomenon evidenced by the change in the observed frequency of a sound or radio wave caused by a time rate of change in the effective length of the path of travel between the source and the point of observation.

This article needs additional citations for verification. Please help improve this article by adding reliable references. Unsourced material may be challenged and removed. (January 2008)

A source of waves moving to the left. The frequency is higher on the left than on the right.

The Doppler effect (or Doppler shift), named after Austrian physicist Christian Doppler who proposed it in 1842, is the change in frequency of a wave for an observer moving relative to the source of the wave. It is commonly heard when a vehicle sounding a siren or horn approaches, passes, and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession.

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 general relativity, only the relative difference in velocity between the observer and the source needs to be considered.

Contents 1 Development 2 General 3 Analysis 4 A common misconception 5 Applications 5.1 Sirens 5.2 Astronomy 5.3 Temperature measurement 5.4 Radar 5.5 Medical imaging and blood flow measurement 5.6 Flow measurement 5.7 Velocity profile measurement 5.8 Underwater acoustics 5.9 Audio 5.10 Vibration Measurement 6 See also 7 Notes 8 Further reading 9 External links

Development

Doppler first proposed the 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).^[1] 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).^[2]

An English translation of Doppler's 1842 treatise can be found in the book The Search for Christian Doppler by Alec Eden.^[1]

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 v_s and v_r 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 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 v_s,r = v_s − v_r.

However the limitations mentioned above still apply. When the more complicated exact equation is derived without using any approximations (just assuming that source, receiver, and wave or signal are moving linearly relatively to each other) 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 conclusions 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 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 derived for the classical, i.e., non-relativistic, Doppler effect, but hold for the relativistic Doppler effect as well.^{[citation needed]}

The first attempt to extend Doppler's analysis to light waves was soon made by Fizeau. However, light waves do not require a medium to propagate, and correct understanding of the Doppler effect for light requires knowledge of the special theory of relativity. See relativistic Doppler effect.

A common misconception

Craig Bohren pointed out in 1991 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 and that this change in intensity is misperceived as a change in frequency.

Applications

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 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 θ is the angle between the object's forward velocity and the line of sight from the object to the observer.

Astronomy

Redshift of spectral lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to that of the Sun (left).

The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blue shift. 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 blue shift and those of a receding astronomical light source exhibit a redshift.

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 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. 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 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

Main article: Doppler 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 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, developed during World War II, relies upon Doppler radar to explode at the correct time, height, distance, etc.

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 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. 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.^[4]

Flow measurement

Instruments such as the laser Doppler velocimeter (LDV), and acoustic Doppler velocimeter (ADV) have been developed to measure velocities 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 using both passive and active sonar systems. As a submarine passes by a passive sonobuoy, 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 can be calculated.

Audio

The Leslie speaker, associated with and predominantly used with the Hammond B-3 Organ, takes advantage of the Doppler Effect by using an electric motor to rotate a horn around a speaker continuously, rapidly alternating the received frequency of a keyboard note.

Vibration Measurement

A Laser Doppler Vibrometer (LDV) is a non-contact method for measuring vibration. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the laser beam frequency due to the motion of the surface.

See also

• Relativistic Doppler effect
• Dopplergraph
• Fizeau experiment
• Fading
• Photoacoustic Doppler effect
• Rayleigh fading

Notes

1. ^ ^{a b} Alec Eden The search for Christian Doppler,Springer-Verlag, Wien 1992. Contains a facsimile edition with an English translation.
2. ^ Scott Russell, John (1848). "On certain effects produced on sound by the rapid motion of the observer". Report of the Eighteen Meeting of the British Association for the Advancement of Science (John Murray, London in 1849) 18 (7): 37–38. http://www.ma.hw.ac.uk/~chris/doppler.html. Retrieved 2008-07-08. 
3. ^ Bohren, C. F. (1991). What light through yonder window breaks? More experiments in atmospheric physics. New York: J. Wiley.
4. ^ D. H. Evans and W. N. McDicken, Doppler Ultrasound, Second Edition, John Wiley and Sons, 2000.

Further reading

• "Doppler and the Doppler effect", E. N. da C. Andrade, Endeavour Vol. XVIII No. 69, January 1959 (published by ICI London). Historical account of Doppler's original paper and subsequent developments.
• Adrian, Eleni (24 June, 1995). "Doppler Effect". NCSA. http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html. Retrieved 2008-07-13. 

External links

Wikimedia Commons has media related to: Doppler effect

• Doppler Effect, ScienceWorld
• Java simulation of Doppler effect
• Doppler Shift for Sound and Light at MathPages
• The Doppler Effect and Sonic Booms (D.A. Russell, Kettering University)
• Video Mashup with Doppler Effect videos
• Practical Doppler flow meters- Doppler flow meters with engineering examples and applications
• Wave Propagation from John de Pillis. An animation showing that the speed of a moving wave source does not affect the speed of the wave.
• EM Wave Animation from John de Pillis. How an electromagnetic wave propagates through a vacuum
• Signal-Processing - Ultrasonic Doppler Velocimeters for real time measurement of velocity profiles in liquids
• Doppler Shift Demo - Interactive flash simulation for demonstrating Doppler shift.
• [1] Excellent interactive applet, go to applet thumbnails>upcoming applets.

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)