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If the wave source moves relative to the medium, then the distance between the wave crests (wavelength) depends on the speed and direction of movement. If the source moves towards the receiver, that is, it catches up with the wave it emits, then the wavelength decreases. If removed, the wavelength increases.

The wave frequency in general depends only on how fast the receiver is moving

As soon as the wave has gone from the source, the speed of its propagation is determined only by the properties of the medium in which it propagates, while the source of the wave no longer plays any role. On the surface of water, for example, waves, having been excited, then propagate only due to the interaction of forces of pressure, surface tension and gravity. Acoustic waves propagate in air (and other sound-conducting media) due to the directional transfer of the pressure difference. And none of the wave propagation mechanisms depends on the wave source. Hence and doppler effect.

To make it clearer, consider an example on a car with a siren.

Let's assume for a start that the car is stationary. The sound from the siren reaches us because the elastic membrane inside it periodically affects the air, creating compression in it - areas of increased pressure - alternating with discharges. Compression peaks - the “crests” of an acoustic wave - travel through the medium (air) until they reach our ears and act on the eardrums. So, while the car is standing, we will still hear the unchanged tone of its signal.

But as soon as the car starts to move in your direction, a new one will be added the effect... During the time from the moment of emission of one peak of the wave to the next, the car will travel a certain distance towards you. Because of this, the source of each next peak of the wave will be closer. As a result, the waves will reach your ears more often than they did while the car was stationary, and the pitch of the sound you perceive will increase. Conversely, if the car drives in the opposite direction with the beep, the acoustic peaks will reach your ears less often and the perceived frequency of the sound will decrease.

Essential in astronomy, sonar and radar. In astronomy, the Doppler shift of a certain frequency of the emitted light can be used to judge the speed of a star along its line of observation. The most surprising result is the observation of the Doppler shift in the frequencies of light in distant galaxies: the so-called redshift indicates that all galaxies are moving away from us at speeds up to about half the speed of light, increasing with distance. The question of whether the Universe is expanding in this way or whether the redshift is due to something other than the "recession" of galaxies remains open.

The Doppler effect is a physical phenomenon that changes the frequency of waves depending on the movement of the source of these waves relative to the observer. As the source approaches, the frequency of the waves emitted by it increases, and the length decreases. As the wave source moves away from the observer, their frequency decreases and the wavelength increases.

For example, in the case of sound waves, the sound pitch decreases as the source moves away, and the sound becomes higher as it approaches. So, by changing the pitch, you can determine whether a train is approaching or moving away, a car with a special sound signal, etc. Electromagnetic waves also exhibit the Doppler effect. The observer will notice a shift of the spectrum towards the "red" side in case of removal of the source; in the direction of longer waves, and when approaching - in the "violet", i.e. towards shorter waves.

The Doppler effect turned out to be an extremely useful discovery. Thanks to him, the expansion of the Universe was discovered (the spectra of galaxies are shifted to the red side, therefore, they are moving away from us); a method for the diagnosis of the cardiovascular system has been developed by determining the blood flow velocity; various radars have been created, including those used by the traffic police.

The most popular example of the propagation of the Doppler effect: a car with a siren. When she goes to or from you, you hear one sound, and when she drives by, then a completely different sound - a lower one. The Doppler effect is associated not only with sound waves, but also with any others. Using the Doppler effect, you can determine the speed of something, be it a car or celestial bodies, provided that we know the parameters (frequency and wavelength). Everything related to telephone networks, Wi-Fi, burglar alarms - the Doppler effect can be observed everywhere.

Or take a traffic light - it has red, yellow and green colors. Depending on the speed at which we are moving, these colors can change, but not among themselves, but shift towards purple: yellow will go to green, and green to blue.

Why not? If we move away from the light source and look back (or the traffic light moves away from us), then the colors will shift towards red.

And, probably, it is worth clarifying that the speed at which red can be confused with green is much higher than that at which you can drive on the roads.

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The essence of the Doppler effect is that if a sound source approaches the observer or moves away from him, then the frequency of the sound emitted by him changes from the point of view of the observer. This, for example, changes the sound of the engine of a car driving by you. It is higher as it approaches you and drops sharply as it flies past you and begins to recede. The higher the speed of the sound source, the stronger the change in frequency.

By the way, this effect is valid not only for sound, but also, say, for light. It's just clearer for sound - it can be observed at relatively low speeds. Visible light has such a high frequency that small changes due to the Doppler effect are invisible to the naked eye. However, in some cases, the Doppler effect should be taken into account even in radio communications.

If you do not delve into strict definitions and try to explain the effect, as they say, on the fingers, then everything is quite simple. Sound (like light or radio signal) is a wave. For clarity, let's assume that the frequency of the received wave depends on how often we receive the "crests" of the schematic wave (dropboxusercontent.com). If the source and receiver are stationary (yes, relative to each other), then we will receive "ridges" with the same frequency with which the receiver emits them. If the source and receiver begin to approach each other, then we will begin to receive the more often, the higher the approach speed - the speeds will add up. As a result, the sound frequency at the receiver will be higher. If the source begins to move away from the receiver, then each next "ridge" will take a little more time to reach the receiver - we will begin to receive "ridges" a little less often than the source emits them. The sound frequency at the receiver will be lower.

This explanation is somewhat schematic, but it reflects the general principle.

In short, the change in the observed frequency and wavelength in the event that the source and receiver move relative to each other. It is associated with the finiteness of the wave propagation speed. If the source approaches the receiver, the frequency increases (the peak of the wave is recorded more often); move away from each other - the frequency drops (the peak of the wave is recorded less often). A common illustration of the effect is the siren of the special services. If an ambulance drives up to you - the siren squeals, drives off - it buzzes in a bass. A separate case - the propagation of an electromagnetic wave in a vacuum - there is also added a relativistic component and the Doppler effect is also manifested in the case when the receiver and the source are stationary relative to each other, which is explained by the properties of time.

The essence of the Doppler effect is the dependence of the oscillation frequency on the speed of the oscillation source relative to the receiver. For example, if you throw a tuning fork away from you, the sound will seem lower (the vibration frequency will decrease), and if the tuning fork is thrown at you, the sound will seem higher to you (the vibration frequency will increase). This also applies to vibrations of other nature - light and radio waves. Notable examples. 1) Due to the shift of the radiation of distant stars down the spectrum, towards the red color, the hypothesis of an "expanding universe" arose. 2) Homing missiles aiming at high-speed targets (aircraft and enemy missiles) on a radio wave reflected from the targets receive oscillations of a changed frequency, this change is called "Doppler shift", and radio heads are sometimes called "Doppler".

The Doppler effect is described by the formula:

where is the frequency of the wave recorded by the receiver; - the frequency of the wave emitted by the source; - in the environment; and are the speeds of the receiver and the source relative to the elastic medium, respectively.

If the sound source approaches the receiver, then its speed has a plus sign. If the source moves away from the receiver, its velocity has a minus sign.

It can be seen from the formula that with such a movement of the source and receiver, at which the distance between them decreases, the frequency perceived by the receiver turns out to be greater than the frequency of the source. If the distance between the source and receiver increases, it will be less than.

The Doppler effect is at the heart of the radars used by the traffic police to determine the speed of the car. In medicine, the Doppler effect is used to distinguish veins from arteries using an ultrasound device during injections. Thanks to the Doppler effect, astronomers have established that the Universe is expanding - galaxies are scattering from each other. Using the Doppler effect, the parameters of the motion of planets and spacecraft are determined.

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  Based on his own observations of water waves, Doppler suggested that similar phenomena occur in the air with other waves. On the basis of the wave theory, in 1842, he deduced that the approach of the light source to the observer increases the observed frequency, the distance decreases it (article "On the colored light of binary stars and some other stars in the sky (eng.)russian"). Doppler theoretically substantiated the dependence of the frequency of sound and light vibrations perceived by the observer on the speed and direction of motion of the wave source and the observer relative to each other. This phenomenon was later named after him.

  Doppler used this principle in astronomy and drew a parallel between acoustic and optical phenomena. He believed that all stars emit white light, but the color changes due to their movement towards or away from the Earth (this effect is very small for the binary stars considered by Doppler). Although changes in color could not be observed with the equipment of the time, the theory of sound was already tested in 1845. Only the discovery of spectral analysis made it possible to experimentally test the effect in optics.

  Criticism of Doppler's publication

  The main reason for criticism was that the article had no experimental confirmation and was purely theoretical. While the general explanation of his theory and the supporting illustrations he provided for sound were correct, the explanations and nine supporting arguments for changing the color of the stars were not. The error occurred due to the delusion that all stars emit white light, and Doppler, apparently, did not know about the discoveries of infrared (W. Herschel, 1800) and ultraviolet radiation (I. Ritter, 1801).

  Although by 1850 the Doppler effect was experimentally confirmed for sound, its theoretical basis sparked a heated debate, which was provoked by Josef Petzval. Petzval's main objections were based on the exaggeration of the role of higher mathematics. He responded to Doppler's theory with his paper On Basic Principles of Wave Motion: The Law of Conservation of Wavelength, presented at a meeting of the Academy of Sciences on January 15, 1852. In it, he argued that a theory cannot be of value if it is published on only 8 pages and uses only simple equations. In his objections, Petsval mixed two completely different cases of motion of the observer and the source and motion of the medium. In the latter case, according to Doppler's theory, the frequency does not change.

  Experimental verification

  In 1845, a Dutch meteorologist from Utrecht, Christopher Henrik Diederik Beuis-Bullot, confirmed the Doppler effect for sound on the railway between Utrecht and Amsterdam. The locomotive, which reached an incredible speed of 40 mph (64 km / h) at the time, was pulling an open carriage with a group of trumpeters. Ballot listened to the changes in tone as the car moved in and out. In the same year, Doppler conducted an experiment using two groups of trumpeters, one of which moved away from the station, and the other remained stationary. He confirmed that when orchestras play one note, they are in dissonance. In 1846, he published a revised version of his theory, in which he considered both the movement of the source and the movement of the observer. Later in 1848, the French physicist Armand Fizeau generalized Doppler's work, extending his theory to light (he calculated the displacement of lines in the spectra of celestial bodies). In 1860, Ernst Mach predicted that absorption lines in the spectra of stars associated with the star itself should reveal the Doppler effect, and there are also absorption lines of terrestrial origin in these spectra that do not detect the Doppler effect. The first relevant observation was made in 1868 by William Huggins.

  Direct confirmation of the Doppler formulas for light waves was obtained by G. Vogel in 1871 by comparing the positions of Fraunhofer lines in spectra obtained from opposite edges of the solar equator. The relative speed of the edges, calculated from the values \u200b\u200bof the spectral intervals measured by G. Vogel, turned out to be close to the speed calculated from the displacement of sunspots.

  The essence of the phenomenon

  Also important is the case when a charged particle moves in a medium with a relativistic velocity. In this case, Cherenkov radiation is registered in the laboratory system, which is directly related to the Doppler effect.

  Mathematical description of the phenomenon

  If the wave source moves relative to the medium, then the distance between the wave crests (wavelength λ) depends on the speed and direction of movement. If the source moves towards the receiver, that is, it catches up with the wave emitted by it, then the wavelength decreases, if it moves away, the wavelength increases:

  where is the angular frequency at which the source emits waves, c (\\ displaystyle c) - the speed of propagation of waves in the medium, v (\\ displaystyle v) - the speed of the wave source relative to the medium (positive, if the source approaches the receiver and negative, if it moves away).

  Frequency recorded by a fixed receiver

  Likewise, if the receiver moves towards the waves, it registers their crests more often and vice versa. For a stationary source and a moving receiver

  ω \u003d ω 0 (1 + u c), (\\ displaystyle \\ omega \u003d \\ omega _ (0) \\ left (1 + (\\ frac (u) (c)) \\ right),)

  (2)

  where u (\\ displaystyle u) - the speed of the receiver relative to the medium (positive if it moves towards the source).

  Substituting instead of ω 0 (\\ displaystyle \\ omega _ (0)) in formula (2) the frequency value ω (\\ displaystyle \\ omega) from formula (1), we obtain the formula for the general case:

  ω \u003d ω 0 (1 + u c) (1 - v c). (\\ displaystyle \\ omega \u003d \\ omega _ (0) (\\ frac (\\ left (1 + (\\ frac (u) (c)) \\ right)) (\\ left (1 - (\\ frac (v) (c) ) \\ right))).)

  (3)

  Relativistic Doppler effect

  ω \u003d ω 0 ⋅ 1 - v 2 c 2 1 + vc ⋅ cos \u2061 θ (\\ displaystyle \\ omega \u003d \\ omega _ (0) \\ cdot (\\ frac (\\ sqrt (1 - (\\ frac (v ^ (2) ) (c ^ (2))))) (1 + (\\ frac (v) (c)) \\ cdot \\ cos \\ theta)))

  where c (\\ displaystyle c) - the speed of light, v (\\ displaystyle v) - the speed of the source relative to the receiver (observer), θ (\\ displaystyle \\ theta) - the angle between the direction to the source and the velocity vector in the receiver's frame of reference. If the source is radially away from the observer, then θ \u003d 0 (\\ displaystyle \\ theta \u003d 0), if it approaches, then θ \u003d π (\\ displaystyle \\ theta \u003d \\ pi).

  The relativistic Doppler effect is due to two reasons:

  • classical analogue of frequency change with relative motion of the source and receiver;

  The last factor leads to transverse Doppler effectwhen the angle between the wave vector and the source velocity is θ \u003d π 2 (\\ displaystyle \\ theta \u003d (\\ frac (\\ pi) (2)))... In this case, the change in frequency is a purely relativistic effect that has no classical analogue.

  Observing the Doppler effect

  Since the phenomenon is typical for any waves and particle flows, it is very easy to observe it for sound. The frequency of sound vibrations is perceived by ear as the pitch. You have to wait for a situation when a fast moving car or train will pass you, making a sound, for example, a siren or just a beep. You will hear that when the car approaches you, the pitch will be higher, then when the car is level with you, it will drop sharply and further, when moving away, the car will honk at a lower note.

  Application

  The Doppler effect is an integral part of modern theories about the beginning of the Universe (Big Bang and redshift). The principle has received numerous applications in astronomy for measuring the speeds of motion of stars along the line of sight (approaching or moving away from the observer) and their rotation around the axis, parameters of the rotation of planets,

  Doppler radar

  A radar that measures the change in frequency of a signal reflected from an object. By changing the frequency, the radial component of the object's velocity is calculated (the projection of the velocity onto a straight line passing through the object and the radar). Doppler radars can be used in a wide variety of fields: to determine the speed of aircraft, ships, cars, hydrometeors (for example, clouds), sea and river currents, and other objects.

  [edit] Astronomy

  • The radial velocity of motion of stars, galaxies and other celestial bodies is determined by the shift of the spectrum lines

  Using the Doppler effect, their radial velocity is determined from the spectrum of celestial bodies. Changing the wavelengths of light oscillations leads to the fact that all spectral lines in the spectrum of the source are shifted towards long waves if its radial velocity is directed from the observer (redshift), and towards short ones, if the direction of the radial velocity is towards the observer (violet shift) ... If the speed of the source is small compared to the speed of light (300,000 km / s), then the radial speed is equal to the speed of light multiplied by the change in the wavelength of any spectral line and divided by the wavelength of the same line in a stationary source.

  • The increase in the width of the spectral lines determines the temperature of the stars

  [edit] Non-invasive flow rate measurement

  The Doppler effect measures the flow rate of liquids and gases. The advantage of this method is that you do not need to put sensors directly into the stream. The velocity is determined by the scattering of ultrasound on inhomogeneities of the medium (particles of suspension, liquid droplets that do not mix with the main flow, gas bubbles).

  [edit] Car alarm

  For detecting moving objects near and inside the vehicle

  [edit] Determination of coordinates

  In the Cospas-Sarsat satellite system, the coordinates of the emergency transmitter on the ground are determined by the satellite from the radio signal received from it, using the Doppler effect.