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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, catches up with the wave it emits, then the wavelength decreases. If it is removed, the wavelength increases.

The frequency of the wave in general depends only on the speed at which the receiver is moving

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

To make it more clear, let's consider an example on a car with a siren.

Let's first assume that the car is stationary. The sound from a siren reaches us because the elastic membrane inside it periodically acts on the air, creating compressions in it - areas of increased pressure - alternating with vacuums. Compression peaks - the “crests” of an acoustic wave - propagate through the medium (air) until they reach our ears and impact the eardrums. So, while the car is stationary, we will continue to hear the unchanged tone of its signal.

But as soon as the car starts moving in your direction, a new one will be added Effect. During the time from the emission of one wave peak to the next, the car will travel some distance towards you. Because of this, the source of each subsequent wave peak 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 sound you perceive will increase. Conversely, if a car with a horn is driven in the opposite direction, the peaks of the acoustic waves will reach your ears less often, and the perceived frequency of the sound will decrease.

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

Christian Doppler in 1842, working at the Czech Technical University, theoretically, as they say, “at the tip of his pen,” deduced the dependence of the frequency of oscillations perceived by the observer on the speed and direction of movement of the wave source and the observer relative to each other.
As an example to explain this phenomenon, it is now customary to describe how the tone of a train whistle changes as it approaches or moves away from an observer standing on the platform.
Who among us has not heard this high, rising tone, suddenly turning sharply into a low one?

The horn creates vibrations (sound waves), but moving towards it seems to compress them, and moving away it stretches them.
It compresses because the distance decreases and each subsequent wave requires less time to reach the observer, but in the opposite direction, on the contrary, it takes more time - the waves stretch.
Frequency (number of waves per unit time - F), propagation speed (V) and wavelength (from crest to crest - L) are related by a simple formula:

F=V/L

Christian Doppler discovered this effect by studying the nature of light, i.e. It’s not just sound waves or water waves from a swimming duck that behave this way.
In the same way, the frequency of electromagnetic oscillations changes depending on the direction of movement of the source or receiver of these oscillations. This means that if you irradiate any moving object with an electromagnetic wave of a given frequency, and then compare this frequency with the received reflected one, then from the difference you can determine the speed of this object and the direction of its movement.

This is how the "Doppler velocity meter" or radar was invented.

The frequency of the reflected wave of an approaching car is higher than the frequency emitted by the radar, and the frequency of the reflected wave of a moving car is lower. This is the Doppler effect.
The vehicle's speed is calculated from the frequency difference between the emitted and reflected waves.

Curiously, there is confusion over the spelling of the name (and effect) "Doppler". Thus, in classical reference literature, for example, in

Have you ever noticed that the sound of a car siren has a different pitch as it approaches or moves away from you?

The difference in the frequency of the whistle or siren of a receding and approaching train or car is perhaps the most obvious and widespread example of the Doppler effect. Theoretically discovered by the Austrian physicist Christian Doppler, this effect would later play a key role in science and technology.

For an observer, the wavelength of the radiation will have a different value at different speeds of the source relative to the observer. As the source approaches, the wavelength will decrease, and as it moves away, it will increase. Consequently, the frequency also changes with wavelength. Therefore, the frequency of the whistle of an approaching train is noticeably higher than the frequency of the whistle as it moves away. Actually, this is the essence of the Doppler effect.

The Doppler effect underlies the operation of many measuring and research instruments. Today it is widely used in medicine, aviation, astronautics and even everyday life. The Doppler effect powers satellite navigation and road radars, ultrasound machines and security alarms. The Doppler effect has become widely used in scientific research. Perhaps he is best known in astronomy.

Explanation of the effect

To understand the nature of the Doppler effect, just look at the surface of the water. Circles on the water perfectly demonstrate all three components of any wave. Let's imagine that some stationary float creates circles. In this case, the period will correspond to the time elapsed between the emission of one and the next circle. The frequency is equal to the number of circles emitted by the float in a certain period of time. The wavelength will be equal to the difference in the radii of two successively emitted circles (the distance between two adjacent crests).

Let's imagine that a boat is approaching this stationary float. Since it moves towards the ridges, the speed of the boat will be added to the speed of propagation of the circles. Therefore, relative to the boat, the speed of oncoming ridges will increase. The wavelength will decrease at the same time. Consequently, the time that will pass between the impacts of two adjacent circles on the side of the boat will decrease. In other words, the period will decrease and, accordingly, the frequency will increase. In the same way, for a receding boat, the speed of the crests that will now catch up with it will decrease, and the wavelength will increase. Which means increasing the period and decreasing the frequency.

Now imagine that the float is located between two stationary boats. Moreover, the fisherman on one of them pulls the float towards himself. Acquiring speed relative to the surface, the float continues to emit exactly the same circles. However, the center of each subsequent circle will be shifted relative to the center of the previous one towards the boat towards which the float is approaching. Therefore, on the side of this boat, the distance between the ridges will be reduced. It turns out that circles with a reduced wavelength, and therefore with a reduced period and increased frequency, will come to the boat with the fisherman pulling the float. Similarly, waves with increased length, period and reduced frequency will reach another fisherman.

Multi-colored stars

Such patterns of changes in the characteristics of waves on the water surface were once noticed by Christian Doppler. He described each such case mathematically and applied the data obtained to sound and light, which also have a wave nature. Doppler suggested that the color of stars thus directly depends on the speed at which they approach or move away from us. He outlined this hypothesis in an article that he presented in 1842.

Note that Doppler was mistaken about the color of stars. He believed that all stars emit a white color, which is subsequently distorted due to their speed relative to the observer. In fact, the Doppler effect does not affect the color of stars, but the pattern of their spectrum. For stars moving away from us, all the dark lines of the spectrum will increase the wavelength - shift to the red side. This effect is established in science under the name “red shift”. In approaching stars, on the contrary, the lines tend to the part of the spectrum with a higher frequency - the violet color.

This feature of spectral lines, based on Doppler formulas, was theoretically predicted in 1848 by the French physicist Armand Fizeau. This was experimentally confirmed in 1868 by William Huggins, who made a major contribution to the spectral study of space. Already in the 20th century, the Doppler effect for lines in the spectrum would be called “red shift,” to which we will return.

Concert on rails

In 1845, the Dutch meteorologist Beuys-Ballot, and later Doppler himself, conducted a series of experiments to test the Doppler “sound” effect. In both cases, they used the previously mentioned effect of the horn of an approaching and departing train. The role of the whistle was played by groups of trumpeters who played a certain note while in an open carriage of a moving train.

Beuys-Ballot sent trumpeters past people with good hearing, who recorded the change in note at different speeds of the composition. He then repeated this experiment, placing the trumpeters on a platform and the listeners in a carriage. Doppler recorded the dissonance of the notes of two groups of trumpeters, who approached and moved away from him at the same time, playing one note.

In both cases, the Doppler effect for sound waves was successfully confirmed. Moreover, each of us can conduct this experiment in everyday life and confirm it for ourselves. Therefore, despite the fact that the Doppler effect was criticized by contemporaries, further research made it undeniable.

As noted earlier, the Doppler effect is used to determine the speed of space objects relative to the observer.

Dark lines on the spectrum of cosmic objects are initially always located in a strictly fixed location. This location corresponds to the absorption wavelength of a particular element. For an approaching or receding object, all bands change their positions to the violet or red region of the spectrum, respectively. By comparing the spectral lines of terrestrial chemical elements with similar lines in the spectra of stars, we can estimate the speed at which an object is approaching or moving away from us.

The red shift in the spectra of galaxies was discovered by the American astronomer Vesto Slifer in 1914. His compatriot Edwin Hubble compared the distances to galaxies discovered by him with the magnitude of their red shift. So in 1929 he came to the conclusion that the further away the galaxy is, the faster it is moving away from us. As it turns out later, the law he discovered was rather inaccurate and did not quite correctly describe the real picture. However, Hubble set the right trend for further research by other scientists, who would subsequently introduce the concept of cosmological redshift.

Unlike the Doppler redshift, which arises from the proper motion of galaxies relative to us, the cosmological redshift arises from the expansion of space. As you know, the Universe is expanding uniformly throughout its entire volume. Therefore, the farther two galaxies are from each other, the faster they move away from each other. So each megaparsec between galaxies will remove them from each other by about 70 kilometers every second. This quantity is called the Hubble constant. Interestingly, Hubble itself initially estimated its constant at as much as 500 km/s per megaparsec.

This is explained by the fact that he did not take into account the fact that the redshift of any galaxy is the sum of two different redshifts. In addition to being driven by the expansion of the Universe, galaxies also undergo their own movements. If the relativistic redshift has the same distribution for all distances, then the Doppler redshift accepts the most unpredictable discrepancies. After all, the proper motion of galaxies within their clusters depends only on mutual gravitational influences.

Near and far galaxies

Between nearby galaxies, the Hubble constant is practically not applicable to estimating the distances between them. For example, the Andromeda galaxy has a total violet shift relative to us, as it approaches the Milky Way at a speed of about 150 km/s. If we apply Hubble's law to it, then it should be moving away from our galaxy at a speed of 50 km/s, which does not correspond to reality at all.

For distant galaxies, the Doppler redshift is almost imperceptible. Their speed of removal from us is directly dependent on the distance and, with a small error, corresponds to the Hubble constant. So the most distant quasars are moving away from us at a speed greater than the speed of light. Oddly enough, this does not contradict the theory of relativity, because this is the speed of expanding space, and not the objects themselves. Therefore, it is important to be able to distinguish the Doppler redshift from the cosmological one.

It is also worth noting that in the case of electromagnetic waves, relativistic effects also occur. The accompanying distortion of time and changes in linear dimensions when the body moves relative to the observer also affect the character of the wave. As in any case with relativistic effects

Of course, without the Doppler effect, which enabled the discovery of redshift, we would not know about the large-scale structure of the Universe. However, astronomers owe more than this to this property of waves.

The Doppler effect can detect slight deviations in the positions of stars, which can be created by planets orbiting around them. Thanks to this, hundreds of exoplanets have been discovered. It is also used to confirm the presence of exoplanets previously discovered using other methods.

The Doppler effect played a decisive role in the study of close star systems. When two stars are so close that they cannot be seen separately, the Doppler effect comes to the aid of astronomers. It allows you to trace the invisible mutual movement of stars along their spectrum. Such star systems have even been called “optical binaries.”

Using the Doppler effect, you can estimate not only the speed of a space object, but also the speed of its rotation, expansion, the speed of its atmospheric flows and much more. The speed of Saturn's rings, the expansion of nebulae, the pulsations of stars are all measured thanks to this effect. It is even used to determine the temperature of stars, because temperature is also an indicator of movement. We can say that modern astronomers measure almost everything related to the velocities of space objects using the Doppler effect.

Sound can be perceived differently by a person if the sound source and the listener move relative to each other. It may appear taller or shorter than it actually is.

If the source of sound waves and the receiver are in motion, then the frequency of the sound that the receiver perceives is different from the frequency of the sound source. As they approach, the frequency increases, and as they move away, it decreases. This phenomenon is called Doppler effect , named after the scientist who discovered it.

Doppler effect in acoustics

Many of us have observed how the tone of the whistle of a train moving at high speed changes. It depends on the frequency of the sound wave that our ear picks up. As a train approaches, this frequency increases and the signal becomes higher. As we move away from the observer, the frequency decreases and we hear a lower sound.

The same effect is observed when the sound receiver is moving and the source is stationary, or when both are in motion.

Why the frequency of the sound wave changes was explained by the Austrian physicist Christian Doppler. In 1842, he first described the effect of changing frequency, called Doppler effect .

When a sound receiver approaches a stationary source of sound waves, per unit time it encounters more waves on its path than if it were stationary. That is, it perceives a higher frequency and hears a higher pitch. When it moves away, the number of waves crossed per unit time decreases. And the sound seems lower.

When a sound source moves towards the receiver, it seems to catch up with the wave created by it. Its length decreases, therefore its frequency increases. If it moves away, then the wavelength becomes longer and the frequency lower.

How to calculate the frequency of a received wave

A sound wave can only propagate in a medium. Its length λ depends on the speed and direction of its movement.

Where ω 0 - circular frequency with which the source emits waves;

With - speed of wave propagation in the medium;

v - the speed with which the wave source moves relative to the medium. Its value is positive if the source is moving towards the receiver, and negative if it is moving away.

The fixed receiver perceives the frequency

If the sound source is stationary and the receiver is moving, then the frequency that it will perceive is equal to

Where u - speed of the receiver relative to the medium. It has a positive value if the receiver is moving towards the source, and negative if it is moving away.

In general, the formula for the frequency perceived by the receiver is:

The Doppler effect is observed for waves of any frequency, as well as electromagnetic radiation.

Where is the Doppler effect applied?

The Doppler effect is used wherever it is necessary to measure the speed of objects that are capable of emitting or reflecting waves. The main condition for the appearance of this effect is the movement of the wave source and receiver relative to each other.

Doppler radar is an instrument that emits a radio wave and then measures the frequency of the wave reflected from a moving object. By changing the frequency of the signal, it determines the speed of the object. Such radars are used by traffic police officers to identify violators exceeding the permissible speed limit. The Doppler effect is used in sea and air navigation, in motion detectors in security systems, for measuring wind and cloud speeds in meteorology, etc.

We often hear about such a study in cardiology as Doppler echocardiography. The Doppler effect is used in this case to determine the speed of movement of the heart valves and the speed of blood flow.

And even the speed of movement of stars, galaxies and other celestial bodies has been learned to be determined by the shift of spectral lines using the Doppler effect.