The Doppler effect is one of the remarkable discoveries in the field of property research wave phenomena. Its universal nature determines that today thousands and thousands of a wide variety of devices operate on the basis of this effect. various fields human activity. The phenomenon, which was then named after its discoverer, was discovered by the Austrian physicist Christian Doppler back in the mid-nineteenth century. Doppler measured the properties of waves that arrived at the receiver from a moving and stationary source.
If we consider the Doppler effect in its simplest form, it should be noted that this describes the change in the frequency of the signal in relation to the amount of movement of the source of this signal from the receiver that receives it. For example, a wave that comes from a certain source and that has a certain fixed frequency will be received by the receiver at a different frequency if, during its passage, the source and the receiver have changed their location relative to each other, that is, they have moved. In this case, the frequency indicator will increase or decrease, depending on which direction the source is shifted relative to the receiver. Taking into account the Doppler effect, we can clearly state that if the receiver moves away from the source, the value of the wave frequency decreases. If the receiver approaches the source of wave radiation, then the wave frequency increases. Accordingly, from these laws it is concluded that if the source and receiver of the wave have not changed their location during its passage, then the value of the wave frequency will remain the same.
Another important caveat that characterizes the Doppler effect. This property, to a certain extent, contradicts the laws. The fact is that the value of the frequency change is determined not only by whether the receiver and the radiation source are moving or not, but also by what exactly is moving. Measurements have shown that the frequency shift, determined by which particular object is moving, is more noticeable, the smaller the discrepancy between the displacement speeds of the receiver and the source from the wave speed. In fact, in cases where the Doppler effect occurs, no contradiction with the theory of relativity is found, because what is important here is not the relative movement of the receiver and the source, but the nature of the movement of the wave in the elastic medium in which it moves.
The Doppler effect exhibits such properties both in relation to waves of acoustic origin and to electromagnetic waves, except that in the case of electromagnetic waves, the frequency shift phenomena do not depend on whether the source or receiver is moving.
How this rather abstract effect manifests itself is, however, quite easy to see. For example, the Doppler effect in acoustics can be seen, or more precisely, heard, at the moment when, standing in traffic jam, you hear the siren of a special vehicle passing by. Surely everyone has noted the fact that if such a car is approaching, the sound of the siren sounds in one way, high, and when such a car overtakes you, the sound of the siren sounds lower. This precisely confirms the presence of a change in the frequency value of the acoustic signal.
Great value Doppler frequency plays a role in radar, in relation to. Based on this effect, all radar stations and other devices for detecting moving objects operate in a wide variety of branches of human activity.
Its properties are used in medical technology to determine blood flow; a procedure such as Doppler echocardiography is also widely known. Navigation instruments for underwater vessels have been built on the basis of the Doppler effect, and meteorologists use it to measure the speed of movement of cloud masses.
Even astronomy uses the Doppler effect in its measurements. Thus, by the magnitude of the shift in the spectra of various astronomical objects, their speed of movement in space is determined, in particular, it was on the basis of this effect that the hypothesis about the expansion of the Universe was put forward.
The perceived frequency of the wave depends on relative speed its source.
You've probably at least once in your life had the opportunity to stand by the road along which a car with a special signal and a siren is rushing past. As the howl of the siren approaches, its pitch is higher, then, when the car reaches you, it lowers, and finally, when the car begins to move away, it lowers even more, and you get the familiar:yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyymmmmmmmmmmm—that's roughly the scale. Perhaps without realizing it, you are observing the most fundamental (and most useful) property of waves.
Waves are a strange thing in general. Imagine an empty bottle dangling near the shore. She walks up and down, not approaching the shore, while the water seems to rush onto the shore in waves. But no - the water (and the bottle in it) remain in place, oscillating only in a plane perpendicular to the surface of the reservoir. In other words, the motion of the medium in which the waves propagate does not correspond to the motion of the waves themselves. At least, football fans have learned this well and learned to use it in practice: when sending a “wave” around the stadium, they themselves do not run anywhere, they just get up and sit down in their turn, and the “wave” (in the UK this phenomenon is usually called the “Mexican wave” ") runs around the stands.
It is customary to describe waves frequency(number of wave peaks per second at the observation point) or length(distance between two adjacent ridges or troughs). These two characteristics are interconnected through the speed of wave propagation in the medium, therefore, knowing the speed of wave propagation and one of the main wave characteristics, you can easily calculate the other.
Once the wave has started, 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, having become 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 the Doppler effect.
Let's think again about the wailing siren example. Let us first assume that the special vehicle is stationary. The sound from the siren reaches us because the elastic membrane inside it periodically acts on the air, creating compression in it - areas high blood pressure, - alternating with rarefaction. Compression peaks—the “crests” of an acoustic wave—propagate through the medium (air) until they reach our ears and impact the eardrums, which send a signal to our brain (this is how hearing works). We traditionally call the frequency of sound vibrations we perceive as tone or pitch: for example, a vibration frequency of 440 hertz per second corresponds to the note “A” of the first octave. So, while the special vehicle is stationary, we will continue to hear the unchanged tone of its signal.
But as soon as the special vehicle starts moving in your direction, it will add new 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 the sound you perceive will increase. And, conversely, if the special vehicle starts in reverse direction, peaks acoustic waves will reach your ears less frequently and the perceived frequency of the sound will decrease. This is the explanation why when a car with special signals passes by you, the tone of the siren decreases.
We looked at the Doppler effect in relation to sound waves, but it equally applies to any others. If the source visible light approaches us, the wavelength we see shortens, and we observe the so-called purple shift(of all visible colors scales light spectrum violet corresponds to the shortest wavelengths). If the source moves away, there is an apparent shift towards the red part of the spectrum (lengthening of the waves).
This effect is named after Christian Johann Doppler, who first predicted it theoretically. The Doppler effect has interested me all my life because of how it was first tested experimentally. The Dutch scientist Christian Buys Ballot (1817-1870) put a brass band in an open railway carriage, and on the platform gathered a group of musicians with absolute pitch. (Perfect pitch is the ability, after listening to a note, to accurately name it.) Every time a train with a musical carriage passed by the platform, the brass band played a note, and observers (listeners) wrote down the musical score they heard. As expected, the apparent pitch of the sound was directly dependent on the speed of the train, which, in fact, was predicted by Doppler's law.
The Doppler effect is widely used both in science and in everyday life. Around the world it is used in police radars to catch and fine rule violators. traffic exceeding the speed. A radar gun emits a radio wave signal (usually in the VHF or microwave range) that reflects off the metal body of your car. The signal arrives back to the radar with a Doppler frequency shift, the value of which depends on the speed of the vehicle. By comparing the frequencies of the outgoing and incoming signals, the device automatically calculates the speed of your car and displays it on the screen.
The Doppler effect found a somewhat more esoteric application in astrophysics: in particular, Edwin Hubble, for the first time measuring distances to nearest galaxies on the newest telescope, simultaneously discovered them in the spectrum atomic radiation red Doppler shift, from which it was concluded that galaxies are moving away from us ( cm. Hubble's Law). In fact, this was as clear a conclusion as if you, having closed your eyes, suddenly heard that the tone of the engine of a car of a model you were familiar with was lower than necessary, and concluded that the car was moving away from you. When did Hubble discover, moreover, that what next galaxy, the stronger the red shift (and the faster it flies away from us), it realized that the Universe is expanding. This was the first step towards the Big Bang theory - and this is a much more serious thing than a train with a brass band.
Christian Johann Doppler, 1803-53
Austrian physicist. Born in Salzburg into the family of a mason. Graduated Polytechnical Institute in Vienna, remained there in junior teaching positions until 1835, when he received an offer to head the department of mathematics at the University of Prague, which at the last moment forced him to abandon his long-term decision to emigrate to America, despairing of achieving recognition in academic circles at home. He ended his career as a professor at the Royal Imperial University of Vienna.
– the most important phenomenon in wave physics. Before going straight to the heart of the matter, a little introductory theory.
Hesitation– to one degree or another, a repeating process of changing the state of a system around an equilibrium position. Wave- this is an oscillation that can move away from the place of its origin, spreading in the medium. The waves are characterized amplitude, length And frequency. The sound we hear is a wave, i.e. mechanical vibrations air particles propagating from a sound source.
Armed with information about waves, let's move on to the Doppler effect. And if you want to learn more about vibrations, waves and resonance, welcome to our blog.
The essence of the Doppler effect
The most popular and simple example that explains the essence of the Doppler effect is a stationary observer and a car with a siren. Let's say you are standing at a bus stop. An ambulance with a siren on is heading down the street towards you. The frequency of sound you will hear as the car approaches is not the same.
The sound will initially be of a higher frequency as the car comes to a stop. You will hear the true frequency of the siren sound, and the frequency of the sound will decrease as you move away. That's what it is Doppler effect.
The frequency and wavelength of the radiation perceived by the observer changes due to the movement of the radiation source.
If Cap is asked who discovered the Doppler effect, he will answer without hesitation that Doppler did it. And he will be right. This phenomenon, theoretically substantiated in 1842 year by Austrian physicist Christian Doppler, was subsequently named after him. Doppler himself derived his theory by observing ripples on water and suggesting that the observations could be generalized to all waves. It was later possible to experimentally confirm the Doppler effect for sound and light.
Above we looked at an example of the Doppler effect for sound waves. However, the Doppler effect is not only true for sound. There are:
- Acoustic Doppler effect;
- Optical Doppler effect;
- Doppler effect for electromagnetic waves;
- Relativistic Doppler effect.
It was experiments with sound waves that helped provide the first experimental confirmation of this effect.
Experimental confirmation of the Doppler effect
Confirmation of the correctness of Christian Doppler's reasoning is associated with one of the interesting and unusual physical experiments. IN 1845 meteorologist from Holland Christian Ballot took a powerful locomotive and an orchestra consisting of musicians with perfect pitch. Some of the musicians - they were trumpeters - rode on the open area of the train and constantly played the same note. Let's say it was A of the second octave.
Other musicians were at the station listening to what their colleagues were playing. Absolute hearing of all participants in the experiment reduced the likelihood of error to a minimum. The experiment lasted two days, everyone was tired, a lot of coal was burned, but the results were worth it. It turned out that the pitch of sound really depends on the relative speed of the source or observer (listener).
Application of the Doppler effect
One of the most widely known applications is determining the speed of moving objects using speed sensors. Radio signals sent by radar are reflected from cars and returned back. In this case, the frequency offset at which the signals return is directly related to the speed of the machine. By comparing speed and frequency change, speed can be calculated.
The Doppler effect is widely used in medicine. The operation of devices is based on it ultrasound diagnostics. There is a separate technique in ultrasound called Dopplerography.
The Doppler effect is also used in optics, acoustics, radio electronics, astronomy, radar.
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The discovery of the Doppler effect played important role during the formation modern physics. One of the confirmations theories big bang is based on this effect. How are the Doppler effect and the Big Bang related? According to the Big Bang theory, the Universe is expanding.
When observing distant galaxies, a red shift is observed - a shift of spectral lines to the red side of the spectrum. Explaining the red shift using the Doppler effect, we can draw a conclusion consistent with the theory: galaxies are moving away from each other, the Universe is expanding.
Formula for the Doppler effect
When the theory of the Doppler effect was criticized, one of the arguments of the scientist’s opponents was the fact that the theory was contained on only eight pages, and the derivation of the Doppler effect formula did not contain cumbersome mathematical calculations. In our opinion, this is only a plus!
Let u – speed of the receiver relative to the medium, v – speed of the wave source relative to the medium, With - speed of propagation of waves in the medium, w0 - frequency of source waves. Then the formula for the Doppler effect itself general case will look like this:
Here w – frequency that the receiver will record.
Relativistic Doppler effect
In contrast to the classical Doppler effect, when electromagnetic waves propagate in a vacuum, to calculate the Doppler effect, SRT should be used and relativistic time dilation should be taken into account. Let the light - With , v – speed of the source relative to the receiver, theta – the angle between the direction to the source and the velocity vector associated with the receiver’s reference frame. Then the formula for the relativistic Doppler effect will look like:
Today we talked about the most important effect of our world - the Doppler effect. Do you want to learn how to solve Doppler effect problems quickly and easily? Ask them and they will be happy to share their experience! And at the end - a little more about the Big Bang theory and the Doppler effect.
Have you ever noticed that the sound of a car siren has different heights when it approaches or moves away relative to you?
The difference in the frequency of the whistle or siren of a moving 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 key role in science and technology.
For an observer, the wavelength of radiation will have different meaning 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 applicable 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 radiate 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. 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’s 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 yourself. 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 speed 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. Comparing spectral lines earthly chemical elements With similar lines on the spectra of stars, we can estimate how fast 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 real picture. However, Hubble set the right trend for further research other scientists who would later 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 proper movement 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 relative to us has a total violet shift, as it approaches 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 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 They even got the name “optical double”.
Using the Doppler effect, you can estimate not only speed 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 speeds of space objects using the Doppler effect.
The Doppler effect is described by the formula:
where is the frequency of the wave recorded by the receiver; - frequency of the wave emitted by the source; - in the environment; and are the velocities of the receiver and 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 speed has a minus sign.
It is clear from the formula that when the source and receiver move in such a way that the distance between them decreases, the frequency perceived by the receiver turns out to be greater than the source frequency. If the distance between the source and receiver increases, it will be less than .
The Doppler effect is the basis of radars, with the help of which traffic police officers determine the speed of a car. In medicine, the Doppler effect is used to ultrasonic device distinguish veins from arteries when performing injections. Thanks to the Doppler effect, astronomers have found that the Universe is expanding - galaxies are moving away from each other. Using the Doppler effect, the parameters of the motion of planets and spacecraft are determined.
Examples of problem solving
EXAMPLE 1
| Exercise | Two cars approach each other on a highway at speeds m/s and m/s. The first of them produces a sound signal with a frequency of 600 Hz. Determine the frequency of the signal that the driver of the second car will hear: a) before the meeting; b) after the meeting. The speed of sound is taken to be 348 m/s. |
| Solution | Before meeting, the cars approach each other, i.e. the distance between them decreases and the sound source (the first car) approaches the sound receiver (the second car), so the speed of the first car will enter the formula with a plus sign. Let's calculate:
After the meeting, the cars will move away from each other, i.e. the source of the sound signal will move away from the receiver, so the speed of the source will enter the formula with a minus sign:
|
| Answer | The frequency of the signal that the driver of the second car will hear before meeting the first will be 732 Hz, and after the meeting – 616 Hz. |
Hz
HzEXAMPLE 2
| Exercise | A fast train approaches an electric train standing on the tracks at a speed of 72 km/h. The electric train emits a sound signal with a frequency of 0.6 kHz. Determine the apparent frequency of the sound signal that the driver of the fast train will hear. The speed of sound is taken to be 340 m/s. |
| Solution | Let's write the formula for the Doppler effect: In the reference frame associated with the fast train, the driver of the fast train (signal receiver) is stationary, therefore , and the electric train (signal source) moves towards the fast train at a speed , which has a plus sign, since the distance between the source and receiver of the sound signal decreases . Let's convert the units to the SI system: speed of movement of an electric train relative to a fast train km/h m/s; frequency of the electric train sound signal kHz Hz. Let's calculate:
|
| Answer | The apparent frequency that a fast train driver will hear is 638 Hz. |
HzEXAMPLE 3
| Exercise | An electric train passes by the railway platform. An observer standing on the platform hears the sound of a train siren. When is the train coming? an observer hears a sound of 1100 Hz as the train moves away, the apparent frequency of the sound is 900 Hz. Find the speed of the electric locomotive and the frequency of the sound made by the siren. The speed of sound in air is taken to be 340 m/s. |
| Solution | Since the observer standing on the platform is motionless, the speed of the receiver is . Let's write down the formula for the Doppler effect for both cases. a) when the train is approaching:
b) when the train moves away:
Let us express the frequencies of the siren sound signal and equate the right-hand sides of the resulting equalities: |
