What is the Doppler effect? Application - Doppler effect How Doppler effect works
Registered by the receiver, caused by the movement of their source and/or the movement of the receiver. It is easy to observe in practice when a car with a siren on drives past the observer. Suppose the siren produces a certain tone, and it does not change. When the car is not moving relative to the observer, then he hears exactly the tone that the siren makes. But if the car moves closer to the observer, the frequency of the sound waves will increase (and the length will decrease), and the observer will hear a higher pitch than the siren actually emits. At the moment when the car passes by the observer, he will hear the very tone that the siren actually makes. And when the car drives further and moves away rather than closer, the observer will hear a lower tone due to the lower frequency (and, accordingly, longer length) of the sound waves.
For waves propagating in any medium (for example, sound), it is necessary to take into account the movement of both the source and the receiver of the waves relative to this medium. For electromagnetic waves (such as light), which do not require any medium to propagate, all that matters is the relative motion of the source and receiver.
Also important is the case when a charged particle moves in a medium at a relativistic speed. In this case, Cherenkov radiation, which is directly related to the Doppler effect, is recorded in the laboratory system.
Where f 0 is the frequency with which the source emits waves, c- speed of propagation of waves in the medium, 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
u- the speed of the receiver relative to the medium (positive if it moves towards the source).
Substituting the frequency value from formula (1) into formula (2), we obtain the formula for the general case.
 |
(3) |
Relativistic Doppler effect
In the case of electromagnetic waves, the formula for frequency is derived from the equations of special relativity. Since the propagation of electromagnetic waves does not require a material medium, only the relative speed of the source and the observer can be considered.
 |
Where With- speed of light, v- relative speed of the receiver and source (positive if they move away from each other).
How to observe the Doppler effect
Since the phenomenon is characteristic of any oscillatory processes, it is very easy to observe for sound. The frequency of sound vibrations is perceived by ear as pitch. You need to wait for a situation when a fast-moving car passes by you, making a sound, for example, a siren or just a beep. You will hear that when the car approaches you, the pitch of the sound will be higher, then, when the car reaches you, it will drop sharply and then, as it moves away, the car will honk at a lower note.
Application
Doppler radar
Links
- Using the Doppler effect to measure ocean currents
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See what “Doppler shift” is in other dictionaries:
Doppler shift- Doplerio poslinkis statusas T sritis fizika atitikmenys: engl. Doppler displacement; Doppler shift vok. Doppler Verschiebung, f rus. Doppler shift, m; Doppler shift, n pranc. déplacement Doppler, m; déviation Doppler, f … Fizikos terminų žodynas
Doppler frequency shift- Doplerio dažnio poslinkis statusas T sritis radioelektronika atitikmenys: engl. Doppler frequency displacement; Doppler frequency shift vok. Doppler Frequenzverschiebung, f rus. Doppler frequency shift, m; Doppler frequency shift, n… … Radioelektronikos terminų žodynas
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Increasing wavelengths (l) of lines in electricity. mag. source spectrum (shift of lines towards the red part of the spectrum) compared to the lines of the reference spectra. Quantitatively K. s. characterized by the value z=(lprin lsp)/lsp, where lsp and lprin... ... Physical encyclopedia
The gravitational blue shift of a quantum (photon) or other elementary particle (such as an electron or proton) when it falls into a gravitational field (created by a yellow star at the bottom ... Wikipedia
Frequency reduction electromagnetic radiation, one of the manifestations of the Doppler effect. The name "K. With." due to the fact that in the visible part of the spectrum, as a result of this phenomenon, the lines are shifted towards its red end; K. s. observed... ... Great Soviet Encyclopedia
The change in the oscillation frequency w or wavelength l perceived by the observer when the source of oscillations and the observer move relative to each other. The emergence of D. e. The easiest way to explain is by following. example. Let a motionless source emits... Physical encyclopedia
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Based on his own observations of waves on water, Doppler suggested that similar phenomena occur in the air with other waves. Based on the wave theory, he concluded in 1842 that approaching a light source to an observer increases the observed frequency, distance decreases it (article “On the Colored Light of Double Stars and Some Other Stars in the Heavens” (English) Russian"). Doppler theoretically substantiated the dependence of the frequency of sound and light vibrations perceived by the observer on the speed and direction of movement of the wave source and the observer relative to each other. This phenomenon was subsequently 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 for those considered by Doppler double stars very small). Although changes in color could not be observed with the equipment of the time, the theory about sound was tested as early as 1845. Only the discovery of spectral analysis made it possible to experimentally test the effect in optics.
Criticism of Doppler's publication
The main basis for criticism was that the article had no experimental evidence and was purely theoretical. Although the general explanation of his theory and the supporting illustrations he gave for sound were correct, the explanations and nine supporting arguments about the color change of stars were not correct. The error occurred due to the misconception 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 the Doppler effect had been confirmed experimentally for sound by 1850, it theoretical basis caused a heated debate, which was provoked by Josef Petzval. Petzval's main objections were based on exaggerating the role higher mathematics. He responded to Doppler's theory with his paper "On the Fundamental 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, Petzval mixed two completely different cases of the movement of the observer and the source and the movement of the medium. In the latter case, according to Doppler theory, the frequency does not change.
Experimental verification
In 1845, a Dutch meteorologist from Utrecht, Christopher Henrik Diederik Buys-Ballot, confirmed the Doppler effect for sound on the railway between Utrecht and Amsterdam. The locomotive, which reached a then incredible speed of 40 mph (64 km/h), pulled an open car with a group of trumpeters. Ballot listened to the changes in tone as the carriage moved as it approached and moved away. That same year, Doppler conducted an experiment using two groups of trumpeters, one moving away from the station and the other remaining 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 motion of the source and the motion 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 exhibit the Doppler effect, and that in these spectra there are absorption lines of terrestrial origin that do not exhibit the Doppler effect. The first relevant observation was made in 1868 by William Huggins.
Direct confirmation of Doppler's 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 of 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 speed. In this case, Cherenkov radiation, which is directly related to the Doppler effect, is recorded in the laboratory system.
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, catches up with the wave emitted by it, then the wavelength decreases; if it moves away, the wavelength increases:
where is the angular frequency with which the source emits waves, c (\displaystyle c)- 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
Similarly, 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 = ω 0 (1 + u c) , (\displaystyle \omega =\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 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 = ω 0 (1 + u c) (1 − v c) . (\displaystyle \omega =\omega _(0)(\frac (\left(1+(\frac (u)(c))\right))(\left(1-(\frac (v)(c) )\right))).) (3) Relativistic Doppler effect
ω = ω 0 ⋅ 1 − v 2 c 2 1 + v c ⋅ cos θ (\displaystyle \omega =\omega _(0)\cdot (\frac (\sqrt (1-(\frac (v^(2) )(c^(2))))(1+(\frac (v)(c))\cdot \cos \theta ))) Where c (\displaystyle c)- speed of light, v (\displaystyle v)- 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 reference system. If the source moves radially away from the observer, then θ = 0 (\displaystyle \theta =0), if it approaches, then θ = π (\displaystyle \theta =\pi ).
The relativistic Doppler effect is due to two reasons:
- classical analogue of frequency change with relative movement of the source and receiver;
The last factor leads to transverse Doppler effect, when the angle between the wave vector and the source velocity is equal to θ = π 2 (\displaystyle \theta =(\frac (\pi )(2))). In this case, the change in frequency is a purely relativistic effect that has no classical analogue.
Observation of the Doppler effect
Since the phenomenon is characteristic of any waves and particle flows, it is very easy to observe for sound. The frequency of sound vibrations is perceived by ear as pitch. You need to wait for a situation when a fast-moving car or train passes by you, making a sound, for example, a siren or just a beep. You will hear that when the car approaches you, the pitch of the sound will be higher, then, when the car reaches you, it will drop sharply and then, as it moves away, the car will honk at a lower note.
Application
The Doppler effect is an integral part modern theories about the beginning of the Universe (Big Bang and red shift). The principle has received numerous applications in astronomy for measuring the speed of movement of stars along the line of sight (approaching or moving away from the observer) and their rotation around an axis, the rotation parameters of planets,
1Yushkevich R.S., Degtyareva E.R.
The article provides a derivation of formulas for the Doppler effect without using the law of addition of velocities, but using the principle of constancy of the speed of light only relative to the light source. The spatial limit of the possibility of receiving electromagnetic waves has been determined. The dependence of the speed of light on distance is considered. The coefficient for calculating the speed of light is determined.
To explain the effect, we assume that the light coming from the light source is connected to the source and propagates from it at a speed s = 3 10 8 m/s relative to the source. For the receiver, the speed of light relative to the source will be added to the speed of the source v.
To determine the frequency dependence of light ν from speed v, consider the propagation of light from two sources, one of which Ѕ moves away from the receiver at a speed v, and the other S 0 rests.
Rice. 1.
Identical sources emit light of the same frequency ν 0 . Light relative to sources propagates with same speedWith, therefore the emitted wavelength λ 0 will be the same. Light will approach the receiver from a moving source at a speed With-v and wavelength λ 0 will be accepted in time T =(period), and from a stationary source - in time T 0 =. Periods are the reciprocal quantities of the oscillation frequencies and . Let's substitute the values T And T 0 into the resulting equalities
dividing them term by term, we get
,we get [p. 181].
(1)In the case when the source and receiver are approaching, you need a sign v replace with the opposite, we get
. Note that With-v And c are the speeds of light relative to the receiver and the light source, respectively.Now consider the case when the light source moves perpendicular to the direction of the receiver. Considering that light is associated with a source, it propagates relative to it at a speed With and carries him with speed v in order for it to hit the receiver it must be directed at a certain angle α So sinα= . In this case, the component of the speed of light coinciding with the direction to the receiver A will be , the component v in this direction is equal to 0. In order not to repeat the previous reasoning, we use formula (1), With-v we replace it with , and the speed c relative to the source remains unchanged. As a result we get:
which corresponds to the result obtained in the experiments of Ives [p. 181].
Rice. 2.
When light passes from a source to a receiver, its frequency changes from ν 0 before ν. From the formula с=λν it follows that the wavelength must also change. If a wave of length came from a light source λ 0 , then the receiver will receive it differently, say λ . Get value λ it is possible by taking advantage of the fact that λ And ν quantities are inversely proportional
. Substituting the value ν
from the formula (1),
we getTo be more confident, we obtain this formula in a different way.
Any light receiver can also be an emitter, which means that it has the same light-carrying medium as the source, and light propagates in it at speed With. Light, passing from the source medium to the receiver medium, gains speed With relative to the receiver.
Wave length λ 0 from the source to the interface between the source and receiver media approaches at a speed With -v and the boundary will pass in time C from the very beginning of the wave’s entry into the sphere of the receiver’s medium, its beginning acquires speed c relative to the receiver and in time T it will travel the distance λ = cT. Substituting the value T, we get:
Rice. 3.
In the first half of the twentieth century. The American scientist Hubble discovered in the spectra of distant stars a shift of spectral lines towards the red part of the spectrum compared to laboratory spectra - “red shift”. This meant that the received wavelength λ is greater than λ 0 and the farther the star is, the greater the “red shift”.
Into the formula (2) includes four quantities λ, λ 0 , s And v. By the time the “red shift” was discovered, the speed of light with Einstein’s postulate was fixed constant relative to any frame of reference, which means λ 0 , associated with the speed of light c and the source of radiation, turned out to be constant. In the formula (2) variable quantity λ , turned out to be related to the speed of the source v. Increase λ causes an increase v.
“Redshift” is observed in stars located in all directions, so the expansion of the Universe was recognized.
In astronomy, the connection between λ And v determined by another formula
(3)for a receding radiation source.
For the same phenomenon and the same quantities, two formulas establish different dependences! To understand this, let’s compare the results that these formulas give for different v. Restrictions on the speed value v no formula required. For convenience, we denote the wavelengths λ 3 And λ 2 according to the designation of the formulas (3) And ( 2 ) in which they are included. At v=0 :
At 0< v< с compare by division:
If v"With, then λ 3 ≈ λ 2. Under these two conditions, the results are practically consistent with each other.
When v = c;
λ 2 turns to infinity, while formula (1) gives 
. It turns out that the light wave does not reach the receiver from the source, it travels at a speed With will move from the source to the receiver and, together with the source, will move away from it at the same speed c - c = 0.The third comparison requires concluding which formula correctly reflects reality. Origin of the formula (2) discussed at the beginning of the article. Now let's look at how the formula is obtained (3).
Rice. 4.
Let's imagine that the light source is surrounded by a medium in which the light propagates to the receiver at a speed With. Light source at a point A began to emit a wave. Let us denote the emission time of one wave T(period). From the moment the wave begins to appear, it begins to move towards the receiver at environment with speed With and for the time T will move away from the point A to a distance st. But during this same time, the source, moving from the receiver, will end up at the point WITH, having covered the distance AC =vT, where the end of the wave will be. Distance from WITH to B and will be the wavelength λ = сТ +vT = (c +v)T
If the source is not moving, then v = 0 and the wavelength will be λ 0 = cT. By dividing λ on λ 0, we get:
At the beginning of the article, we looked at the medium that provides the speed of light c; it is either connected to the source or to the receiver of light. The first one gives formulas (1) and (2). The probability that the second one, from a distant light receiver, influenced the speed of light more than the environment of the light source is negligible. A medium remains, not connected with either the source or the receiver of light, which acts like air (matter) on the propagation of sound. But the negative result of Michelson’s experiments to detect the “ethereal wind” proved that such a medium does not exist in nature. It remains to give preference to formula (2). It was previously noted that when the light source moves away at a speed v = c, the wave will not reach the receiver and the signal will not be received.
Hubble introduced the law that bears his name [p. 120]
v= HD,
where v is the speed of removal of the light source, D is the distance between the source and the receiver, H is the coefficient of proportionality, called the Hubble constant.
.1 Mpc = 10 6 pc; 1pc (parsec) = 3.26 light years= 3 . 10 13 km.
Let's find the distance at which v = c:
;D- this is the radius of the sphere that limits the reception of direct electromagnetic radiation from the vastness of the Universe. From the zones adjacent to this sphere in its inner part, electromagnetic radiation can only come in the form of radio waves. In nature, there is no priority direction in the distribution of stars, so radio emission must come from all directions evenly.
Let's consider the option when v>s. In this case, formulas (1) and (2) give:
And .This means that the wave must come from the direction opposite to where the emitter is located.
At v= 2s we have
.The wave will arrive without a “red shift”. The limit of possible reception of electromagnetic radiation defined in the article will be correct if Hubble’s law is true and the “red shift” is caused solely by the removal of the emitter. If other factors are discovered that reduce the speed of light relative to the receiver (and they may exist), then the wave reception limit can be approached.
Let us now turn to the formulas (1) And (2). In them c-v is the speed of light relative to the receiver, let's denote it c 1 =c-v where v=c-c 1.In formulas v represents the difference in the speed of light, regardless of the nature of its occurrence. It is generally accepted that this is the result of removing the light source. But this speed difference can also arise due to the decrease in the speed of light with increasing distance. Light is a flow of energy quanta and it is possible that their speed may decrease.
Let us assume that the speed of light decreases with increasing distance from the light source, figuratively speaking, “light ages.”
It is known that the speed of light decreases when passing from an optically less dense medium to a more dense one. This is due to the fact that the conditions for the passage of light change. The decrease in speed is characterized by the refractive index n;, Where With- speed of light in vacuum a from 1- speed in another environment.
If, by assumption, the speed of light decreases with increasing distance from the light source, then the conditions for its passage also change, which can also be characterized by the refractive index n. We find that the reduced speed of light will be .
In the article “Fizeau's Experience” (journal “Modern Science-Intensive Technologies” No. 2, 2007) to determine the speed of light in a moving medium, the refractive index n was used in the form
, where part of the indicator is determined by the emitting atom, and is determined by the conditions for the passage of light in the medium.Let us apply this representation of the refractive index for vacuum. If we accepted the assumption that the speed of light decreases in a vacuum, and vacuum is a homogeneous medium, then the decrease in the speed of light should depend only on the distance and is proportional to it. Therefore we can write where D- distance to light source, μ - proportionality coefficient is a constant value. The speed of received light will be
The difference between the initial and reduced speeds of light will be
This expresses the relationship between the decrease in the speed of light and the distance D. The connection between these same quantities is expressed by Hubble’s law where v- the speed of removal of the star, which is for the light receiver difference s-s 1 .
Let's compare the values v, which these two equations give for the distance limits D.
If , then from the first equation we obtain: , n=1 (for short distances) and . From Hubble's law we also get .
If this coincidence is not accidental, it can be assumed that the quanta of light energy are associated with the emitter; this is also indicated by the connection of the light-carrying medium with the light source.
To determine the speed from 1, we need to decide regarding n the equation:
and find the speed through n from 1.
For small values of D, Hubble's law can be used.
There is a clear contradiction in the article. Based on the concept of the expansion of the Universe, it was concluded that there is a limit to the possible reception of electromagnetic waves, but based on the natural decrease in the speed of light, there is no such limit. It turns out that the discovery of such a boundary will be evidence of the expansion of the Universe.
The article also assumes, without convincing grounds, that the speed of light depends on distances. The basis for this assumption will be discovered when considering the process of emission of light quanta by an atom.
BIBLIOGRAPHY:
- Zisman G.A., Todes O.M., Course of general physics vol.3. - M.: “Science”, 1972.
- Vorontsov - Velyaminov B.A. Astronomy 10. - M.: “Enlightenment”, 1983.
Bibliographic link
Yushkevich R.S., Degtyareva E.R. DOPPLER EFFECT AND SPEED OF LIGHT // Basic Research. – 2008. – No. 3. – P. 17-24;
URL: http://fundamental-research.ru/ru/article/view?id=2764 (access date: 02/16/2020). We bring to your attention magazines published by the publishing house "Academy of Natural Sciences"Message from the administrator:
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ClickIf 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 red shift is due to something other than the “scattering” of galaxies remains open.
It is known that when a fast moving electric train approaches a stationary observer, its sound signal seems higher, and when moving away from the observer, it appears lower than the signal of the same electric train, but stationary.
Doppler effect call the change in the frequency of waves recorded by the receiver, which occurs due to the movement of the source of these waves and the receiver.
The source, moving towards the receiver, seems to compress a spring - a wave (Fig. 5.6).
This effect is observed during the propagation of sound waves (acoustic effect) and electromagnetic waves (optical effect).
Let's consider several cases of manifestation acoustic Doppler effect .
Let the receiver of sound waves P in a gaseous (or liquid) medium be motionless relative to it, and the source I move away from the receiver with a speed along the straight line connecting them (Fig. 5.7, A).
The source moves in the medium over a period of time equal to the period its oscillations, at a distance , where is the oscillation frequency of the source.
Therefore, when the source moves, the wavelength in the medium is different from its value with a stationary source:
,where is the phase velocity of the wave in the medium.
The wave frequency recorded by the receiver is
(5.7.1) If the source velocity vector is directed at an arbitrary angle to the radius vector connecting the stationary receiver with the source (Fig. 5.7, b), That
(5.7.2) If the source is stationary and the receiver approaches it at a speed along the straight line connecting them (Fig. 5.7, V), then the wavelength in the medium is . However, the speed of propagation of the wave relative to the receiver is equal to , so the frequency of the wave recorded by the receiver
(5.7.3) In the case when the speed is directed at an arbitrary angle to the radius vector connecting the moving receiver with a stationary source (Fig. 5.7, G), we have:
This formula can also be represented as (if)
, (5.7.6) where is the speed of the wave source relative to the receiver, and is the angle between the vectors and . The quantity equal to the projection onto the direction is called radial velocity of the source.
Optical Doppler effect
When the source and receiver of electromagnetic waves move relative to each other, it is also observed Doppler effect , i.e. wave frequency change, registered by the receiver. In contrast to the Doppler effect we considered in acoustics, the laws of this phenomenon for electromagnetic waves can only be established on the basis of the special theory of relativity.
Relationship describing Doppler effect For electromagnetic waves in vacuum, taking into account Lorentz transformations, has the form:
.
(5.7.7) At low speeds of movement of the wave source relative to the receiver, the relativistic formula for the Doppler effect (5.7.7) coincides with the classical formula (5.7.2).
If the source moves relative to the receiver along the straight line connecting them, then we observe longitudinal Doppler effect .
In case of approaching the source and receiver ()
,
(5.7.8) and in case of their mutual removal ()
.
(5.7.9) In addition, from the relativistic theory of the Doppler effect it follows the existence transverse Doppler effect , observed at and , i.e. in cases where the source moves perpendicular to the line of observation (for example, the source moves in a circle, the receiver is in the center):
.
(5.7.10) The transverse Doppler effect is inexplicable in classical physics. It represents a purely relativistic effect.
As can be seen from formula (5.7.10), the transverse effect is proportional to the ratio, therefore it is much weaker than the longitudinal one, which is proportional to (5.7.9).
In the general case, the relative velocity vector can be decomposed into components: one provides a longitudinal effect, the other provides a transverse effect.
The existence of the transverse Doppler effect follows directly from time dilation in moving reference frames.
The first experimental verification of the existence of the Doppler effect and the correctness of the relativistic formula (5.7.7) was carried out by American physicists G. Ives and D. Stilwell in the 30s. Using a spectrograph, they studied the radiation of hydrogen atoms accelerated to speeds of m/s. In 1938 the results were published. Summary: the transverse Doppler effect was observed in full accordance with relativistic frequency transformations (the emission spectrum of atoms turned out to be shifted to the low-frequency region); the conclusion about time dilation in moving inertial frames of reference has been confirmed.
The Doppler effect has found wide application in science and technology. This phenomenon plays a particularly important role in astrophysics. Based on the Doppler shift of absorption lines in the spectra of stars and nebulae, it is possible to determine the radial velocities of these objects relative to the Earth: at using formula (5.7.6)
.
(5.7.11) American astronomer E. Hubble discovered in 1929 a phenomenon called cosmological redshift and consisting in the fact that the lines in the emission spectra of extragalactic objects are shifted towards lower frequencies (longer wavelengths). It turned out that for each object the relative frequency shift ( is the frequency of the line in the spectrum of a stationary source, is the observed frequency) is exactly the same for all frequencies. Cosmological redshift is nothing more than the Doppler effect. It indicates that the Metagalaxy is expanding, so that extragalactic objects are moving away from our Galaxy.
The Metagalaxy is understood as the totality of all star systems. With modern telescopes you can observe a part of the Metagalaxy, the optical radius of which is equal to
. The existence of this phenomenon was theoretically predicted back in 1922 by the Soviet scientist A.A. Friedman based on development general theory relativity.Hubble established a law according to which the relative redshift of galaxies increases in proportion to their distance .
Hubble's Law can be written in the form
,
(5.7.12) Where H– Hubble constant. According to the most recent estimates, conducted in 2003, . (1 pc (parsec) is the distance that light travels in a vacuum in 3.27 years (
)).In 1990, the Hubble Space Telescope was launched into orbit aboard the Discovery shuttle (Fig. 5.8).
Rice. 5.8 Rice. 5.9 Astronomers have long dreamed of a telescope that would operate in the visible range, but would be located outside the earth's atmosphere, which greatly interferes with observations. Hubble not only did not disappoint the hopes placed on it, but even exceeded almost all expectations. He fantastically expanded the “field of vision” of humanity, looking into the unimaginable depths of the Universe. During its operation, the space telescope transmitted 700 thousand magnificent photographs to earth (Fig. 5.9). In particular, he helped astronomers determine the exact age of our Universe - 13.7 billion years; helped confirm the existence of a strange but powerful form of energy in the Universe - dark energy; proved the existence of supermassive black holes; amazingly clearly captured the fall of a comet on Jupiter; showed that the process of formation of planetary systems is widespread in our Galaxy; discovered small protogalaxies by detecting the radiation emitted by them when the age of the Universe was less than 1 billion years.
Radar laser methods for measuring the speeds of various objects on Earth (for example, a car, an airplane, etc.) are based on the Doppler effect. Laser anemometry is an indispensable method for studying the flow of liquid or gas. The chaotic thermal motion of the atoms of a luminous body also causes a broadening of lines in its spectrum, which increases with increasing speed of thermal motion, i.e. with increasing gas temperature. This phenomenon can be used to determine the temperature of hot gases.
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