Doppler effect in radar formula. In the general case, when both the source and the observer are moving with velocities x H and x H, the formula for the Doppler effect takes the form

The Doppler effect is a physical phenomenon consisting in a change in 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 source of waves moves away from the observer, their frequency decreases and the wavelength increases.

For example, in the case of sound waves, as the source moves away, the pitch will decrease, and as the source approaches, the pitch will become higher. 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. If the source is removed, the observer will notice a shift of the spectrum to the "red" side, i.e. in the direction of longer waves, and when approaching - in the "violet", i.e. towards shorter wavelengths.

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 redshifted, therefore, they are moving away from us); developed a method for diagnosing the cardiovascular system through the determination of 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 rides towards you or away from you, you hear one sound, and when she passes by, then a completely different one - 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 - everywhere you can observe the Doppler effect.

Or take a traffic light - it has red, yellow and green colors. Depending on how fast 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 are moving away from the light source and looking back (or the traffic light is moving away from us), then the colors will shift towards red.

And, perhaps, 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 the sound source approaches or moves away from the observer, then the frequency of the sound emitted by it changes from the point of view of the observer. So, for example, the sound of the engine of a car that passes by you changes. It is higher as it approaches you and drops sharply lower as it flies past you and begins to move away. The change in frequency is the stronger, the higher the speed of the sound source.

By the way, this effect is true not only for sound, but also, say, for light. It's just that for sound it is clearer - 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 must be taken into account even in radio communication.

If you do not delve into strict definitions and try to explain the effect, as they say, on your fingers, then everything is quite simple. Sound (like light or a 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 (). If the source and receiver are stationary (yes, relative to each other), then we will receive "ridges" with the same frequency as the receiver emits them. If the source and the receiver begin to approach, then we will begin to receive the more often, the higher the speed of approach - the speeds will add up. As a result, the frequency of the sound at the receiver will be higher. If the source starts to move away from the receiver, then each next "ridge" will need a little more time to reach the receiver - we will begin to receive "ridges" a little less often than they are emitted by the source. The frequency of the sound at the receiver will be lower.

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

In short, the change in the observed frequency and wavelength in the event that the source and receiver are moving relative to each other. Associated with the finiteness of the speed of wave propagation. 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 frequently). A typical illustration of the effect is a special services siren. If an ambulance drives up to you - the siren squeals, drives off - it buzzes in a bass voice. A separate case is the propagation of an electromagnetic wave in vacuum - a relativistic component is added there, and the Doppler effect also manifests itself in the case when the receiver and source are stationary relative to each other, which is explained by the properties of time.

I'll try to answer in the simplest way:
Imagine that you are standing still and every second you launch a wave (for example, with your voice), which propagates radially from you at a speed of 100 m/s.

Let a device perceiving vibrations of the medium, which we will call a receiver, be located in a gas or liquid at some distance from the source of waves. If the source and receiver of waves are stationary relative to the medium in which the wave propagates, then the frequency of oscillations perceived by the receiver will be equal to the frequency of oscillations of the source. If the source or receiver, or both of them, are moving relative to the medium, then the frequency v perceived by the receiver may turn out to be different from This phenomenon is called the Doppler effect.

Assume that the source and receiver are moving along a straight line connecting them. The source velocity will be considered positive if the source is moving towards the receiver, and negative if the source is moving away from the receiver. Similarly, the receiver speed will be considered positive if the receiver is moving towards the source, and negative if the receiver is moving away from the source.

If the source is stationary and oscillates with a frequency, then by the time the source completes the oscillation, the “crest” of the wave generated by the first oscillation will have time to pass the path v in the medium (v is the speed of wave propagation relative to the medium). Consequently, the “crests” and “troughs” of the waves generated by the source per second will fit into the length v. If the source moves relative to the medium with a speed, then at the moment when the source completes the oscillation, the “ridge” generated by the first oscillation will be at a distance from the source (Fig. 103.1). Consequently, the "crests" and "troughs" of the wave will fit on the length , so that the wavelength will be equal to

In a second, “ridges” and “troughs” will pass by a fixed receiver, fitting on a length v. If the receiver is moving at a speed, then at the end of a lasting 1 s time interval, it will perceive a “trough”, which at the beginning of this interval was separated from its current position by a distance numerically equal to .

Thus, the receiver will perceive in a second the vibrations corresponding to the "crests" and "troughs" that fit on a length numerically equal to (Fig. 103.2), and will oscillate with a frequency

Substituting expression (103.1) for K into this formula, we obtain

(103.2)

From formula (103.2) it follows that with such a movement of the source and receiver, in which the distance between them decreases, the frequency v perceived by the receiver is greater than the frequency of the source

If the distance between source and receiver increases, v will be less than

If the directions of the velocities do not coincide with the straight line passing through the source and the receiver, instead of using the formula (103.2), you need to take the projections of the vectors onto the direction of the specified straight line.

From formula (103.2) it follows that the Doppler effect for sound waves is determined by the velocities of the source and receiver relative to the medium in which the sound propagates. For light waves, the Doppler effect is also observed, but the formula for changing the frequency has a different form than (103.2). This is due to the fact that for light waves there is no material medium whose vibrations would represent "light". Therefore, the speeds of the source and receiver of light relative to the "medium" do not make sense. In the case of light, we can only speak of the relative speed of the receiver and source. The Doppler effect for light waves depends on the magnitude and direction of this velocity. The Doppler effect for light waves is discussed in § 151.

Registered by the receiver, caused by the movement of their source and / or the movement of the receiver. It is easy to observe it in practice when a car passes by the observer with the siren turned on. Suppose the siren gives out 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 emits. But if the car approaches the observer, then the frequency of the sound waves will increase (and the length will decrease), and the observer will hear a higher tone than the siren actually emits. At that moment, when the car passes by the observer, he will hear the very tone that the siren actually emits. And when the car goes further and will already be moving away, and not approaching, the observer will hear a lower tone, due to the lower frequency (and, accordingly, greater length) of sound waves.

For waves propagating in some medium (for example, sound), one must take into account the movement of both the source and the receiver of waves relative to this medium. For electromagnetic waves (for example, light), for the propagation of which no medium is needed, only the relative motion of the source and receiver matters.

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.

where f 0 is the frequency with which the source emits waves, c is the speed of wave propagation in the medium, v- the speed of the wave source relative to the medium (positive if the source is approaching the receiver and negative if it is moving 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 a formula for the general case.

where with- the speed of light, v- the relative velocity of the receiver and source (positive if they are removed from each other).

How to observe the Doppler effect

Since the phenomenon is characteristic of any oscillatory processes, it is very easy to observe it for sound. The frequency of sound vibrations is perceived by ear as a sound pitch. It is necessary to wait for a situation when a fast moving car will pass you, making a sound, for example, a siren or just a sound signal. You will hear that when the car is approaching you, the pitch will be higher, then when the car is close to you, it will drop sharply, and then, when moving away, the car will honk on a lower note.

Application

doppler radar

Links

• Applying the Doppler effect to measure currents in the ocean

Wikimedia Foundation. 2010 .

1

Yushkevich R.S., Degtyareva E.R.

The article gives 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 boundary of the possibility of receiving electromagnetic waves is 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 associated with the source and propagates from it at a speed s = 3 10 8 m/s regarding the source. For the receiver, the speed of light relative to the source will add up to the speed of the source v.

To determine the dependence of the frequency 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. one.

Identical sources emit light of the same frequency ν 0 . Light travels at the same speed relative to sources with, so the length of the emitted wave λ 0 will be the same. From a moving source, light will approach the receiver at a speed with-v and wavelength λ 0 will be accepted in time T =(period), and from a source at rest - in time T 0 =. The periods are the reciprocals of the oscillation frequencies and . 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 it with the opposite, we get . Note that with-v and c are the speeds of light, respectively, relative to the receiver and light source.

Now consider the case when the light source moves perpendicular to the direction of the receiver. Given that the light is associated with the source, it propagates relative to it with a speed with and go with it at 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 BUT 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 replace by , and the velocity 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 was emitted from a light source λ 0 , then the receiver will receive it differently, let's say λ . Get value λ is possible using the λ and ν quantities are inversely proportional . Substituting the value ν from the formula (1), we get

For greater certainty, 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 a speed with. Light, passing from the source medium to the receiver medium, gains speed with regarding 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 entering the sphere of the receiver’s medium, its beginning acquires a speed c relative to the receiver and in time T it will pass the path λ = cT. Substituting the value T, we get:

Rice. 3.

In the first half of the twentieth century. The American scientist Hubble in the spectra of distant stars discovered a shift of spectral lines towards the red part of the spectrum compared to laboratory spectra - the "redshift". This meant that the length of the received wave λ is greater than λ 0 and the farther the star, the greater the "redshift".

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 as constant with respect to any frame of reference, which means that λ 0 , related to the speed of light c and the radiation source turned out to be constant. In the formula (2) variable λ , turned out to be related to the source velocity v. Increase λ causes an increase v.

"Redshift" is observed in stars located in all directions, so the fact of the expansion of the Universe was recognized.

In astronomy, the connection between λ and v is defined by another formula

(3)

for a receding radiation source.

For the same phenomenon and the same quantities, two formulas establish a different dependence! To understand this, let's compare the results that these formulas give for various v. Restrictions on the speed value v formulas are not required. For convenience, we denote the wavelengths λ 3 and λ2 according to the designation of the formulas (3) and ( 2 ) in which they are included. At v=0 :

At 0< v< с compare division:

If a v"with, then and λ 3 ≈ λ 2 . Under these two conditions, the results practically do not contradict each other.

When v = c; λ 2 turns to infinity, while formula (1) gives . It turns out that the light wave from the source to the receiver does not get, it is 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 us to conclude which formula correctly reflects reality. Origin of the formula (2) discussed at the beginning of the article. Now let's see how the formula is obtained (3).

Rice. 4.

Imagine that the light source is surrounded by a medium in which light propagates towards the receiver at a speed with. Light source at a point BUT began to emit a wave. The emission time of one wave is denoted T(period). From the moment the wave begins to appear, it begins to move towards the receiver in the environment at a speed with and for time T move away from the point BUT at a distance st. But during the same time, the source, moving from the receiver, will be at the point With, passing the distance AC =vT where the end of the wave will be. Distance from With up to B and will be the wavelength λ = cT +vT = (c +v)T

If the source is not moving, then v = 0 and the wavelength will be λ 0 = st. Dividing λ on λ 0 , we get:

At the beginning of the article, we considered the medium that provides the speed of light c, it is either associated with a light source or with a light receiver. The first one gives formulas (1) and (2). The probability that the second, from a far located light receiver, influenced the speed of light more than the environment of the light source, is negligible. There remains a medium that is not connected with either the source or the receiver of light, which acts like air (substance) 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 make a preference for formula (2). It was noted earlier that when the light source is removed 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 removal speed 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.

Find the distance at which v = c: ;

D is the radius of the sphere that limits the reception of direct electromagnetic radiation from the expanses 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 should come from all sides evenly.

Consider the case when v>s. In this case, formulas (1) and (2) give: and .

This means that the wave must come from a direction opposite to where the emitter is located.

At v= 2s we have

.

The wave will come without "redshift". The limit of possible reception of electromagnetic radiation defined in the article will be correct if the Hubble law is correct and the "redshift" is caused solely by the removal of the emitter. If other factors are found that reduce the speed of light relative to the receiver (and they can be), then the limit of wave reception can be approximated.

Let's turn now 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 \u003d c-v where v=c-c 1.In formulas v represents the difference in the speeds of light, regardless of the nature of its occurrence. It is generally accepted that this is the result of the removal of 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 gets old”.

It is known that the speed of light decreases when moving 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 are changing. The decrease in speed is characterized by the refractive index n;, where with is the 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, therefore, the conditions for its passage also change, which can also be characterized by the refractive index n. We get that the reduced speed of light will be .

In the article "Fizo's Experiment" (j. "Modern high technologies" No. 2, 2007) to determine the speed of light in a moving medium, the refractive index n was used in the form , where the part of the indicator determined by the emitting atom, and is determined by the conditions of light passage in the medium.

Let us apply this representation of the refractive index for vacuum as well. If we accepted the assumption that the speed of light decreases in vacuum, and vacuum is a homogeneous medium, then the decrease in the speed of light should depend only on the distance and proportional to it. Therefore, one can write where D- distance to the light source, μ - coefficient of proportionality is a constant value. The speed of the received light will be

The difference between the initial and reduced speeds of light will be

Here is the relationship between the decrease in the speed of light and the distance D. The connection between these quantities also expresses the Hubble law where v- the speed of removal of the star, which for the light receiver is the difference c-c 1 .

Compare values v, which give these two equations for the limit values ​​of the distance D.

If , then from the first equation we get: , n=1 (for small 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, it is necessary to decide on n the equation:

and through n find the speed 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, a conclusion was made about the existence of a boundary for the possible reception of electromagnetic waves, and based on the natural decrease in the speed of light, there is no such boundary. It turns out that the discovery of such a boundary will be proof of the expansion of the universe.

In the article, the assumption about the dependence of the speed of light on distances is also accepted without convincing grounds. The grounds for this assumption will be discovered when considering the process of emission of light quanta by an atom.

BIBLIOGRAPHY:

1. Zisman G.A., Todes O.M., Course of General Physics v.3. - M.: "Nauka", 1972.
2. Vorontsov - Velyaminov B.A. Astronomy 10. - M .: "Enlightenment", 1983

Bibliographic link

Yushkevich R.S., Degtyareva E.R. DOPPLER EFFECT AND SPEED OF LIGHT // Fundamental Research. - 2008. - No. 3. - P. 17-24;
URL: http://fundamental-research.ru/ru/article/view?id=2764 (date of access: 03/04/2019). We bring to your attention the journals published by the publishing house "Academy of Natural History"

The source of the waves moves to the left. Then the frequency of the waves becomes higher (more) on the left, and lower (less) on the right, in other words, if the wave source catches up with the waves emitted by it, then the wavelength decreases. If removed, the wavelength increases.

Doppler effect- change in the frequency and length of the waves recorded by the receiver, caused by the movement of their source and / or the movement of the receiver.

The essence of the phenomenon

The Doppler effect is easy to observe in practice when a car passes by the observer with the siren turned on. Suppose the siren gives out 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 emits. But if the car approaches the observer, then the frequency of the sound waves will increase (and the length will decrease), and the observer will hear a higher tone than the siren actually emits. At that moment, when the car passes by the observer, he will hear the very tone that the siren actually emits. And when the car goes further and will already be moving away, and not approaching, the observer will hear a lower tone, due to the lower frequency (and, accordingly, greater length) of sound waves.

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

If the wave source is moving 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 emitted by it, then the wavelength decreases, if it moves away, the wavelength increases:

,

where is the frequency with which the source emits waves, is the speed of wave propagation in the medium, is the speed of the wave source relative to the medium (positive if the source is approaching the receiver and negative if it is moving away).

Frequency recorded by a fixed receiver

where is the speed of the receiver relative to the medium (positive if it moves towards the source).

Substituting in formula (2) the frequency value from formula (1), we obtain the formula for the general case:

where is the speed of light, is the speed of the source relative to the receiver (observer), is the angle between the direction to the source and the velocity vector in the receiver reference frame. If the source is radially moving away from the observer, then if it is approaching - .

The relativistic Doppler effect is due to two reasons:

• a classic analog of frequency change with relative motion of the source and receiver;

The latter factor leads to the transverse Doppler effect when the angle between the wave vector and the source velocity is . In this case, the change in frequency is a purely relativistic effect that has no classical analogue.

How to observe the Doppler effect

Since the phenomenon is characteristic of any waves and particle flows, it is very easy to observe it for sound. The frequency of sound vibrations is perceived by ear as a sound pitch. It is necessary to wait for a situation when a fast moving car or train will pass by you, making a sound, for example, a siren or just a sound signal. You will hear that when the car is approaching you, the pitch will be higher, then when the car is close to you, it will drop sharply, and then, when moving away, the car will honk on a lower note.

Application

• Doppler radar is a radar that measures the change in frequency of a signal reflected from an object. From the change in 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 variety of areas: to determine the speed of aircraft, ships, cars, hydrometeors (for example, clouds), sea and river currents, as well as other objects.

• Astronomy
  • By shifting the lines of the spectrum, the radial velocity of the movement of stars, galaxies and other celestial bodies is determined. With the help of the Doppler effect, their radial velocity is determined from the spectrum of celestial bodies. A change in the wavelengths of light vibrations 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 away from the observer (red shift), and towards short ones if the direction of the radial velocity is towards the observer (violet shift) . If the source speed is small compared to the speed of light (300,000 km/s), then the radial velocity 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.
  • By increasing the width of the lines of the spectrum determine the temperature of stars
• Non-invasive flow rate measurement. The Doppler effect measures the flow velocity of liquids and gases. The advantage of this method is that it is not necessary to place the sensors directly into the flow. The speed is determined by the scattering of ultrasound on the inhomogeneities of the medium (suspension particles, liquid drops that do not mix with the main flow, gas bubbles).
• Security alarms. To detect moving objects
• 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.

Art and culture

• In the 6th episode of the 1st season of the American comedy television series The Big Bang Theory, Dr. Sheldon Cooper goes to Halloween, for which he put on a costume symbolizing the Doppler effect. However, everyone present (except friends) thinks he is a zebra.

Notes

see also

Links

• Applying the Doppler effect to measure currents in the ocean

Wikimedia Foundation. 2010 .

• Wax
• Polymorphism of computer viruses

See what the "Doppler Effect" is in other dictionaries:

doppler effect- Doppler effect The change in frequency that occurs when the transmitter is moved relative to the receiver, or vice versa. [L.M. Nevdyaev. Telecommunication technologies. English Russian explanatory dictionary reference book. Edited by Yu.M. Gornostaev. Moscow … Technical Translator's Handbook

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