Doppler effect for sound waves. Doppler effect for electromagnetic waves

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 removed, the wavelength increases.

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

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

In order to be more understandable, consider an example on a car with a siren.

Let's start with the car being parked. The sound from the siren reaches us because the elastic membrane inside it periodically acts on the air, creating compression in it - areas of increased pressure - alternating with discharges. Compression peaks - the "crests" of an acoustic wave - propagate in the medium (air) until they reach our ears and affect the eardrums. So, while the car is standing, we will still hear the unchanged tone of its signal.

But as soon as the car starts moving in your direction, a new one will be added. the effect. In the time from the moment one peak of the wave is emitted to the next, the car will travel some distance towards you. Because of this, the source of each next peak of the wave will be closer. As a result, the waves will reach your ears more often than they did when the car was stationary, and the pitch of the sound you perceive will increase. Conversely, if the car with the horn drives 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 the emitted light can be used to judge the speed of a star 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 redshift indicates that all galaxies are moving away from us at speeds up to about half the speed of light, increasing with distance. The question of whether the Universe is expanding in a similar way or the redshift is due to something else, and not the "retreat" of galaxies, remains open.

In the formula we used

Purpose of work:

Investigation of the dependence of the Doppler frequency shift on the frequency of the sound source and on the speed of the reflecting surface.

Instruments and accessories:

Sound generator (GZ-44).

School sound generator (GZSH-63).

Oscilloscope S-11 (138049).

Current source IPPP-2.

Voltage regulator (RNSH).

High-frequency emitter (2GD-36, power 1-2W)

Double Doppler effect.

In 1842 K. Doppler (Austrian physicist and astronomer) found that the frequency of the perceived sound depends both on the speed of the source (relative to the medium) and on the speed of the observer: it is higher than the source frequency 0 if the observer and the source are approaching and lower 0 if they are removed. This is the Doppler effect.

With the simultaneous movement of the sound source and receiver, the frequency fixed by the receiver , is determined by the formula:

(1)

where is the speed of sound in the medium,

- the speed of the receiver and source,

,
are the angles formed by the source and receiver velocity vectors with the vector connecting the receiver and source.

If the source and observer move along the straight line connecting them, then cos
and formula 1 takes the form:

(2)

The upper signs in formulas (1) and (2) are used when the receiver and source are approaching, the lower ones are moving away.

A variation of the Doppler effect is the so-called double Doppler effect - a change in the frequency of waves when they are reflected from moving bodies, since a reflecting object can be considered as a receiver, and then as a re-radiator of waves.

Let us determine the frequency of the Doppler shift when the receiver (microphone - mcr Fig. 1) and the emitter (radi) are at rest, and the sound-reflecting plate (pl) moves at a speed
(approach; cos
one). At the first stage, the plate plays the role of a receiver moving at a speed (
) pr, and the sound source is at rest (
). Using formula (2), we obtain the frequency of waves falling on the plate (
) etc

)pr=
(3)

At the second stage, the plate reflects the received (
) pr waves and is a source of sound that moves at a speed towards the microphone.

Wave frequency (
) fixed by the microphone, according to formula (2)

(4)

Substituting formula (3) into (4) we obtain

(5)

Now let's determine how much the frequency has changed (Doppler frequency shift).

If the waves incident on the plate and reflected from the plate are superimposed on each other (as in the case considered), then a superposition of waves is observed, the frequencies of which differ little from each other, and this leads to the appearance of beats. The beat frequency is equal to the difference between the frequencies of the incident and reflected waves (
). That. by determining the beat frequency recorded by the microphone and knowing the speed of the reflecting plate, it is possible to determine both the Doppler frequency shift and the frequency of the sound waves reflected by the moving plate and received by the microphone.

(6)

Experimental setup.

The scheme of the experimental setup is shown in Figure 2. The sound source is a high-frequency emitter 1, which converts electrical vibrations generated by a sound generator 2 into sound waves. The sound is reflected from the plates 3, which are mounted on a rotating platform 4. The rotational speed of the platform can be changed over a wide range by changing the voltage supplied to the motor windings 5 ​​from the voltage regulator 6 (RNSH, 0-60V).

Microphone 7, located next to the emitter, receives sound waves directly from the emitter with a frequency and waves reflected from the plates 3. The signal entering the microphone is amplified (DC source). Moreover, the sound signal reflected from the rotating plates hits the microphone only in short (compared to the platform rotation period) time intervals corresponding to a certain relative position of the plates, emitter and microphone.

A felt pad 9 is installed between the emitter and the microphone to reduce the power of direct sound entering the microphone directly from the emitter.

The microphone is connected to an oscilloscope 10. The speed of the plates is slow, so the Doppler frequency shift much less frequency . On the oscilloscope screen, there is a periodically appearing pattern of beats with a frequency

, which is the result of the addition of two sound waves entering the microphone at certain points in time.

The speed of convergence of plates and loudspeaker

where R is the distance from the axis of rotation to the middle of the plates,

- frequency of rotation of the plates.

Completing of the work.

ATTENTION: Devices can be connected to the electrical network only after the teacher has checked the electrical circuit.

It is known that when a fast moving electric train approaches a stationary observer, its sound signal seems to be higher, and when moving away from the observer, it sounds lower than the signal of the same electric train, but stationary.

Doppler effect called the change in the frequency of the 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 stationary relative to it, and the source And move away from the receiver at a speed along the straight line connecting them (Fig. 5.7, a).

The source is displaced in the medium for a time equal to the period of its oscillations by a distance , where is the oscillation frequency of the source.

Therefore, when the source is moving, the wavelength in the medium is different from its value when the source is stationary:

,

where is the phase velocity of the wave in the medium.

The frequency of the wave recorded by the receiver,

(5.7.1)

If the source velocity vector is directed at an arbitrary angle to the radius vector connecting the fixed receiver with the source (Fig. 5.7, b), then

(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, in), then the wavelength in the medium . However, the propagation speed of the wave relative to the receiver is , 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 velocity of the wave source relative to the receiver, and is the angle between the vectors and . The value 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, there is also doppler effect , i.e. wave frequency change registered by the receiver. In contrast to the Doppler effect we have considered in acoustics, the regularities of this phenomenon for electromagnetic waves can be established only on the basis of the special theory of relativity.

The relation describing doppler effect for electromagnetic waves in vacuum, taking into account the Lorentz transformations, has the form:

.

(5.7.7)

At low speeds of the wave source relative to the receiver, the relativistic formula of 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 longitudinal Doppler effect .

In case of convergence of source and destination ()

,

(5.7.8)

and in case of their mutual removal ()

.

(5.7.9)

In addition, the relativistic theory of the Doppler effect implies 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 effect, 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 - a transverse one.

The existence of the transverse Doppler effect follows directly from the dilation of time in moving frames of reference.

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 the American physicists G. Ives and D. Stilwell in the 1930s. Using a spectrograph, they studied the radiation of hydrogen atoms accelerated to velocities of m/s. In 1938 the results were published. Summary: the transverse Doppler effect was observed in full accordance with relativistic frequency transformations (the radiation spectrum of atoms turned out to be shifted to the low-frequency region); the conclusion about time dilation in moving inertial frames of reference is 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 the absorption lines in the spectra of stars and nebulae, it is possible to determine the radial velocities of these objects with respect to the Earth: at using formula (5.7.6)

.

(5.7.11)

The 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 line frequency in the spectrum of a stationary source, is the observed frequency) is exactly the same for all frequencies. Cosmological redshift is nothing but 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. In modern telescopes, one 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 the development of the general theory of relativity.

Hubble established the law that the relative redshift of galaxies increases in proportion to their distance .

Hubble law can be written in the form

,

(5.7.12)

where H is the Hubble constant. According to the latest estimates, carried out in 2003, . (1 pc (parsec) is the distance that light travels in vacuum in 3.27 years ( )).

In 1990, the Hubble Space Telescope was launched aboard the Space Shuttle Discovery (Figure 5.8).

Rice. 5.8	Rice. 5.9

Astronomers have long dreamed of a telescope that would operate in the visible range, but was outside the earth's atmosphere, which greatly interferes with observations. "Hubble" not only did not deceive the hopes placed on it, but even exceeded almost all expectations. He fantastically expanded the "field of vision" of mankind, looking into the unthinkable depths of the universe. During its operation, the space telescope transmitted 700 thousand magnificent photographs to the earth (Fig. 5.9). He, in particular, 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 photographed 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 registering the radiation emitted by them when the age of the Universe was less than 1 billion years.

Radar laser methods for measuring the velocities 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 a 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 an increase in the speed of thermal motion, i.e. with an increase in gas temperature. This phenomenon can be used to determine the temperature of hot gases.

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 travels 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 .

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 travels 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 it emits, 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 oscillations leads to the fact that all spectral lines in the spectrum of the source are shifted towards long waves, if its radial velocity is directed away from the observer (redshift), 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 .

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

doppler effect- Doplerio reiškinys statusas T sritis fizika atitikmenys: engl. Doppler effect vok. Doppler Effect, m rus. Doppler effect, m; Doppler phenomenon, n pranc. effet Doppler, m … Fizikos terminų žodynas

doppler effect- Doppler io efektas statusas T sritis automatika atitikmenys: engl. Doppler effect vok. Doppler Effect, m rus. Doppler effect, m; Doppler effect, m pranc. effet Doppler, m ryšiai: sinonimas – Doplerio efektas … Automatikos terminų žodynas

doppler effect- Doplerio efektas statusas T sritis Energetika apibrėžtis Spinduliuotės stebimo bangos ilgio pasikeitimas, šaltiniui judant stebėtojo atžvilgiu. atitikmenys: engl. Doppler effect vok. Dopplereffekt, m rus. Doppler effect, m; Doppler effect, m … Aiškinamasis šiluminės ir branduolinės technikos terminų žodynas

doppler effect- Doplerio efektas statusas T sritis Standartizacija ir metrologija apibrėžtis Matuojamosios spinduliuotės dažnio pokytis, atsirandantis dėl reliatyviojo judesio tarp pirminio ar antrinio šaltinio ir stebėtojo. atitikmenys: engl. Doppler effect vok … Penkiakalbis aiskinamasis metrologijos terminų žodynas