School encyclopedia. Laboratory work Studying the Doppler effect in acoustics

01.10.2019

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Course work

in the discipline "Physical foundations of measurements"

Using the Doppler effect to measure physical quantities

INTRODUCTION

Doppler effect measurement error

The Doppler effect is a change in the perceived frequency of vibrations caused by the movement of the source and/or receiver of waves. This effect is named after Christian Johann Doppler, who first predicted it theoretically.

This effect is especially noticeable in the case of sound waves, as exemplified by the change in perceived pitch of a passing train whistle.

In radio communications and radio broadcasting using only terrestrial receivers and transmitters, the Doppler effect is neglected (the frequency shift of an FM radio station received in a car moving at a speed of 100 km/h does not exceed 10 Hz). However, satellite communication channels are quite susceptible to it. For example, in the two-meter range used for communication via amateur radio satellites, the Doppler shift reaches several kilohertz, continuously changing as the satellite passes through the visibility zone.

1. DOPPLER EFFECT

The Doppler effect is a change in the length of an electromagnetic wave caused by the movement of a source, which is recorded by a receiver. It is easy to observe in practice when a car with a siren on drives past the observer. Suppose the siren sounds some kind of certain tone, and it doesn't 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.

Figure 2.1 - Propagation of sound waves

For waves (for example, sound) propagating in any medium, 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(for example, light), for which no medium is needed for propagation, only the relative motion of the source and receiver matters.

The effect was first described by Christian Doppler in 1842.

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.

2.1 The essence of the Doppler phenomenon

If the wave source moves relative to the medium, then the distance between the wave crests (wavelength) depends on the speed and direction of movement. If the source moves towards the receiver, that is, catches up with the waves it emits, then the wavelength decreases. If it moves away, the wavelength increases.

(2.1)

Where sch 0 -- frequency with which the source emits waves; c -- speed of wave propagation 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

(2.2)

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.

(2.3)

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

Substituting the frequency value from formula (2.1) into formula (2.2), we obtain a formula for the general case.

(2.4)

2.2 Relativistic Doppler effect

In the case of electromagnetic waves, the formula for frequency is derived from the equations of special relativity. Since electromagnetic waves do not require a material medium to propagate, only the relative speed of the source and the observer can be considered.

(2.5)

Where With-- speed of light, v-- relative speed of the receiver and source (positive if they move away from each other), And- the angle between the wave vector and the speed of the source.

The relativistic Doppler effect is due to two reasons:

- a classic analogue of frequency change with relative movement of the source and receiver;

- relativistic time dilation.

The last factor leads to the transverse Doppler effect, when the angle between the wave vector and the source velocity is equal to And = R/ 2. In this case, the change in frequency is a relativistic effect that has no classical analogue.

If the sound source and the observer are moving relative to each other, the frequency of the sound perceived by the observer is not the same as the frequency of the sound source. This phenomenon, discovered in 1842, is called the Doppler effect.

Sound waves propagate in air (or other homogeneous medium) at a constant speed, which depends only on the properties of the medium. However, the wavelength and frequency of sound can change significantly as the sound source and observer move.

Let's consider a simple case when the source speed X And and the speed of the observer X H relative to the medium are directed along the straight line that connects them. For a positive direction for X And and X H can take the direction from the observer to the source. Sound speed X is always considered positive.

Figure 2.2 - Doppler effect, case of a moving observer, successive positions of the observer are shown through the period TN of the sound perceived by the observer

Figure 2.2 illustrates the Doppler effect in the case of a moving observer and a stationary source. The period of sound vibrations perceived by the observer is designated by TN. From Figure 2.2 it follows:

(2.6)

Taking this into account we get:

(2.7)

If the observer moves in the direction of the source (x H > 0), then f H > f And, if the observer moves away from the source (x H< 0), то f Н < f И.

Figure 2.3 - Doppler effect, case of a moving source, successive positions of the source are shown through the period T of the sound emitted by the source

In Figure 2.3, the observer is stationary, and the sound source is moving at a certain speed X I. In this case, according to Figure 2.3, the following relation is valid:

or (2.8)

Where and

This implies:

(2.9)

If the source moves away from the observer, then X And > 0 and therefore f N< f I. If the source approaches the observer, then X AND< 0 и f N> f AND.

In general, when both the source and the observer are moving at speeds X And and X H, the formula for the Doppler effect takes the form:

(2.10)

This ratio expresses the relationship between f N and f I. Speed X And and X H are always measured relative to air or other medium in which sound waves propagate. This is the so-called non-relativistic Doppler effect.

In the case of electromagnetic waves in vacuum (light, radio waves), the Doppler effect is also observed. Since electromagnetic waves do not require a material medium to propagate, only the relative speed x of the source and the observer can be considered. The expression for the relativistic Doppler effect is:

(2.11)

Where c- speed of light. When X> 0, the source moves away from the observer and f N< f And, in case X < 0 источник приближается к наблюдателю, и f N> f AND.

The Doppler effect is widely used in technology to measure the speed of moving objects (“Doppler location” in acoustics, optics and radio).

2.3 Doppler phenomenon

Numerous interference and diffraction phenomena discussed above provide us with methods for directly measuring the wavelength of light in a vacuum environment

.

From these two quantities one can also determine the frequency of the emitted radiation or its period.

The frequency or period of emitted almost monochromatic radiation is a characteristic of those intra-atomic processes that determine the emission. We have no methods at our disposal to directly measure these frequencies.

Doppler's reasoning is applicable to all wave phenomena - optical, acoustic and others. Doppler observed (qualitatively) the phenomenon he predicted in acoustic processes and suggested that the difference in the color of some stars was due to their motion relative to the Earth. The last conclusion is incorrect. For the vast majority of stars, the influence of their motion is reflected only in minor changes in the position of spectral lines in the stellar spectrum. Nevertheless, the applicability of the Doppler principle to optical phenomena does not raise doubts. For the first time, a reliable experimental establishment of the optical Doppler phenomenon and its most fruitful applications were actually made in the observation of astronomical phenomena.

The interpretation of the problem essentially depends on whether we can only talk about the relative motion of the source and receiver relative to each other, or whether it makes sense to talk about the speed of the disturbance relative to the medium, i.e. take into account the movement of the source and receiver in this environment.

2.4 Doppler phenomenon in acoustics

For sound waves, the second case undoubtedly occurs: acoustic waves propagate in a medium (gas), within which the source and receiver can move, so it makes sense to ask not only about their motion relative to each other (relative motion), but also about their movement in relation to the environment.

Figure 2.4 - To derive the Doppler formula in the case of source motion relative to the medium

Let us therefore consider both cases separately:

a) movement of the source;

b) movement of the receiving device.

a) The source moves relative to the medium at a speed v. The speed of a wave in a medium c is constant, independent of the movement of the source.

Let the receiver be at point B and the source S 1 moving at speed v along the S 1 V line connecting the source to the receiving device, in accordance with Figure 2.4. The wave emitted at the moment t 1, when the source is at a distance S 1 V=a from the device, will reach the latter by the time

(2.12)

a wave emitted at the moment t1=t2+ф will reach the receiver at the moment

, (2.13)

because by the time t 2 the distance between the source and the device becomes equal (a+xf) or (a-hf) depending on the direction of movement.

So, the waves emitted by the source during the time f = t 2 - t 1, act on devices for a period of time

(2.14)

If X 0 is the frequency of the source, then during the time f it will emit N=X 0 f waves and, therefore, the frequency perceived by the device is X=N/? . It is equal

in case of source removal, (2.15)

when the source approaches. (2.16)

Since the speed of a wave in a medium is determined by the properties of the latter, i.e. does not depend on the movement of the source and remains equal to c, then in the case considered there must necessarily be a change in the wavelength.

If we denote by l 0 is the wavelength observed in the absence of source motion, and after l-- wavelength perceived in the case of source motion, then we find

(2.17)

So, when a source moves in a medium, the speed of the wave relative to the device located in this medium remains constant, but the frequency and wavelength perceived by the receiver change. In other words, an experiment of the Fizeau type gives the same value for the speed of an acoustic wave as with a stationary sound source, and an interference experiment gives a changed wavelength; the same applies to frequency, which in the case of acoustic waves can be observed directly, for example, by comparison with a siren sounding in unison.

Figure 2.5 - To derive the Doppler formula in the case of motion of the receiver relative to the medium

b) The receiver moves relative to the medium at a speed v, the wave speed in the medium is equal to c, in accordance with Figure 2.5. Repeating the reasoning given above, we would have to And 1 and And 2 write accordingly:

(2.18)

because the approach between the wave and the device occurs at a speed c=X(wave speed relative to the device), in accordance with Figure 2.5. Thus,

(2.19)

and the frequency perceived by the receiver will be equal to

in case of removal of the device, (2.20)

when the device approaches. (2.21)

When the receiver moves, the speed of the wave relative to it is the sum of the speed of the wave relative to the medium and the speed of the device relative to the medium, i.e. equal to

(2.22)

The wavelength perceived by the receiver thus remains unchanged. Really,

(2.23)

So, if the receiver moves, the frequency and speed of the wave relative to the device change, but the wavelength perceived by it remains unchanged.

3 . METHODS FOR MEASUREMENT OF PHYSICAL QUANTITIES BASED ON THIS PHYSICAL EFFECT

3.1 Forward and reverse flow

Doppler frequency shift is also useful for determining the movement of a liquid or gas towards or away from a transmission system. In manufacturing industries this requirement is not common. However, in the medical field this is extremely relevant. For example, backflow may occur near the heart valve.

The reflected signal can be represented as:

(3.1)

Where A i -- amplitude of the reflected transmitter signal with frequency w 0 ; F j - amplitude of the reflected signal received from scattering objects moving towards the receiver; IN To -- amplitude of the reflected signal from particles moving in the opposite direction. In practice, the reflected signal will be continuous, but in the FFT representation, as described above, individual spectral lines will be obtained. Reception of frequency-shifted components is relatively correct as long as the desired frequency is shifted. To determine the frequency shift up or down, more detailed signal processing is required. Nippa et al. (1975) have proposed several methods for this, which will be discussed below. For 10 MHz, with a flow rate of 0.9 * 10 -2 to 9 * 10 -2 m·s -1 , the frequency shift will be between 100 Hz and 10 kHz. The spectrum for forward and reverse flow shown in Figure 3.1, although not suitable for measurement, reflects the nature of the process.

1) Separation using direct filtering

One might assume that simply filtering the input reflected spectrum is a suitable solution. The frequency of the reflected signal components at 10 MHz will range from 10.0001 h 10.001 MHz to 9.9999 h 9.99 MHz. However, as Nippa et al. note, separating frequencies in the range from 10 MHz to 10.0001 MHz at 40 dB is an impossible task using filters, especially when the frequency of interest is drifting.

Figure 3.1 - Reflected spectrum for forward and reverse flows

2) Frequency shift

A downward shift in the frequency of the Doppler spectrum means that the requirements placed on the filter become less stringent. Frequency shifting is a common procedure in telecommunications. For example, composite stereo in the UK and high-frequency FM broadcasting use frequency shifting to improve the use of the transmitter's frequency range.

The frequency shift can again be achieved using a multiplication procedure. The procedure used here is called heterodyning by radio engineers. Frequency w T, which is related to, but slightly lower than, the transmission frequency, is multiplied by the reflected signal. In this case, as usual, two components are obtained with the difference and the sum of the frequencies. Frequency used for multiplication w T , must be such that the frequency difference component places the frequency band of the reflected signal in a suitable range at the lower end of the frequency spectrum.

Figure 3.2 - Reflected spectrum for forward and reverse flows

To generate w T you can use a phase synchronization system. Let's express the value w T in the following way:

(3.2)

where w het is generated by a fixed low-frequency oscillator. Because the w T derived from w 0, no drift w 0 will not cause the reconstructed signal to drift. It's clear that w het must be higher than the highest expected frequency in the Doppler effect.

After dropping the high frequency there will be two spectral bands,

and spectrum line w het.

A very strict notch filter can then be used to remove w het, but with the modern technical approach, preference is given to processor processing rather than analog technology. FFT allows you to calculate the spectrum directly and ignores w het.

3) Phase rotation

Because of the requirements stated in the two previous methods, the main part of the paper by Nipp et al. (1975) is devoted to the phase shifting system. The technique on which this system is designed is similar to phase-quadrature detection, as shown in Figure 3.3, used in telecommunications engineering. It includes two elements that shift the phase exactly 90°, as shown below.

Figure 3.3 - Phase-quadrature detection

For convenience, a separate component of the reflected spectrum velocity from expression (3.1) is used for illustration:

(3.3)

Multiplying the reflected signal by the phase-shifted transmission frequency, we obtain:

(3.4)

Using the trigonometric identity and filtering the high frequency DC component will give:

(3.5)

or

(3.6)

But the signal Va subsequently shifted by 90° and formula (3.6) will be presented as

(3.7)

After simplification we arrive at the expression:

(3.8)

Accordingly, multiplying the reflected signal by the transmission frequency

Dcos w 0 t leads to

(3.9)

After simplification and filtering, the expression is reduced to

(3.10)

Then the output signals look like:

(3.11) (3.12)

Let us formulate two necessary conditions for normal operation of the system:

The amplitudes DB in the signals U" A and U" B must be identical in absolute value for the correctness of the summation and subtraction procedures in expressions (3.11) and (3.12). A similar requirement holds for amplitudes DF. This will require some settings for the signal amplifier located in the system. The signal in the system developed by Knipp et al. (1979) varies by less than 0.2 dB.

The two 90-degree phase shifters should function well over the entire frequency range. A high-frequency phase shifter has a relatively low propagation frequency, so it is less demanding to design. The second low-frequency phase shifter covers a wide range. According to Knipp et al (1975), the design used in their system was octapolar. A transistor filter that rotates 90° ±0.6° over the entire range from 50 Hz to 7.5 kHz. The circuit published by Dickey (1975) uses op-amps to generate a 90-degree phase shift for the range from 100 Hz to 10 kHz.

Due to the advantage of digital devices, in modern design the low-frequency part of the system: filtering, phase shift, addition and subtraction are performed digitally. Digital systems are more promising for design and are very stable in operation, since the settings do not depend on the values of the system components, unlike analog systems, the parameters of which drift with age and temperature.

3.2 Blood flow measurement

Blood flow measurement has an important place in a number of medical fields. However, measuring this speed directly is difficult. Some medical areas where flow rate information is useful are listed below.

In order to evaluate heart parameters, it is necessary to know the speed of blood flow. Currently the dilution method is used. Cold water is injected into the artery and changes the average temperature, with the help of which the degree of dilution of the blood and thereby its volume can be calculated. Obviously, like any invasive procedure, it causes discomfort and, moreover, is not without risk for the patient.

For collateral research internal organs fetal oxygen, it is necessary to determine the patency of the umbilical cord. When the umbilical cord is damaged, the mother's blood pressure increases. High blood pressure is a sign of a condition known as preeclampsia and can be dangerous for mother and baby. Ultrasound can be used to determine velocity components, but not full meaning flow speed.

Some areas of blood flow measurement where volumetric flow rates are not required, but only individual indicators of changes in the velocity profile are needed.

- Partial blockage caused by a thrombus may result in increased flow rates near the obstruction. In the very simple version, a portable ultrasonic transmitter with audio frequency output can be used to detect the location of a blood clot.

Tumor growth is marked by a stage where, in order to support growth, the vascular system within the tumor must develop. Wells et al. (1977) published work on the Doppler signal shift increasing from micro-circulations within a malignant breast tumor. The structure of new vessels in the tumor differs from normal tissues; they are much larger in diameter, the walls are thinner, and there is a lack of compressive elements. Berne et al., (1982) report that the Doppler shift of the spectrum from blood flow near and in the chest tumor has different character, and from this a useful diagnostic procedure can be designed.

Currently, ultrasonic imaging systems are very well developed. Duplex systems not only reproduce the image, but can also present a Doppler shift measurement on the image at a selected location by overlaying the cursor on the image displayed on the monitor. Some duplex systems color encode the image so that the flow detected by the Doppler shift appears as shades of red or blue in other monochrome images. In addition green color can be used as a function for a signal variant. In this way, clinicians can see where the flow is flowing from or to the sample site, and also, if turbulence is represented by green, a mixture of red and blue produces yellow or blue shading, respectively.

One might think that with complex duplex systems, it is possible to reliably estimate the flow rate value by measuring the vessel diameter and measuring the average flow velocity based on the Doppler shift. Unfortunately, in addition to the problems in obtaining a reliable estimate of the average velocity from the reflected signal, as described above, there are a number of other problems:

- the vessels may not be round;

- the diameter of the vessel can vary along systole and diastole;

- the type of flow regime may change during the cardiac cycle, so estimates of average velocity may be erroneous;

- Estimating the average cross-section and average velocity during the cardiac cycle will not provide a correct measurement of the average flow rate because both quantities are non-linear. Attempting to simultaneously measure mean velocity and cross-section is difficult due to signal processing limitations.

Many modern duplex systems have algorithms for calculating blood flow rates, and reasonable estimates can be obtained on vessels ranging from 4 to 8 mm in diameter (Ivane et al., 1989).

On the other hand, certain flow estimates have become popular and can be carried out in a manner suitable for medical purposes. Measuring the maximum frequency offset is a relatively straightforward method and can be useful for gaining insight into flow abnormalities. Figure 3.4 shows the type of changes possible in one cardiac cycle, shown for forward flow only. Mo et al. (1988) compare different methods for estimating maximum frequency.

Although waterfall display is sometimes used in research, most modern Doppler blood flow analyzes display the FFT spectrum as a consequence of vertically oriented frames. The location of a simple frame is shown in Fig. 3.4. These images are obtained in a sliding format on the monitor and correspond to sonograms. Intensity information is located on the z axis (outside the figure) and is shown as a color code in this type of analysis.

Understanding the collected data becomes the task of recognition systems. Over the years, many algorithms have been invented in an attempt to automate the future process of information extraction. The following measurement parameters are used:

- consumption S/ D;

- pulsation index:

S - D/ average speed (3.13)

- Parselot resistance index:

(S - D)/ S (3.14)

Figure 3.4 - Typical maximum frequency of Doppler shift in the cardiac cycle

To obtain the value of S, some threshold values must be accepted initially. When using low pass filters, care must be taken to ensure that the values D unaffected by external vibrations. average speed is assessed over the entire period of the cardiac cycle, which is conveniently done through a moving average and an FFT algorithm.

Although flow measurements have been taken for millennia, there is still a lot of research work. In addition, the design of working devices requires expert assessments across the entire spectrum of engineering physics.

3.3 Basic mathematical relationships

The Doppler effect measures:

- speed

- drift to determine the ground speed vector

- speed of movement of solid bodies

- flow rates of liquid or granular media

- fluid flow

- change the signal frequency

The operation of Doppler meters is based on the use of the Doppler effect in continuous radiation mode. The essence of the Doppler effect is that the oscillation frequency f d received from any source turns out to be not equal to the frequency of oscillations emitted by this source if the source and receiver of the oscillations move relative to each other.

The frequency change is greater, the more more speed movements of the receiver and transmitter relative to each other, and if the source approaches the receiver, then the received frequency will be higher than the emitted one, and vice versa. The same effect occurs if the transmitter and receiver are stationary relative to each other and are located on an aircraft, and the vibrations are received after reflection from the surface of the earth.

The amount of frequency deviation of the received signal is called the Doppler frequency shift, or Doppler frequency f d:

f pr = f+ f d (3.15)

The value of the Doppler frequency shift is determined by the equality

F d =; (3.16)

Where W s is the projection of the total speed of the aircraft in the direction of radiation;

l- wavelength of vibrations emitted by the transmitter.

In the coordinate system associated with the aircraft (aircraft coordinate system X, U, Z), the direction of radiation S is determined by the angles ? And d, in accordance with Figure 3.5,

Where ? - the angle between the direction of the longitudinal axis of the aircraft X and direction of radiation S;

d- the angle between the reverse direction of the vertical axis of the aircraft Y and projection S yz direction of radiation S to the plane YZ.

The aircraft's full speed vector W can be decomposed in the aircraft coordinate system into three components: W x, W y, W z, in accordance with Figure 3.5.

Designing Full Speed Components W x, W y, W z to the direction of radiation S and summing them up, we get:

W s = W x cozy - W Y cos8 cos(90°-y) + W z cos(90°-8) cos(90°--y),

or

W s = W x cozy -W y cos5 siny + W z sin5 siny. (3.17)

Figure 3.5 - Reciprocity of ground speed and direction of radiation in the aircraft coordinate system

f =~W xcosY--W Ycos8sinY + -W zsm5sinY. (3.18)

Since equation (3.18) contains three unknowns, to determine all components of the total speed ( W x ; W Y W z) it is necessary to have three equations of type (3.18), which can be obtained by using an antenna system with three non-coplanar (not lying in the same plane) beams.

To simplify calculations, the viewing angles of the antenna beams are selected:

.

Substituting the angle values for each of the beams into equation (3.18), we obtain a system of equations for the absolute value of the Doppler frequencies for each of the antenna beams:

(3.19)

Using the expressions of system (3.19), we determine the approximate values W x (1) , W y(1) , W z (1) components of the full speed of the aircraft W:

(3.20)

Formulas (3.20) are a first approximation, since they do not take into account:

- deviation of the real fragile sighting of the antenna beams from the nominal ones;

- Doppler frequency shift, determined by the nature of the reflecting surface;

- the actual value of the wavelength of vibrations emitted by the transmitter.

The first component of the error can be reduced to an acceptable value by measuring the deviation of the actual angles of sight of the beams from their nominal value and introducing corrections for these deviations in the on-board computers or specialized computers that are part of the PNC interfaced with the DISS.

The second component of the error arises as a result of deformation of the Doppler spectrum and a shift of its maximum towards low frequencies, which are caused by changes in the reflection coefficient o within the antenna beam.

Reflection coefficient a generally depends on the angle of incidence B (Figure 3.5), and this dependence is different for different reflecting surfaces (Figure 3.6).

Figure 3.6 - Dependence of the reflection coefficient on the angle of incidence of the antenna beam for various reflective surfaces

Dependency graphs correspond to the following types of surfaces: I - sea, 7-8 points; P - forest; Ш - snow; IV - green grass; V - sea, 1 point.

From the graphs in Figure 3.6 it can be seen that the reflection coefficient changes most strongly depending on the angle of incidence for the sea surface (graph V), therefore this phenomenon is often called the “sea effect”.

As a result, the spectrum of reflected signals within the antenna beam is distorted, the power of low frequencies increases and the power of high frequencies decreases, since low frequencies correspond to points irradiated at a greater angle of incidence B than points corresponding to high frequencies.

As a result of this, the maximum power in the spectrum of the signal reflected from the earth's surface shifts, and, consequently, the average Doppler frequency of the spectrum. The magnitude of the displacement hop varies from 0 to 3% and gives an error in measuring the speed of the aircraft due to the nature of the reflecting surface.

If we take two points on the curve of d versus the angle of incidence, corresponding to different angles of incidence, for example B 1 and IN 2, then the difference in the logarithms of the reflection coefficients corresponding to these points will be proportional to hop.

Based on this dependence, in the DISS-7 meter, for example, a correction for the nature of the reflecting surface is calculated by comparing the powers of the signals received along two beams (beams 1 and 4 in Fig. 3.7 inclined to the reflecting surface under different angles falls B 3 and IN 4 . The power ratio between the fourth and first beams of the receiving antenna is determined by the nature of the reflecting surface.

Figure 3.7 - Layout of DISS-7 antenna beams

This relationship allows us to calculate the magnitude of the Doppler spectrum shift A hop and output it to the systems interfaced with the meter in the form of voltage G hop - Magnitude U hop related to D hop ratio

U hop = K hop* D hop (3.21)

Where K hop is a constant scale factor.

Full velocity projection values W x, W Y W z taking into account the shift of the Doppler spectrum due to the nature of the reflecting surface and the deviation of the actual viewing angles of the antenna beams and the transmitter frequency from their nominal ones.

In the DISS-7 meter it is accepted that W x = W x, W Y= W y, W z = W z.

In the DISS-15 meter, correction for the nature of the reflective surface is carried out by the LAND-SEA switch. When operating in the “Sea” mode, the scale of measurement of the parameters of the components of the velocity vector is forcibly increased by (2.0 ± 0.3)% relative to the scale in the “Land” mode. .

Calculation of full speed components W x, W Y W z is carried out in an on-board computer or in specialized navigation computers according to data generated by the DISS meter.

3.4 Application of the Doppler effect

Doppler radar

Radar, which measures the change in frequency of a signal reflected from an object. Based on 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 applications: to determine speed aircraft, ships, cars, hydrometeors (such as clouds), sea and river currents, and other objects.

Astronomy

Figure 3.8 - Proof of the Earth's rotation around the Sun using the Doppler effect.

- The radial velocity of motion of stars, galaxies and other celestial bodies is determined by the displacement of spectral lines

Using the Doppler effect across the spectrum celestial bodies their radial velocity is determined. 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 speed of the source is small compared to the speed of light (300,000 km/s), then the radial speed 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.

The temperature of stars is determined by increasing the width of spectral lines.

Non-invasive flow rate measurement

The Doppler effect is used to measure the flow rate of liquids and gases. The advantage of this method is that it does not require placing sensors directly into the flow. The speed is determined by the scattering of ultrasound on inhomogeneities of the medium (suspension particles, drops of liquid that do not mix with the main flow, gas bubbles).

Car alarms

To detect moving objects near and inside the vehicle

Determining coordinates

In the Cospas-Sarsat satellite system, the coordinates of an emergency transmitter on the ground are determined by the satellite from the radio signal received from it, using the Doppler effect.

4 . SOURCES OF ERRORS LIMITING THE ACCURACY OF MEASUREMENTS BASED ON THIS PHYSICAL EFFECT

Due to the occurrence of this effect, the following types of errors may occur:

Instrumental / instrument errors - errors that are determined by the errors of the measuring instruments used and are caused by imperfections in the operating principle, inaccuracy of scale calibration, and lack of visibility of the device;

Methodological errors are errors caused by the imperfection of the method, as well as simplifications underlying the methodology;

Subjective / operator / personal errors - errors caused by the degree of attentiveness, concentration, preparedness and other qualities of the operator.

The main sources of error are:

Mechanical deformation of device parts due to temperature changes;

Magnetic sensor disturbances;

Electrostatic field;

Magnetic fields from devices located in close proximity to the meter can affect metal components of the meter.

The Doppler ground speed and drift angle meter DISS-7 is designed for continuous automatic calculation of the components of the full ground speed vector in the aircraft XYZ coordinate system.

This is equivalent to measuring the ground speed, drift angle, and angle in the vertical plane between the vectors and, where is the ground speed vector, which is the projection of the total ground speed vector onto the horizontal plane.

DISS-7 operates as part of the PNK flight and navigation complex and has the following tactical and technical data.

Tactical and technical data of DISS-7:

Type of radiation - continuous;

Frequency of emission of high-quality vibrations in normal climatic conditions, in other climatic conditions - MHz;

Transmitter power is not< 2 Вт;

The range of measured Doppler frequencies is 1.5 h 32 kHz;

Antenna beam switching frequency 2.5 ± 0.25 Hz;

Continuous operation time 12 hours;

The operating altitude is measured from 200 to 20,000 m, at roll and pitch angles not > ± 30 degrees and at altitudes from 20,000 to 30,000 m at and not > ± 5 degrees;

When flying over the water surface, DISS-7 provides measurements with waves not lower than 2 points;

Receiver sensitivity is no worse than 113 dB/mW;

The average measurement error is not > 0.9%;

Meter weight 29 kg;

Overall dimensions 666 x 406 x 231 mm;

Supply voltage:

~ 115 V, 400 Hz, with current consumption up to 2 A;

27 V, with current consumption up to 2.5 A;

Temperature environment, from minus 60 to plus 60° C;

Relative air humidity at a temperature of + 35 °C is not > 98%;

Air pressure, not< 15 мм рт. ст.

Currently, autonomous aircraft navigation aids are widespread. These include Doppler meters of the object's velocity vector. The most common of them are Doppler ground speed and drift angle meters (DISS).

The ground speed of an aircraft is usually understood as horizontal projection its speed relative to the earth's surface. The ground speed W is related to the air speed V and the wind speed U by a navigation triangle, in which the angle μ between the air and ground speed vectors is called the drift angle, since it is caused by the wind. The Doppler meter allows you to directly determine ground speed from the frequency spectrum of the signal reflected by the earth's surface, based on the Doppler effect, which consists in changing the frequency of the signal reflected from an object depending on the speed of movement of this object.

During horizontal flight of the aircraft, in order to ensure a sufficiently large projection of the velocity vector W on the direction of irradiation and to maintain significant reflection from the surface in the direction of DISS, inclined irradiation of the surface is used.

If the reflective properties of the surface in the irradiated area are approximately the same, then the shape of the frequency spectrum envelope of the reflected signal is determined by the shape of the meter's pattern in the vertical plane. In this case, the signal at the middle frequency of the spectrum, corresponding to the direction of the bottom axis, has the maximum power.

To measure the ground speed of an aircraft, it is necessary to find the average frequency of the Doppler spectrum Fw 0 . If the vector W is horizontal and makes an angle r with the axis of the bottom in the horizontal and in 0 in vertical planes, then:

If the direction of irradiation coincides with the vector W in the horizontal plane, then the angle g=0 and the increment reaches its maximum:

If l are known u and in 0 , then the ground speed W can be determined by direct measurement Fw T using a frequency meter.

Single-beam radio speed meters, however, are not used due to the very low measurement accuracy. This inaccuracy is caused, first of all, by the inaccuracy of alignment of the bottom axis with the vector W due to measurement error. The second important reason for errors in speed measurement with a single-beam device is the roll of the aircraft. This error reaches 0.05% deviation of the instrument readings from the true speed for each degree of roll of the aircraft.

The roll error can be compensated by stabilizing the aircraft antenna in the horizontal plane or introducing roll corrections when processing data in a computing device. However, this naturally leads to the complexity and weight of the calculator, without eliminating the organic disadvantages of the single-beam measurement method, which also include high requirements for the stability of the frequency of the measured oscillations.

The most reasonable way to increase the accuracy of speed measurements is to use multi-beam meters emitting in two, three or four directions.

Multibeam velocity vector meters based on the Doppler effect are divided into aircraft and helicopter ones. In aircraft DISS, the longitudinal and transverse components of the velocity vector are measured, while in helicopter systems the vertical component of velocity is also measured. In addition, for aircraft DISS the sign of the velocity vector is unknown in advance, which may even be zero in hovering mode. The maximum values of the measured speeds and the altitude measurement ceiling differ - for aircraft systems they are tens of times higher. However, the output of helicopter meters is larger due to the need to measure the full velocity vector. Helicopter DISS are also used for soft landing of spacecraft, and airplane ones are used for control cruise missiles and ekranoplanes.

Figure 4.1 - Block diagram of DISS

The velocity vector meter, a simplified block diagram of which is shown in the figure, includes an antenna device that forms three or four beams, a transceiver, a signal processing device, a velocity component calculator and a display device. Typically, DISS data is directly entered into the system automatic control LA.

Let us consider the principle of operation of multi-beam DISS for horizontal flight, in which the vector W is always directed forward and there is no vertical component of speed. To understand the need to use three or four beams, let's first study two-beam systems.

When measuring ground speed and drift angle, the antenna system is rotated until the signal spectra at the output of the receiver channels corresponding to the two antenna beams are combined. In this case, the axis of symmetry of the rays is aligned with the vector W, and the angle between this axis and the axis of the aircraft equal to angle demolition c. The accuracy of a double-beam system is higher than that of a single-beam system, since when the antenna is rotated, the beams intersect lines of equal frequencies at an angle close to a straight line, and this ensures greater sensitivity of the system.

If during measurement the equality of frequencies Fw 1 And Fw 2 established inaccurately, this leads to an error in determining the drift angle, but almost 30 times less than that of a single-beam system. However, the error due to roll remains approximately the same as that of a single-beam system, that is, unreasonably high.

The accuracy of ground speed measurements is greatly improved when using two-way systems with beams directed forward and backward. This design solution makes it possible to reduce ground speed measurement errors by another 3-5 times. However, the drift angle measurement error remains almost the same as that of a single beam system.

Obviously, a simultaneous increase in the measurement accuracy of both the drift angle and ground speed can only be achieved by using three or four beams in the system.

Having achieved equality of difference frequencies by rotating the antenna system, it is possible to determine the drift angle from the position of the antenna system relative to the aircraft axis, and the ground speed from the measured difference frequency.

When the antenna system is stationary relative to the axis of the aircraft, the values of W and μ are found by solving simple equations using a computing device.

The four-beam system combines the advantages of the longitudinal and transverse two-beam systems, which consist in a significant reduction in errors due to the longitudinal and transverse rolls of the apparatus, since their influence is practically compensated by subtracting the Doppler shifts of oppositely directed beams. High sensitivity to changes in the Doppler shift when the aircraft axis deviates in the horizontal plane is maintained, which makes it possible to find the drift angle or transverse velocity component with high accuracy. A great advantage of the system is also the reduction of requirements for short-term frequency stability, since the interacting channel signals come from approximately equal distances and their time shift is small. Almost the same results can be obtained when using three beams in a system.

The technical construction of DISS largely depends on the selected radiation mode. Currently, systems of continuous radiation without modulation or with frequency modulation are used, as well as systems with pulsed radiation of low and high duty cycles.

The main advantage of a continuous radiation system without modulation is the concentration of the spectrum of the reflected signal within one frequency band, which ensures the most complete use of signal energy, as well as a relatively simple design of the transmitter, receiver and indicator. The disadvantage of this system is that it is very high level noise modulated in phase and amplitude, which leads to a decrease in receiver sensitivity.

To reduce the influence of noise, systems with frequency or pulse modulation are used. Frequency modulation has become more widespread.

To use pulsed radiation, two spaced apart antennas are used on one aircraft. This method makes the system heavier and more complex.

The use of DISS, especially in combination with such navigation devices as an inertial navigation system, airspeed sensor, heading vertical, angular-rangefinder short-range navigation system, long-range navigation radio system, on-board radar, can significantly increase the reliability and accuracy of flight control, so a radio speed meter has become integral element of flight navigation systems.

CONCLUSION

The Doppler effect is widely used both in science and in everyday life. Around the world it is used in police radars to catch and fine speeding traffic offenders. A radar gun emits a radio wave signal (usually in the VHF or microwave range) that reflects off the metal body of your car. The signal arrives back to the radar with a Doppler frequency shift, the value of which depends on the speed of the vehicle. By comparing the frequencies of the outgoing and incoming signals, the device automatically calculates the speed of your car and displays it on the screen.

The Doppler effect found a somewhat more esoteric application in astrophysics: in particular, Edwin Hubble, for the first time measuring the distances to nearby galaxies with a new telescope, simultaneously discovered a red Doppler shift in the spectrum of their atomic radiation, from which it was concluded that the galaxies are moving away from us. In fact, this was as clear a conclusion as if you, having closed your eyes, suddenly heard that the tone of the engine of a car of a model you were familiar with was lower than necessary, and concluded that the car was moving away from you. When Hubble also discovered that the further away a galaxy is, the stronger the redshift (and the faster it flies away from us), it realized that the Universe is expanding. This was the first step towards the Big Bang theory.

The most striking thing is that the Doppler effect also works in the case when the oscillation frequencies are huge, as in the case of radioactive radiation, and the relative speeds of the source and absorber are only millimeters per second. That is, the energy of gamma quanta changes due to the Doppler effect by a very insignificant amount. This is used in nuclear gamma resonance spectrometers (Mössbauer spectrometers).

LIST OF LITERARY RESULTS USED SOURCES

1 Jackson R.G. The latest sensors, 2007. - 352 p.

2 Flerov A.G. Doppler devices and navigation systems / A. G. Flerov, V. G. Timofeev - M.: Transport, 1987. - 191 p.

3 Krasilnikov A. S. Sound and ultrasonic waves in air, water and solids/ A. S. Krasilnikov - 3rd ed. - M., 1960. - 327 p.

4 Enochovich A. S. Brief reference book on physics / A. S. Enochovich - 2nd ed. - M.: graduate School, 1976. - 288 p.

5 Osipov M. L. Radio engineering / M. L. Osipov. - M., 1995.

6 Bunkin B.V. Letters to ZhTP / B.V. Bunkin. - M., 1989.

7 Van Trees, G. Theory of detection, estimation and modulation / G. Van Trees. - K., 1987. - 187 p.

8 Tikhonov V.I. Optimal signal reception / V.I. Tikhonov. - M., 1979. - 153 s.

9 Kulikov E.I. Estimation of signal parameters against a background of interference / E.I. Kulikov, A.P. Trifonov. - M., 1983. - 97 s.

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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

Wikimedia Foundation. 2010.

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

Redshift shift of spectral lines chemical elements to the red (long wavelength) side. This phenomenon may be an expression of the Doppler effect or gravitational redshift, or a combination of both. Spectrum shift... Wikipedia

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

The theories of relativity form an essential part of the theoretical basis of modern physics. There are two main theories: particular (special) and general. Both were created by A. Einstein, particular in 1905, general in 1915. In modern physics, particular... ... Collier's Encyclopedia

A branch of astronomy that studies space objects by analyzing the radio emission coming from them. Many cosmic bodies emit radio waves that reach the Earth: these are, in particular, the outer layers of the Sun and planetary atmospheres, clouds of interstellar gas.… … Collier's Encyclopedia

Hot glowing celestial bodies like the Sun. Stars vary in size, temperature and brightness. In many respects, the Sun is a typical star, although it seems much brighter and larger than all other stars, since it is located much closer to... ... Collier's Encyclopedia

The Doppler effect for elastic waves is due to the constancy of the speed of propagation of an elastic wave in a medium that serves as a certain selected reference frame. For electromagnetic waves, such a dedicated reference frame (medium) does not exist, and an explanation of the Doppler effect for electromagnetic waves can only be given within the framework special theory relativity.

Let the source S approaches a stationary receiver with speed R. In this case, the source emits electromagnetic pulses with a frequency (natural frequency) in the direction of the receiver. The time interval between two successive pulses in the reference frame associated with the source is equal to . Since the source is moving, the corresponding period of time in the stationary frame of reference associated with the receiver, due to the slowing down effect of the moving clock, will be greater, namely

, (40.1)

The distance between adjacent pulses in the reference frame associated with the receiver will be equal to

. (40.2)

Then the pulse repetition rate perceived by the receiver will be equal to , or

. (40.3)

The resulting formula (40.3) corresponds to longitudinal Doppler effect, which is a consequence of two phenomena: the slowing down of a moving clock and the “compression” (or discharge) of pulses associated with a change in the distance between the source and the receiver. If the source approaches (as in the case considered), then the frequency of the received electromagnetic wave increases (), but if it moves away, then (in this case the sign of the speed changes to the opposite).

If the speed is much less than the speed of light, then (40.3) can be replaced, up to terms, by an approximate formula (non-relativistic approximation):

. (40.4)

In the general case, when the source velocity vector forms an angle with the direction to the receiver (line of sight), the velocity in formula (40.3) should be replaced by its projection to the line of sight and then the frequency of the received electromagnetic waves is determined by the expression

. (40.5)

From the last expression it follows that if the source moves perpendicular to the direction towards the receiver (), then the transverse Doppler effect is observed:

, (40.6)

in which the frequency perceived by the receiver is always less than the natural frequency of the source (). The transverse effect is a direct consequence of the slowing down of the moving clock and is much weaker than the longitudinal one.

The longitudinal Doppler effect is used in location to determine the speed of an object. Taking into account the Doppler frequency shift may be required when organizing communications with moving objects. Double stars were discovered using the Doppler effect. In 1929, the American astronomer E. Hubble discovered that the lines in the emission spectrum of distant galaxies are shifted towards longer wavelengths (cosmological redshift). The red shift occurs as a result of the Doppler effect and indicates that distant galaxies are moving away from us, and the speed at which galaxies are moving away is proportional to their distance:

where is the Hubble constant.

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

Doppler effect- a change in the frequency and length of 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 with a siren on is driving past an 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.

Mathematical description

If the wave source moves relative to the medium, then the distance between the wave crests (wavelength) depends on the speed and direction of movement. If the source moves towards the receiver, that is, catches up with the wave 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 propagation of waves in the medium, is 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

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

Substituting the frequency value from formula (1) in formula (2), 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’s reference system. If the source is moving away radially from the observer, then , if it is approaching - .

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 the transverse Doppler effect, when the angle between the wave vector and the source velocity is equal to . 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 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

Doppler radar is a radar that measures the change in frequency of a signal reflected from an object. Based on 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, and other objects.

Astronomy
- The radial velocity of motion of stars, galaxies and other celestial bodies is determined by the displacement of spectral lines. Using 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 its radial velocity is towards the observer (violet shift) . If the speed of the source is small compared to the speed of light (300,000 km/s), then the radial speed 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.
- The temperature of stars is determined by increasing the width of spectral lines.
Non-invasive flow velocity measurement. The Doppler effect is used to measure the flow rate of liquids and gases. The advantage of this method is that it does not require placing sensors directly into the flow. The speed is determined by the scattering of ultrasound on inhomogeneities of the medium (suspension particles, drops of liquid 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 an emergency transmitter on the ground are determined by the satellite from the radio signal received from it, using the Doppler effect.

Arts 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 wears a costume symbolizing the Doppler effect. However, everyone present (except his friends) thinks that he is a zebra.

Notes

Links

Using the Doppler effect to measure ocean currents

Wikimedia Foundation. 2010.

See what the “Doppler effect” is in other dictionaries:

Doppler effect- Doppler effect A change in frequency that occurs when the transmitter moves relative to the receiver or vice versa. [L.M. Nevdyaev. Telecommunication technologies. English Russian Dictionary directory. Edited by Yu.M. Gornostaeva. Moscow … Technical Translator's Guide

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. Doppler effect, 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 aiškinamasis metrologijos terminų žodynas

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

The essence of the phenomenon

Mathematical description

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

The relativistic Doppler effect is due to two reasons:

classical analogue of frequency change with relative movement of the source and receiver;

How to observe the Doppler effect

Application

Doppler radar is a radar that measures the change in frequency of a signal reflected from an object. Based on 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, and other objects.

Astronomy
- The radial velocity of motion of stars, galaxies and other celestial bodies is determined by the displacement of spectral lines. Using 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 its radial velocity is towards the observer (violet shift) . If the speed of the source is small compared to the speed of light (300,000 km/s), then the radial speed 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.
- The temperature of stars is determined by increasing the width of spectral lines.
Non-invasive flow velocity measurement. The Doppler effect is used to measure the flow rate of liquids and gases. The advantage of this method is that it does not require placing sensors directly into the flow. The speed is determined by the scattering of ultrasound on inhomogeneities of the medium (suspension particles, drops of liquid 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 an emergency transmitter on the ground are determined by the satellite from the radio signal received from it, using the Doppler effect.

Arts 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 wears a costume symbolizing the Doppler effect. However, everyone present (except his friends) thinks that he is a zebra.

Notes

Links

Using the Doppler effect to measure ocean currents

Wikimedia Foundation. 2010.

Wax
Polymorphism of computer viruses

See what the “Doppler effect” is in other dictionaries:

Doppler effect- Doppler effect A change in frequency that occurs when the transmitter moves relative to the receiver or vice versa. [L.M. Nevdyaev. Telecommunication technologies. English-Russian explanatory dictionary reference book. Edited by Yu.M. Gornostaeva. Moscow … Technical Translator's Guide