Doppler effect

physical phenomenon

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Doppler effect is to commemorate Austria Physicist and mathematician Christian John· Doppler （Christian Johann Doppler ）He first put forward this theory in 1842. The main content is the wavelength of object radiation because Wave source and Observer Of relative motion And change. In front of the moving wave source, the wave is compressed, the wavelength becomes shorter, and the frequency becomes higher（ blue shift blue shift ）； When behind the moving wave source, the opposite effect will occur. Wavelength becomes longer and frequency becomes lower（ red shift red shift ）； The higher the velocity of the wave source, the greater the effect. According to the degree of wave red (or blue) shift, the velocity of the wave source moving along the observation direction can be calculated.^[1]

fixed star Spectral line The displacement of 0 indicates the speed of the star moving in the observation direction, unless the speed of the wave source is very close to the speed of light Doppler shift Generally speaking, the degree is very small. All wave phenomena have Doppler effect.

Chinese name: Doppler effect
Foreign name: Doppler effect
Alias: Doppler law
expression: Fo=(fs * v)/(v ± vs) (Note: "fs" and "vs" are wave source parameters)^[2]

Presenter: Christian Johann Doppler
Proposed time: 1842
Applicable fields: Physics, astronomy, communication, medicine, transportation
Applied discipline: Physics

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two find
three formula
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▪ Aviation Applications
seven Related events

principle

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Doppler effect It is pointed out that the wave moves in the direction of the wave source Observer When the wave source is far away from the observer, the receiving frequency becomes lower. The same conclusion can be reached when the observer moves. But due to the lack of Experimental equipment Doppler was not verified by experiment at that time, but was verified by measured data several years later. Assuming that the wavelength of the original wave source is λ, wave velocity Is u, observer Movement speed Is v (the following analysis methods are not applicable to light waves, and the Doppler effect of light waves is shown below):

When the observer approaches the wave source, the observed wave source frequency is

Otherwise, the observed wave source frequency is

。

A commonly used example is light. When a star approaches an observer, its light will be bluer than usual. Astronomers can see the color change of light as stars pass by.

If we regard light waves as pulses emitted at regular intervals, we can imagine that if you send a pulse every step, then every pulse before you is closer to you than when you stand still. The light source behind you is a step further than the original one. Or, before you Pulse frequency It is higher than usual, and the pulse frequency after you is lower than usual.

Cause: The light source is completed once Full vibration It emits a wave of one wavelength outward. The frequency represents the number of complete vibrations completed in a unit time. Therefore, the frequency of the wave source is equal to the number of complete waves emitted by the wave source in a unit time. The color of the light seen by the observer is determined by the frequency received by the observer, that is, the number of complete waves received indirectly in a unit time. When the wave source and the observer have relative motion The frequency received by the observer will change. In unit time, the number of complete waves received by the observer increases, that is, the frequency received increases. In the same way, when the observer is far away from the wave source, the number of complete waves received by the observer in unit time decreases, that is, the frequency received decreases.

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Doppler effect is also an accidental discovery. In 1842, an Austrian mathematician and physicist named Doppler effect. One day, he was passing the railway intersection when a train passed by him. He found that the whistle sound became louder when the train was approaching from far, but the wavelength became shorter, while the whistle sound became smaller when the train was approaching from far, but the wavelength became longer. He's right about this physical phenomenon I was very interested in it and did some research. It is found that this is due to the relative movement between the wave source and the observer, which makes the wavelength heard by the observer different from the wavelength of the wave source. This is the wavelength shift phenomenon. Because the wave source is relative to Observer During movement, the wavelength heard by the observer will change. When the wave source moves away from the observer, the wavelength of the sound wave increases, and when the wave source approaches the observer, the wavelength of the sound wave decreases. The change of wavelength is the same as that between the wave source and the observer relative velocity and sound velocity Is related to the ratio of. The larger this ratio is, the more significant the change will be. Later generations call it "Doppler effect".

formula

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The frequency relationship between the observer and the source is (this formula is not applicable to light waves, and the Doppler effect of light waves is shown below):

Is the observed frequency;

Is the original transmission frequency from the medium;

Is the traveling speed of the wave in the medium;

Is the moving speed of the observer. If it is close to the emission source, the front operation symbol is+, otherwise it is -;

Is the moving speed of the transmission source. If it is close to the observer, the front operation symbol is -, and vice versa.

Through this formula, we can know the reason for the change of mechanical wave length: the molecule in the formula is the sum of the propagation speed of mechanical wave and the speed of the observer（

）， denominator Is the difference between the propagation speed of the mechanical wave and the moving speed of the emission source（

）, and then the original frequency of mechanical wave（

）Perform multiplication. Frequency received by the observer when the observer is close to the emission source

Higher than the original frequency, wavelength

Shorter than the original wavelength. On the contrary, the numerator subtraction becomes smaller and the denominator becomes smaller Addition operation Increase, calculated Frequency ratio The original frequency becomes lower and the wavelength becomes longer.

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Doppler effect Not just for Mechanical wave , it also applies to all types of waves, including electromagnetic wave and Gravitational wave 。 scientist Edwin Hubble Edwin Hubble uses the Doppler effect to conclude that the universe is expanding. He found himself far away Galaxy The frequency of light emitted by the celestial body of red shift The faster the objects leave the Milky Way, the greater the redshift, which indicates that these objects are far away from the Milky Way. Conversely, if the celestial body Forward shift To the Milky Way, light will occur blue shift 。

stay mobile communication Medium, when Mobile station When moving to the base station, the frequency becomes higher, and when moving away from the base station, the frequency becomes lower. Therefore, we should fully consider the Doppler effect in mobile communication. Of course, due to the limitation of our mobile speed in daily life, it is impossible to bring about a very large frequency offset, but this will undeniably affect mobile communication. In order to avoid this impact causing problems in our communication, we have to take various technical considerations. It also increases the complexity of mobile communication.

In the case of monochrome, the color perceived by our eyes can be interpreted as the frequency of light wave vibration, or as the number of changes in the electromagnetic field within one second. In the visible area, the lower the frequency, the more red it tends to be, while the higher the frequency, the more blue and purple it tends to be. For example, the corresponding frequency of bright red produced by helium neon laser is 4.74 × 10 fourteen Hertz, while the corresponding frequency of mercury lamp purple is 7 × 10 fourteen Hertz above. This principle also applies to mechanical waves (sound waves): the "high and low" (subjective) feeling of the "tone" of sound waves corresponds to the wavelength (objective) of sound, and is inversely proportional to the wavelength. The shorter the wavelength, the lower the tone, similar to red, and the longer the wavelength, the higher the tone, similar to (blue) purple.

If the wave source is fixed, the vibration of the wave received by the stationary receiver is the same as the rhythm of the wave emitted by the wave source: the transmitting frequency is equal to the receiving frequency. If the wave source is moving relative to the receiver, such as being far away from each other, the situation will be different. Compared with the receiver, the two peak The distance between the two peaks is lengthened, so it takes longer for the two peaks to reach the receiver. Then the frequency decreases when reaching the receiver, and the perceived color moves towards red (if the wave source is close to the receiver, the opposite is true). In order to give readers a concept of the impact of this effect Doppler shift , approximately giving a light source that is far away from the relative velocity Frequency received when changing. For example, the red color of helium neon laser mentioned above Spectral line When the speed of the wave source is equal to half of the speed of light, the received frequency is 4.74 × 10 fourteen Hz dropped to 2.37 × 10 fourteen Hertz, this value is greatly reduced to infrared Frequency band of.

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Mechanical wave Doppler effect of

Doppler effect 1

Doppler effect, which is based on the discoverer Christian Doppler Is named after. Doppler is Austria Physicists and mathematicians. He first discovered this effect in 1842. To understand this phenomenon, we can observe that when the train approaches at a constant speed, steam whistle The law of mechanical wave propagation. The result is that the sound of the whistle becomes rapid, and the wavelength of the mechanical wave of the whistle is shortened, as if the wave has been compressed; On the contrary, when the train goes far away, the wavelength of the mechanical wave becomes larger, as if the wave is stretched. The reason why the sound becomes sharp when the train approaches is that time interval The number of waves propagating in the forward direction of the train increases, and the sound level is actually Sound wave The frequency per unit time is Observer Why do you feel the "tone" becomes "high". Frequency observed by quantitative analysis

Where u is the propagation velocity ，

by Wave source Relative to the velocity of the medium,

Is the observer's velocity relative to the medium,

Representing the wave source natural frequency 。 When the observer moves towards the wave source,

Front fetch Positive sign ； When the observer moves away from the wave source (i.e. along the wave source),

Prefetch minus sign 。 When the wave source moves towards the observer

Take a negative sign in front, when the wave source moves away from the observer

Take a positive sign before. From the above formula, it is easy to know that when the observer is close to the wave source,

； When the observer and the wave source are far away from each other f one <f。

Set wave source

, Observer

At speed

，

Along the same straight line in the static medium Opposing motion , the propagation speed of the wave from the wave source in the medium is

, and

。 When the wave source does not move, the wave source Transmission frequency by

, wavelength is

The frequency of the wave received by the observer is:

⑴ When the observer and wave source are not moving,

, from the above formula

⑵ When the observer is still and the wave source is close to the observer, the frequency received by the observer is

Obviously, the frequency is higher than the original frequency

All expressions of Doppler effect can be obtained from the above formula.

Doppler effect of light wave

have Volatility This effect will also appear in the light of, which is also called Doppler Fizeau effect. Because French physicist Fizeau (1819-1896) independently explained the frequency shift from stars in 1848, and pointed out that the use of this effect to measure stars relative velocity The way. Light wave（ electromagnetic wave ）And sound waves（ Mechanical wave ）The difference is that the change of light wave frequency makes people feel the change of color. If the star moves away from us, the spectral line of light will move towards the red light, which is called red shift ； If the star moves towards us, the spectral line of light will move in the direction of purple light, which is called blue shift.

Doppler effect of light (electromagnetic wave) Calculation formula There are three types:

Doppler Effect 2 China Aerospace Application Technology

(1) Longitudinal Doppler effect (i.e. the velocity of the wave source and the relationship between the wave source and receiver Connections for Collinear ）：

among

For wave source and receiver relative velocity 。 When the wave source is close to the observer,

Positive, called“ Violet shift ”Or“ blue shift ”； otherwise

Negative, called "redshift".

(2) Transverse Doppler effect (that is, the velocity of the wave source is perpendicular to the connection between the wave source and the receiver):

among

⑶ Universal Doppler effect (general situation of Doppler effect):

among

，

Is the included angle between the line connecting the receiver and the wave source and the speed direction. The longitudinal and transverse Doppler effects are

Special case when 0 or π/2 is taken.

Application classification

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Medical Applications

The Doppler effect of mechanical waves can also be used for medical diagnosis, which is what we usually say Color Doppler ultrasound 。 Color ultrasound is simply high definition black and white B-mode ultrasonography Coupled with color Doppler, let's first talk about the wavelength shift of ultrasound Diagnostic method , i.e D super This method applies the principle of Doppler effect, when there is relative motion When the wavelength of the echo changes, such wavelength change is called wavelength shift, D ultrasound includes pulsed Doppler, continuous Doppler and color Doppler blood flow images. Color Doppler ultrasound Generally used from Related technologies Perform Doppler signal processing , from autocorrelation technology Blood flow signal through Colour coding Post real-time overlay on 2D image Color Doppler ultrasound blood flow image is formed. It can be seen that color Doppler ultrasound (i.e. color ultrasound) not only has the advantages of two-dimensional ultrasound structure image, but also provides Hemodynamics The rich information and practical application of the Angiography ”。

To check the heart and blood vessels motion state To know the blood flow speed, you can transmit ultrasound. Since the blood in the blood vessel is a flowing object, the Doppler effect is generated between the ultrasonic wave source and the relatively moving blood. When the blood moves towards the wave source, reflected wave The wavelength of is compressed, so the frequency increases. When the blood moves away from the wave source, the wavelength of the reflected wave becomes longer, so the frequency decreases. The amount of increase or decrease in the reflected wave length is proportional to the blood flow velocity, so the blood flow velocity can be measured according to the wavelength shift of ultrasound.

We know that Blood flow velocity And blood flow, which is related to cardiovascular Of disease diagnosis It has a certain value, especially for the oxygen supply in the circulation process, the locking capacity, whether there is turbulence Vascular atherosclerosis can provide valuable diagnostic information.

Ultrasonic Doppler This is how the heart process is diagnosed: ultrasonic transducer Produce a short wave equal amplitude ultrasonic signal to excite Transmitting transducer The probe generates continuous ultrasound and emits it to the human cardiovascular organs, which produces Doppler effect. When the ultrasound beam encounters moving organs and blood vessels, the reflected signal is transducer If it is accepted, the blood flow velocity can be calculated according to the wavelength difference between the reflected wave and the emitted wave, and the blood flow direction can be determined according to whether the reflected wave wavelength increases or decreases. In order to make the probe easy to align with the measured blood vessel, a Flatness double Lamination Probe.

Color Doppler ultrasound

Supplement: Doppler effect can also be used for attenuation of wave propagation in the medium theoretical explanation 。 When waves propagate in the medium Wave dispersion As the distance increases, the short wave moves to the long wave.

Doppler effect 3

Medical field The development direction of internal B-mode ultrasound is color ultrasound. Let's talk about the characteristics of color ultrasound:

Its main advantages are:

one
It can quickly and intuitively display the two-dimensional plane distribution of blood flow.
two
It can display the running direction of blood flow.
three
It is helpful to identify arteries and veins.
four
It is helpful to identify vascular diseases and non vascular diseases.
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It is helpful to understand the nature of blood flow.
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It is convenient to know the phase and speed of blood flow.
seven
It can reliably find shunt and backflow.
eight
It can quantitatively analyze the origin, width, length and area of blood flow bundle.

However, the relevant technology adopted by color ultrasound is Pulse wave When the speed of the detected object is too high, the color of the color stream will make errors, which is obviously inferior to spectral Doppler in quantitative analysis Color Doppler ultrasound All of them have the function of spectral Doppler, that is, color duplex ultrasound.

colour Doppler ultrasound Hemogram (CDF), also known as color Doppler ultrasound imaging (CDI), obtains echo The information source is consistent with spectral Doppler, and the distribution and direction of blood flow are 2D display Different speeds are distinguished by different colors. Dual power Doppler ultrasound system, namely B-mode ultrasound image display Location of blood vessels. Doppler measurement of blood flow, this type of B and Doppler system binding energy More precisely locate any particular vessel.

one
Blood flow direction In spectral Doppler display, blood flow direction is distinguished by zero baseline. Those above the zero baseline indicate the flow direction of the blood flow to the probe, and those below the zero baseline indicate that the blood flow leaves the probe. In CDI, use Colour coding Indicates the direction of blood flow, and red or yellow color spectrum indicates the flow direction of blood flow to the probe (warm color); The blue or blue-green color spectrum represents the blood flow flow probe (cold color).
two
The blood vessel distribution CDI displays the blood flow in the vascular lumen, so it belongs to the flow channel type display. It cannot display the vascular wall and adventitia.
three
CDI can be used to classify the blood vessels of liver cancer nodules. It can be distinguished as the circumnodal vessels and the arc-shaped vessels at the inner edge of the donor node. The blood vessel flowing from the nodule, the internal blood vessel of the nodule and the outflow blood vessel of the nodule, etc.

Clinical Application of Color Doppler Ultrasound

(I) vascular disease

35 μ m short wave probe can be used to detect calcification in the lungs , for Carotid atherosclerosis Sexual occlusive disease has good diagnostic value, and blood flow exploration can also be used Local amplification Determine the degree of lumen stenosis, Embolus Is there any possibility of falling off ulcer , Prevention Cerebral embolism Occurrence of.

Color ultrasound for all kinds of Arteriovenous fistula It's the best diagnostic method The diagnosis can be confirmed when the ring color spectrum inlaid with five colors is detected.

about Carotid body tumor , Main vein tumor of abdomen Vasculitis obliterans , Chronic Lower limb veins Disease (including lower limb varicose, primary deep venous insufficiency of lower limb, deep venous insufficiency of lower limb Venous reflux Obstacles Thrombophlebitis and Venous thrombosis ）High definition, local magnification and blood flow of color ultrasound spectrum Exploration can make a more correct diagnosis.

（2） Abdominal viscera

It is mainly used in the liver and kidney, but for the differentiation of benign and malignant lesions in the abdominal cavity, Gallbladder carcinoma And large polyp Identification of chronic and severe inflammation, Common bile duct 、 hepatic artery There is a certain value of auxiliary diagnosis.

about cirrhosis Color Doppler ultrasound can make a better judgment from the speed of various internal flow rates in the liver, the size and direction of vascular lumen, and the establishment of collateral circulation. For black and white, it is extremely difficult to distinguish Tuberous sclerosis 、 diffuse liver cancer It is helpful for short wave exploration and blood flow spectrum exploration to make differential diagnosis.

For benign and malignant in liver Space occupying lesion Identification of, cyst And various arteriovenous tumors have better diagnostic value, Primary liver cancer And Secondary liver cancer It can also be realized through internal Blood supply Circumstances differentiate between probes.

Color Doppler ultrasound is mainly used for renal vascular diseases, as described above Renal arteriovenous fistula , when the clinical manifestation is intermittent and painless hematuria Those who cannot find out the cause have strong indications. about Secondary hypertension One of the common causes of renal artery stenosis Color ultrasound can basically make a clear diagnosis. When the blood flow rate of the stenosis is greater than 150cm/s, the diagnosis accuracy 98.6%, while susceptibility 100%. On the other hand, it is also true renal carcinoma 、 Renal pelvis Transitional carcinoma and Benign tumor The differential diagnosis.

（3） Small organ

Among small organs, the thyroid breast Eyeball. In a way, the 35 μ m probe without color flow Doppler is much clearer than the common black and white 70 μ m probe. The diagnosis and differential diagnosis of thyroid lesions are mainly based on the blood supply inside the thyroid hyperthyroidism The most typical image has Specificity , for a "sea of fire". and Simple goiter Compared with normal thyroid blood circulation, there was no significant change. Subacute thyroiditis ， Hashimoto's thyroiditis It is between the two, and can be distinguished by the nodules and the surrounding blood flow Nodular goiter 、 thyroid adenoma and Thyroid carcinoma Therefore, it is suggested that the thyroid diagnosis is not very clear, and patients with certain financial affordability can make further clear diagnosis with color Doppler ultrasound.

Breast color ultrasound is mainly used for Fibroma of breast and mammary cancer The eyeball has better diagnostic value for ocular vascular disease.

(IV) prostate and seminal vesicle

Because rectal exploration is the best way to diagnose prostate, it is proposed here. This method divides the prostate into transitional area, central area, peripheral area, and the other part of the prostate fiber muscle matrix area. The transitional zone includes the area around the urethra physiological sphincter 100% benign prostatic hyperplasia In normal people, the transitional zone only accounts for 5% of the size of the prostate. Central District Ejaculatory duct Surrounding and pointed by sharp wall Seminal caruncle The surrounding area includes the posterior part of the prostate and the bilateral apex, which is the origin of 70-80% of the cancer, while the capsule of the apex even disappears, forming an anatomical weak area cancer The common metastasis channel of the prostate is the key area for prostate biopsy. Through rectal exploration Seminal vesicle gland The disease has good diagnostic value. When it is combined with prostate biopsy, it can be basically diagnosed clearly Prostate disease , especially prostatic cancer The incidence rate in China is all Upward trend , prostate cancer Europe and America The national incidence rate even ranks among lung cancer Later, it is the second most common cancer, and abdominal exploration of the prostate can hardly make a diagnosis. Therefore, it is recommended to use rectal ultrasound more clinically to diagnose prostate diseases. If rectal exploration can be used, abdominal exploration is not necessary.

（5） Obstetrics and Gynecology

The main advantage of color ultrasound in gynecology and obstetrics lies in Yu Liang Malignant tumor Identification and umbilical cord Assessment of disease, fetal congenital heart disease and placental function Trophoblast The disease has better auxiliary diagnostic value sterility 、 Pelvic varicose vein Through the observation of blood flow spectrum, the diagnosis of black and white ultra difficult can also be made. The use of vaginal probe has certain advantages over abdominal probe, which is mainly reflected in ① Uterine artery Ovarian blood flow sensitivity and display rate are high. ② Shorten the examination time and obtain accurate Doppler spectrum. ③ There is no need to fill the bladder. ④ Free from obesity, abdominal scars Intestinal cavity Air inflation and other interferences. ⑤ With the help of the activity of the tip of the probe, look for the tender part of pelvic organs to determine whether there is pelvic adhesion.

Transportation application

The traffic police send a laser with known frequency (such as green light) to the moving vehicle for simultaneous measurement reflected wave The speed of the vehicle can be known according to the frequency and wavelength of the reflected wave. With Doppler Tachometer Of monitor Sometimes it is installed on the top of the road, and the vehicle number is photographed while measuring the speed, and the measured speed is automatically printed.

Aviation Applications

March 8, 2014 Malaysia Airlines MH370 Lost contact, 17 days later, Prime Minister of Malaysia Najib Held temporarily on the evening of the 24th press conference Announces: "Based on the latest data, MH370 flight the indian ocean The South ends. " Participating in the investigation of missing flights INMARSAT McLaughlin, vice president, explained that they used the Doppler effect theory, combined with other reference factors Data analysis Finally, the final trend of MH370 is given.

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At 10:00 on March 24, 2014, Malaysian Prime Minister Najib held an emergency press conference. He said that according to the new data analysis, Flight MH370 crashed in the South Indian Ocean.

Inmarsat explained on the 24th that they used Doppler effect theoretical analysis Malaysia Airlines MH370 The flight sent a signal that the aircraft had landed in the South Indian Ocean.

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