In the 7th grade physics course, you studied mechanical vibrations. It often happens that, having arisen in one place, vibrations propagate to neighboring regions of space. Recall, for example, the propagation of vibrations from a pebble thrown into the water or the vibrations of the earth's crust propagating from the epicenter of an earthquake. In such cases, they speak of wave motion - waves (Fig. 17.1). In this section, you will learn about the features of wave motion.
We create mechanical waves
Let's take a rather long rope, one end of which we will attach to a vertical surface, and the other we will move up and down (oscillate). Vibrations from the hand will spread along the rope, gradually involving more and more distant points in the oscillatory movement - a mechanical wave will run along the rope (Fig. 17.2).
A mechanical wave is the propagation of oscillations in an elastic medium*.
Now we fix a long soft spring horizontally and apply a series of successive blows to its free end - a wave will run in the spring, consisting of condensations and rarefaction of the coils of the spring (Fig. 17.3).
The waves described above can be seen, but most mechanical waves are invisible, such as sound waves (Figure 17.4).
At first glance, all mechanical waves are completely different, but the reasons for their occurrence and propagation are the same.
We find out how and why a mechanical wave propagates in a medium
Any mechanical wave is created by an oscillating body - the source of the wave. Performing an oscillatory motion, the wave source deforms the layers of the medium closest to it (compresses and stretches them or displaces them). As a result, elastic forces arise that act on neighboring layers of the medium and force them to carry out forced oscillations. These layers, in turn, deform the next layers and cause them to oscillate. Gradually, one by one, all layers of the medium are involved in oscillatory motion - a mechanical wave propagates in the medium.
Rice. 17.6. In a longitudinal wave, the layers of the medium oscillate along the direction of wave propagation
Distinguish between transverse and longitudinal mechanical waves
Let's compare wave propagation along a rope (see Fig. 17.2) and in a spring (see Fig. 17.3).
Separate parts of the rope move (oscillate) perpendicular to the direction of wave propagation (in Fig. 17.2, the wave propagates from right to left, and parts of the rope move up and down). Such waves are called transverse (Fig. 17.5). During the propagation of transverse waves, some layers of the medium are displaced relative to others. Displacement deformation is accompanied by the appearance of elastic forces only in solids, so transverse waves cannot propagate in liquids and gases. So, transverse waves propagate only in solids.
When a wave propagates in a spring, the coils of the spring move (oscillate) along the direction of wave propagation. Such waves are called longitudinal (Fig. 17.6). When a longitudinal wave propagates, compressive and tensile deformations occur in the medium (along the direction of wave propagation, the density of the medium either increases or decreases). Such deformations in any medium are accompanied by the appearance of elastic forces. Therefore, longitudinal waves propagate in solids, and in liquids, and in gases.
Waves on the surface of a liquid are neither longitudinal nor transverse. They have a complex longitudinal-transverse character, while the liquid particles move along ellipses. This is easy to verify if you throw a light chip into the sea and watch its movement on the surface of the water.
Finding out the basic properties of waves
1. oscillatory motion from one point of the medium to another is not transmitted instantly, but with some delay, so the waves propagate in the medium with a finite speed.
2. The source of mechanical waves is an oscillating body. When a wave propagates, the vibrations of parts of the medium are forced, so the frequency of vibrations of each part of the medium is equal to the frequency of vibrations of the wave source.
3. Mechanical waves cannot propagate in a vacuum.
4. Wave motion is not accompanied by the transfer of matter - parts of the medium only oscillate about the equilibrium positions.
5. With the arrival of the wave, parts of the medium begin to move (acquire kinetic energy). This means that when the wave propagates, energy is transferred.
The transfer of energy without the transfer of matter is the most important property of any wave.
Remember the propagation of waves on the surface of the water (Fig. 17.7). What observations confirm the basic properties of wave motion?
We recall the physical quantities characterizing the oscillations
A wave is the propagation of oscillations, so the physical quantities that characterize oscillations (frequency, period, amplitude) also characterize the wave. So, let's remember the material of the 7th grade:
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Physical quantities characterizing oscillations |
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Oscillation frequency ν |
Oscillation period T |
Oscillation amplitude A |
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Define |
number of oscillations per unit of time |
time of one oscillation |
the maximum distance a point deviates from its equilibrium position |
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Formula to determine |
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N is the number of oscillations per time interval t |
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Unit in SI |
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second (s) |
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Note! When a mechanical wave propagates, all parts of the medium in which the wave propagates oscillate with the same frequency (ν), which is equal to the oscillation frequency of the wave source, so the period
oscillations (T) for all points of the medium is also the same, because
But the amplitude of oscillations gradually decreases with distance from the source of the wave.
We find out the length and speed of propagation of the wave
Remember the propagation of a wave along a rope. Let the end of the rope carry out one complete oscillation, that is, the propagation time of the wave is equal to one period (t = T). During this time, the wave propagated over a certain distance λ (Fig. 17.8, a). This distance is called the wavelength.
The wavelength λ is the distance over which the wave propagates in a time equal to the period T:
where v is the speed of wave propagation. The unit of wavelength in SI is the meter:
It is easy to see that the points of the rope, located at a distance of one wavelength from each other, oscillate synchronously - they have the same phase of oscillation (Fig. 17.8, b, c). For example, points A and B of the rope move up at the same time, reach the crest of a wave at the same time, then start moving down at the same time, and so on.
Rice. 17.8. The wavelength is equal to the distance that the wave propagates during one oscillation (this is also the distance between the two nearest crests or the two nearest troughs)
Using the formula λ = vT, we can determine the propagation velocity
we obtain the formula for the relationship between the length, frequency and speed of wave propagation - the wave formula:
If a wave passes from one medium to another, its propagation speed changes, but the frequency remains the same, since the frequency is determined by the source of the wave. Thus, according to the formula v = λν, when a wave passes from one medium to another, the wavelength changes.
Wave formula
Learning to solve problems
A task. The transverse wave propagates along the cord at a speed of 3 m/s. On fig. 1 shows the position of the cord at some point in time and the direction of wave propagation. Assuming that the side of the cage is 15 cm, determine:
1) amplitude, period, frequency and wavelength;
Analysis of a physical problem, solution
The wave is transverse, so the points of the cord oscillate perpendicular to the direction of wave propagation (they move up and down relative to some equilibrium positions).
1) From fig. 1 we see that the maximum deviation from the equilibrium position (amplitude A of the wave) is equal to 2 cells. So A \u003d 2 15 cm \u003d 30 cm.
The distance between the crest and trough is 60 cm (4 cells), respectively, the distance between the two nearest crests (wavelength) is twice as large. So, λ = 2 60 cm = 120 cm = 1.2m.
We find the frequency ν and the period T of the wave using the wave formula:
2) To find out the direction of movement of the points of the cord, we perform an additional construction. Let the wave move over a small distance over a short time interval Δt. Since the wave shifts to the right, and its shape does not change with time, the pinch points will take the position shown in Fig. 2 dotted.
The wave is transverse, that is, the points of the cord move perpendicular to the direction of wave propagation. From fig. 2 we see that point K after a time interval Δt will be below its initial position, therefore, its speed is directed downwards; point B will move higher, therefore, the speed of its movement is directed upwards; point C will move lower, therefore, the speed of its movement is directed downward.
Answer: A = 30 cm; T = 0.4 s; ν = 2.5 Hz; λ = 1.2 m; K and C - down, B - up.
Summing up
The propagation of oscillations in an elastic medium is called a mechanical wave. A mechanical wave in which parts of the medium oscillate perpendicular to the direction of wave propagation is called transverse; a wave in which parts of the medium oscillate along the direction of wave propagation is called longitudinal.
The wave propagates in space not instantly, but with a certain speed. When a wave propagates, energy is transferred without transfer of matter. The distance over which the wave propagates in a time equal to the period is called the wavelength - this is the distance between the two nearest points that oscillate synchronously (have the same phase of oscillation). The length λ, frequency ν and velocity v of wave propagation are related by the wave formula: v = λν.
test questions
1. Define a mechanical wave. 2. Describe the mechanism of formation and propagation of a mechanical wave. 3. Name the main properties of wave motion. 4. What waves are called longitudinal? transverse? In what environments do they spread? 5. What is the wavelength? How is it defined? 6. How are the length, frequency and speed of wave propagation related?
Exercise number 17
1. Determine the length of each wave in fig. one.
2. In the ocean, the wavelength reaches 270 m, and its period is 13.5 s. Determine the propagation speed of such a wave.
3. Do the speed of wave propagation and the speed of movement of the points of the medium in which the wave propagates coincide?
4. Why does a mechanical wave not propagate in a vacuum?
5. As a result of the explosion produced by geologists, in earth's crust the wave propagated at a speed of 4.5 km/s. Reflected from the deep layers of the Earth, the wave was recorded on the Earth's surface 20 s after the explosion. At what depth does the rock lie, the density of which differs sharply from the density of the earth's crust?
6. In fig. 2 shows two ropes along which a transverse wave propagates. Each rope shows the direction of oscillation of one of its points. Determine the directions of wave propagation.
7. In fig. 3 shows the position of two filaments along which the wave propagates, showing the direction of propagation of each wave. For each case a and b determine: 1) amplitude, period, wavelength; 2) the direction in which points A, B and C of the cord are moving at a given time; 3) the number of oscillations that any point of the cord makes in 30 s. Consider that the side of the cage is 20 cm.
8. A man standing on the seashore determined that the distance between adjacent wave crests is 15 m. In addition, he calculated that 16 wave crests reach the shore in 75 seconds. Determine the speed of wave propagation.
This is textbook material.
Waves. General properties waves.Wave - this is the phenomenon of propagation in space over time of change (perturbation) physical quantity carrying energy with it.
Regardless of the nature of the wave, the transfer of energy occurs without the transfer of matter; the latter can only arise side effect. Energy transfer - fundamental difference waves from oscillations in which only "local" energy transformations occur. Waves, as a rule, are able to travel considerable distances from their place of origin. For this reason, waves are sometimes referred to as " vibration detached from the emitter».
Waves can be classified
By it's nature:
Elastic waves - waves propagating in liquid, solid and gaseous media due to the action of elastic forces.
Electromagnetic waves- propagating in space perturbation (change of state) of the electromagnetic field.
Waves on the surface of a liquid- the conventional name for various waves that occur at the interface between a liquid and a gas or a liquid and a liquid. Waves on water differ in the fundamental mechanism of oscillation (capillary, gravitational, etc.), which leads to different dispersion laws and, as a result, to different behavior of these waves.
With respect to the direction of oscillation of the particles of the medium:
Longitudinal waves - the particles of the medium oscillate parallel in the direction of wave propagation (as, for example, in the case of sound propagation).
Transverse waves - the particles of the medium oscillate perpendicular the direction of wave propagation (electromagnetic waves, waves on media separation surfaces).
a - transverse; b - longitudinal.
mixed waves.
According to the geometry of the wave front:
The wave surface (wave front) is the locus of points to which the perturbation has reached a given moment in time. In a homogeneous isotropic medium, the wave propagation velocity is the same in all directions, which means that all points of the front oscillate in one phase, the front is perpendicular to the direction of wave propagation, and the values of the oscillating quantity at all points of the front are the same.
flat wave - phase planes are perpendicular to the direction of wave propagation and parallel to each other.
spherical wave - the surface of equal phases is a sphere.
Cylindrical wave - the surface of the phases resembles a cylinder.
Spiral wave - is formed if a spherical or cylindrical source / sources of the wave in the process of radiation moves along a certain closed curve.
plane wave
A wave is called flat if its wave surfaces are planes parallel to each other, perpendicular to the phase velocity of the wave. = f(x, t)).
Let us consider a plane monochromatic (single frequency) sinusoidal wave propagating in a homogeneous medium without attenuation along the X axis.
,where
The phase velocity of a wave is the speed of the wave surface (front),
- wave amplitude - the module of the maximum deviation of the changing value from the equilibrium position,
– cyclic frequency, T – oscillation period, – wave frequency (similar to oscillations)
k - wave number, has the meaning of spatial frequency,
Another characteristic of the wave is the wavelength m, this is the distance over which the wave propagates during one oscillation period, it has the meaning of a spatial period, this is the shortest distance between points oscillating in one phase. 
y 
The wavelength is related to the wave number by the relation , which is similar to the time relation
The wave number is related to the cyclic frequency and wave propagation speed
x
y
y 
The figures show an oscillogram (a) and a snapshot (b) of a wave with the indicated time and space periods. Unlike stationary oscillations, waves have two main characteristics: temporal periodicity and spatial periodicity.
General properties of waves:
Waves carry energy.
2. Waves exert pressure on bodies (have momentum).
3. The speed of a wave in a medium depends on the frequency of the wave - dispersion. Thus, waves of different frequencies propagate in the same medium at different speeds (phase velocity). 
4. Waves bend around obstacles - diffraction.
Diffraction occurs when the size of the obstacle is comparable to the wavelength.
5. At the interface between two media, waves are reflected and refracted.
The angle of incidence is equal to the angle of reflection, and the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for these two media.
6. When coherent waves are superimposed (the phase difference of these waves at any point is constant in time), they interfere - a stable pattern of interference minima and maxima is formed. 
Waves and the sources that excite them are called coherent if the phase difference of the waves does not depend on time. Waves and the sources that excite them are called incoherent if the phase difference of the waves changes with time.
Only waves of the same frequency, in which oscillations occur along the same direction (i.e., coherent waves), can interfere. Interference can be either stationary or non-stationary. Only coherent waves can give a stationary interference pattern. For example, two spherical waves on the surface of water, propagating from two coherent point sources, will produce a resultant wave upon interference. The front of the resulting wave will be a sphere.
When waves interfere, their energies do not add up. The interference of waves leads to a redistribution of the energy of oscillations between various closely spaced particles of the medium. This does not contradict the law of conservation of energy because, on average, for a large region of space, the energy of the resulting wave is equal to the sum of the energies of the interfering waves.
When superimposing incoherent waves average value of the squared amplitude of the resulting wave is equal to the sum of the squared amplitudes of the superimposed waves. The energy of the resulting oscillations of each point of the medium is equal to the sum of the energies of its oscillations, due to all incoherent waves separately.
7. Waves are absorbed by the medium. With distance from the source, the amplitude of the wave decreases, since the energy of the wave is partially transferred to the medium.
8. Waves are scattered in an inhomogeneous medium.
Scattering - perturbations of wave fields caused by inhomogeneities of the medium and scattering objects placed in this medium. The scattering intensity depends on the size of the inhomogeneities and the frequency of the wave.
mechanical waves. Sound. Sound characteristic .
Wave- perturbation propagating in space.
General properties of waves:
carry energy;
have momentum (put pressure on bodies);
at the boundary of two media they are reflected and refracted;
absorbed by the environment;
diffraction;
interference;
dispersion;
The speed of the waves depends on the medium through which the waves pass.
Mechanical (elastic) waves.
A special case of mechanical waves - waves on the surface of a liquid, waves that arise and propagate along the free surface of a liquid or at the interface between two immiscible liquids. They are formed under the influence of an external influence, as a result of which the surface of the liquid is removed from the equilibrium state. In this case, forces arise that restore balance: the forces of surface tension and gravity.
Mechanical waves are of two types
Longitudinal waves accompanied by tensile and compressive strains can propagate in any elastic media: gases, liquids and solids. Transverse waves propagate in those media where elastic forces appear during shear deformation, i.e., in solids.
Of considerable interest for practice are simple harmonic or sinusoidal waves. The plane sine wave equation is:
- the so-called wave number ,
– circular frequency ,
BUT - particle oscillation amplitude.
The figure shows "snapshots" of a transverse wave at two points in time: t and t + Δt. During the time Δt, the wave moved along the OX axis by a distance υΔt. Such waves are called traveling waves.
The wavelength λ is the distance between two adjacent points on the OX axis, oscillating in the same phases. A distance equal to the wavelength λ, the wave runs over a period T, therefore,
λ = υT, where υ is the wave propagation velocity.
For any chosen point on the graph of the wave process (for example, for point A), the x-coordinate of this point changes over time t, and the value of the expression ωt – kx does not change. After a time interval Δt, point A will move along the OX axis for a certain distance Δx = υΔt. Consequently: ωt – kx = ω(t + Δt) – k(x + Δx) = const or ωΔt = kΔx.
This implies:
Thus, a traveling sinusoidal wave has a double periodicity - in time and space. The time period is equal to the oscillation period T of the particles of the medium, the spatial period is equal to the wavelength λ. The wavenumber is the spatial analog of the circular frequency.
Sound.
Any oscillatory process is described by an equation. It was also derived for sound vibrations:
Basic characteristics of sound waves
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Subjective perception of sound (volume, pitch, timbre) |
objective physical characteristics sound (speed, intensity, spectrum) |
The speed of sound in any gaseous medium is calculated by the formula:
β - adiabatic compressibility of the medium,
ρ - density.
Applying sound
Echo sounders used underwater are called sonars or sonars (the name sonar is derived from the initial letters of three English words: sound - sound; navigation - navigation; range - range). Sonars are indispensable for studying the seabed (its profile, depth), for detecting and studying various objects moving deep under water. With their help, both individual large objects or animals, as well as flocks of small fish or mollusks, can be easily detected.
Waves of ultrasonic frequencies are widely used in medicine for diagnostic purposes. Ultrasound scanners allow you to examine the internal organs of a person. Ultrasonic radiation is less harmful to humans than x-rays.
Electromagnetic waves.
Their properties.
electromagnetic wave is an electromagnetic field propagating in space over time.
Electromagnetic waves can only be excited by rapidly moving charges.
The existence of electromagnetic waves was theoretically predicted by the great English physicist J. Maxwell in 1864. He proposed a new interpretation of the law electromagnetic induction Faraday and developed his ideas further.
Any change in the magnetic field generates a vortex in the surrounding space. electric field, a time-varying electric field generates a magnetic field in the surrounding space.
Figure 1. An alternating electric field generates an alternating magnetic field and vice versa
Properties of electromagnetic waves based on Maxwell's theory:
Electromagnetic waves transverse – vectors and are perpendicular to each other and lie in a plane perpendicular to the direction of propagation.
Figure 2. Propagation of an electromagnetic wave
Electrical and magnetic field in a traveling wave change in one phase.
The vectors in a traveling electromagnetic wave form the so-called right triplet of vectors.
Oscillations of the vectors and occur in phase: at the same moment of time, at one point in space, the projections of the strengths of the electric and magnetic fields reach a maximum, minimum, or zero.
Electromagnetic waves propagate in matter with final speed
Where - the dielectric and magnetic permeability of the medium (the speed of propagation of an electromagnetic wave in the medium depends on them),
Electric and magnetic constants.
The speed of electromagnetic waves in vacuum
Flux density of electromagnetic energy
orintensity
J
called electromagnetic energy, carried by a wave per unit of time through the surface of a unit area:
,
Substituting here the expressions for , and υ, and taking into account the equality of the volumetric energy densities of the electric and magnetic fields in an electromagnetic wave, we can obtain:
Electromagnetic waves can be polarized.
Likewise, electromagnetic waves have all the basic properties of waves : they carry energy, have momentum, they are reflected and refracted at the interface between two media, absorbed by the medium, exhibit the properties of dispersion, diffraction and interference.
Hertz experiments (experimental detection of electromagnetic waves)
For the first time, electromagnetic waves were experimentally studied
Hertz in 1888. He developed successful design generator of electromagnetic oscillations (Hertz vibrator) and a method for detecting them by the resonance method.
The vibrator consisted of two linear conductors, at the ends of which there were metal balls forming a spark gap. When a high voltage was applied from the induction to the carcass, a spark jumped in the gap, it shorted the gap. During its burning, a large number of oscillations took place in the circuit. The receiver (resonator) consisted of a wire with a spark gap. The presence of resonance was expressed in the appearance of sparks in the spark gap of the resonator in response to a spark arising in the vibrator.
Thus, Hertz's experiments provided a solid foundation for Maxwell's theory. The electromagnetic waves predicted by Maxwell turned out to be realized in practice.
PRINCIPLES OF RADIO COMMUNICATIONS
Radio communication transmission and reception of information using radio waves.
On March 24, 1896, at a meeting of the Physics Department of the Russian Physical and Chemical Society, Popov, using his instruments, clearly demonstrated the transmission of signals over a distance of 250 m, transmitting the world's first two-word radiogram "Heinrich Hertz".
SCHEME OF THE RECEIVER A.S. POPOV
Popov used radio telegraph communication (transmission of signals of different duration), such communication can only be carried out using a code. A spark transmitter with a Hertz vibrator was used as a source of radio waves, and a coherer served as a receiver, a glass tube with metal filings, the resistance of which, when an electromagnetic wave hits it, drops hundreds of times. To increase the sensitivity of the coherer, one of its ends was grounded, and the other was connected to a wire raised above the Earth, the total length of the antenna was a quarter of a wavelength. The spark transmitter signal decays quickly and cannot be transmitted over long distances.
Radiotelephone communications (speech and music) use a high-frequency modulated signal. A low (sound) frequency signal carries information, but is practically not emitted, and a high frequency signal is well emitted, but does not carry information. Modulation is used for radiotelephone communication.
Modulation - the process of establishing a correspondence between the parameters of the HF and LF signal.
In radio engineering, several types of modulations are used: amplitude, frequency, phase.
Amplitude modulation - change in the amplitude of oscillations (electrical, mechanical, etc.), occurring at a frequency much lower than the frequency of the oscillations themselves.
High frequency harmonic oscillation ω amplitude modulated harmonic oscillation low frequency Ω (τ = 1/Ω - its period), t - time, A - amplitude of high-frequency oscillation, T - its period.
Radio communication scheme using AM signal
AM oscillator
The amplitude of the RF signal changes according to the amplitude of the LF signal, then the modulated signal is emitted by the transmitting antenna.
In the radio receiver, the receiving antenna picks up radio waves, in the oscillatory circuit, due to resonance, the signal to which the circuit is tuned (the carrier frequency of the transmitting station) is selected and amplified, then the low-frequency component of the signal must be selected.
Detector radio
Detection – the process of converting a high-frequency signal into a low-frequency signal. The signal received after detection corresponds to the sound signal that acted on the transmitter microphone. After amplification, low frequency vibrations can be turned into sound.
Detector (demodulator)
The diode is used to rectify the alternating current
a) AM signal, b) detected signal
RADAR
detection and precise definition the location of objects and the speed of their movement using radio waves is called radar . The principle of radar is based on the property of reflection of electromagnetic waves from metals.
1 - rotating antenna; 2 - antenna switch; 3 - transmitter; 4 - receiver; 5 - scanner; 6 - distance indicator; 7 - direction indicator.
For radar, high-frequency radio waves (VHF) are used, with their help a directional beam is easily formed and the radiation power is high. In the meter and decimeter range - lattice systems of vibrators, in the centimeter and millimeter range - parabolic emitters. Location can be carried out both in continuous (to detect a target) and in a pulsed (to determine the speed of an object) mode.
Areas of application of radar:
Aviation, astronautics, navy: traffic safety of ships in any weather and at any time of the day, prevention of their collision, takeoff safety, etc. aircraft landings.
Warfare: timely detection of enemy aircraft or missiles, automatic adjustment of anti-aircraft fire.
Planetary radar: measuring the distance to them, specifying the parameters of their orbits, determining the period of rotation, observing the surface topography. In the former Soviet Union (1961) - radar of Venus, Mercury, Mars, Jupiter. In the USA and Hungary (1946) - an experiment on receiving a signal reflected from the surface of the moon.
The telecommunication scheme basically coincides with the radio communication scheme. The difference is that, in addition to the sound signal, an image and control signals (line change and frame change) are transmitted to synchronize the operation of the transmitter and receiver. In the transmitter, these signals are modulated and transmitted, in the receiver they are picked up by the antenna and go for processing, each in its own path.
Consider one of the possible schemes for converting an image into electromagnetic oscillations using an iconoscope:
With the help of an optical system, an image is projected onto the mosaic screen, due to the photoelectric effect, the screen cells acquire different positive charge. The electron gun generates an electron beam that travels across the screen, discharging positively charged cells. Since each cell is a capacitor, a change in charge leads to the appearance of a changing voltage - an electromagnetic oscillation. The signal is then amplified and fed into the modulating device. In a kinescope, the video signal is converted back into an image (in different ways, depending on the principle of operation of the kinescope).
Since the television signal carries much more information than the radio, the work is carried out at high frequencies (meters, decimeters).
Propagation of radio waves.
Radio wave - this is electromagnetic wave in the range (10 4
Each section of this range is applied where its advantages can be best used. Radio waves of different ranges propagate at different distances. The propagation of radio waves depends on the properties of the atmosphere. The earth's surface, troposphere and ionosphere also have a strong influence on the propagation of radio waves.
Propagation of radio waves- this is the process of transmitting electromagnetic oscillations of the radio range in space from one place to another, in particular from a transmitter to a receiver.
Waves of different frequencies behave differently. Let us consider in more detail the features of the propagation of long, medium, short and ultrashort waves.
Propagation of long waves.
Long waves (>1000 m) propagate:
At distances up to 1-2 thousand km due to diffraction on the spherical surface of the Earth. Able to go around Earth(Figure 1). Then their propagation occurs due to the guiding action of the spherical waveguide, without being reflected.
Rice. one Connection quality:
reception stability. The quality of reception does not depend on the time of day, year, weather conditions.
Flaws:
Due to the strong absorption of the wave as it propagates over the earth's surface, a large antenna and a powerful transmitter are required.
Atmospheric discharges (lightning) interfere.
Usage:
The range is used for radio broadcasting, for radiotelegraphy, radio navigation services and for communications with submarines.
There are a small number of radio stations transmitting accurate time signals and meteorological reports.
Medium waves ( =100..1000 m) propagate:
Like long waves, they are able to bend around the earth's surface.
Like short waves, they can also be repeatedly reflected from the ionosphere.
Connection quality:
Short communication range. Medium wave stations are audible within a thousand kilometers. But there is a high level of atmospheric and industrial interference.
Used for official and amateur communications, as well as mainly for broadcasting.
Short waves (=10..100 m) propagate:
Repeatedly reflected from the ionosphere and the earth's surface (Fig. 2)
Connection quality:
The quality of reception at short waves depends very much on various processes in the ionosphere associated with the level solar activity, time of year and time of day. No transmitters required high power. For communication between ground stations and spacecraft they are unsuitable because they do not pass through the ionosphere.
Usage:
For communication over long distances. For television, radio broadcasting and radio communication with moving objects. There are departmental telegraph and telephone radio stations. This range is the most "populated".
Ultrashort waves (
Sometimes they can be reflected from clouds, artificial satellites of the earth, or even from the moon. In this case, the communication range may increase slightly.
The reception of ultrashort waves is characterized by the constancy of audibility, the absence of fading, as well as the reduction of various interferences.
Communication on these waves is possible only at a distance of line of sight L(Fig. 7).
Since ultrashort waves do not propagate beyond the horizon, it becomes necessary to build many intermediate transmitters - repeaters.
Repeater- a device located at intermediate points of radio communication lines, amplifying the received signals and transmitting them further.
relay- reception of signals at an intermediate point, their amplification and transmission in the same or in another direction. Retransmission is designed to increase the communication range.
There are two ways of relaying: satellite and terrestrial.
Satellite:
An active relay satellite receives the ground station signal, amplifies it, and through a powerful directional transmitter sends the signal to Earth in the same direction or in a different direction.
Ground:
The signal is transmitted to a terrestrial analog or digital radio station or a network of such stations, and then sent further in the same direction or in a different direction.
1 - radio transmitter,
2 - transmitting antenna, 3 - receiving antenna, 4 - radio receiver.
Usage:
For communication with artificial earth satellites and
VHF are divided into the following ranges:
meter waves - from 10 to 1 meter, used for telephone communication between ships, ships and port services.
decimeter - from 1 meter to 10 cm, used for satellite communications.
centimeter - from 10 to 1 cm, used in radar.
millimeter - from 1cm to 1mm, used mainly in medicine.
When in any place of a solid, liquid or gaseous medium, the excitation of particle oscillations occurs, the result of the interaction of atoms and molecules of the medium is the transmission of oscillations from one point to another with a finite speed.
Definition 1
Wave is the process of propagation of vibrations in the medium.
There are the following types of mechanical waves:
Definition 2
transverse wave: particles of the medium are displaced in a direction perpendicular to the direction of propagation of a mechanical wave.
Example: waves propagating along a string or a rubber band in tension (Figure 2.6.1);
Definition 3
Longitudinal wave: the particles of the medium are displaced in the direction of propagation of the mechanical wave.
Example: waves propagating in a gas or an elastic rod (Figure 2.6.2).
Interestingly, the waves on the liquid surface include both transverse and longitudinal components.
Remark 1
We point out an important clarification: when mechanical waves propagate, they transfer energy, form, but do not transfer mass, i.e. in both types of waves, there is no transfer of matter in the direction of wave propagation. While propagating, the particles of the medium oscillate around the equilibrium positions. In this case, as we have already said, waves transfer energy, namely, the energy of oscillations from one point of the medium to another.
Figure 2. 6. one . Propagation of a transverse wave along a rubber band in tension.
Figure 2. 6. 2. Propagation of a longitudinal wave along an elastic rod.
A characteristic feature of mechanical waves is their propagation in material media, unlike, for example, light waves, which can also propagate in a vacuum. For the occurrence of a mechanical wave impulse, a medium is needed that has the ability to store kinetic and potential energies: i.e. the medium must have inert and elastic properties. In real environments, these properties are distributed over the entire volume. For example, each small element solid body have mass and elasticity. The simplest one-dimensional model of such a body is a set of balls and springs (Figure 2.6.3).
Figure 2. 6. 3 . The simplest one-dimensional model of a rigid body.
In this model, inert and elastic properties are separated. The balls have mass m, and springs - stiffness k . Such a simple model makes it possible to describe the propagation of longitudinal and transverse mechanical waves in a solid. When a longitudinal wave propagates, the balls are displaced along the chain, and the springs are stretched or compressed, which is a stretching or compression deformation. If such deformation occurs in a liquid or gaseous medium, it is accompanied by compaction or rarefaction.
Remark 2
A distinctive feature of longitudinal waves is that they are able to propagate in any medium: solid, liquid and gaseous.
If in the specified model of a rigid body one or several balls receive a displacement perpendicular to the entire chain, we can speak of the occurrence of a shear deformation. Springs that have received deformation as a result of displacement will tend to return the displaced particles to the equilibrium position, and the nearest undisplaced particles will begin to be influenced by elastic forces tending to deflect these particles from the equilibrium position. The result will be the appearance of a transverse wave in the direction along the chain.
In a liquid or gaseous medium, elastic shear deformation does not occur. Displacement of one liquid or gas layer at some distance relative to the neighboring layer will not lead to the appearance of tangential forces at the boundary between the layers. The forces that act on the boundary of a liquid and a solid, as well as the forces between adjacent layers of a fluid, are always directed along the normal to the boundary - these are pressure forces. The same can be said about the gaseous medium.
Remark 3
Thus, the appearance of transverse waves is impossible in liquid or gaseous media.
In terms of practical application of particular interest are simple harmonic or sine waves. They are characterized by particle oscillation amplitude A, frequency f and wavelength λ. Sinusoidal waves propagate in homogeneous media with some constant speed υ .
Let us write an expression showing the dependence of the displacement y (x, t) of the particles of the medium from the equilibrium position in a sinusoidal wave on the coordinate x on the O X axis, along which the wave propagates, and on time t:
y (x, t) = A cos ω t - x υ = A cos ω t - k x .
In the above expression, k = ω υ is the so-called wave number, and ω = 2 π f is the circular frequency.
Figure 2. 6. 4 shows "snapshots" of a shear wave at time t and t + Δt. During the time interval Δ t the wave moves along the axis O X at a distance υ Δ t . Such waves are called traveling waves.
Figure 2. 6. four . "Snapshots" of a traveling sine wave at a moment in time t and t + ∆t.
Definition 4
Wavelengthλ is the distance between two adjacent points on the axis O X oscillating in the same phases.
The distance, the value of which is the wavelength λ, the wave travels in a period T. Thus, the formula for the wavelength is: λ = υ T, where υ is the wave propagation speed.
With the passage of time t, the coordinate changes x any point on the graph displaying the wave process (for example, point A in Figure 2 . 6 . 4), while the value of the expression ω t - k x remains unchanged. After a time Δ t point A will move along the axis O X some distance Δ x = υ Δ t . In this way:
ω t - k x = ω (t + ∆ t) - k (x + ∆ x) = c o n s t or ω ∆ t = k ∆ x .
From this expression it follows:
υ = ∆ x ∆ t = ω k or k = 2 π λ = ω υ .
It becomes obvious that a traveling sinusoidal wave has a double periodicity - in time and space. The time period is equal to the oscillation period T of the particles of the medium, and the spatial period is equal to the wavelength λ.
Definition 5
wave number k = 2 π λ is the spatial analogue of the circular frequency ω = - 2 π T .
Let us emphasize that the equation y (x, t) = A cos ω t + k x is a description of a sinusoidal wave propagating in the direction opposite to the direction of the axis O X, with the speed υ = - ω k .
When a traveling wave propagates, all particles of the medium oscillate harmonically with a certain frequency ω. This means that, as in a simple oscillatory process, the average potential energy, which is the reserve of a certain volume of the medium, is the average kinetic energy in the same volume, proportional to the square of the oscillation amplitude.
Remark 4
From the foregoing, we can conclude that when a traveling wave propagates, an energy flux appears that is proportional to the speed of the wave and the square of its amplitude.
Traveling waves move in a medium with certain velocities, which depend on the type of wave, inert and elastic properties of the medium.
The speed with which transverse waves propagate in a stretched string or rubber band depends on the linear mass μ (or mass per unit length) and the tension force T:
The speed with which longitudinal waves propagate in an infinite medium is calculated with the participation of such quantities as the density of the medium ρ (or the mass per unit volume) and the bulk modulus B(equal to the coefficient of proportionality between the change in pressure Δ p and the relative change in volume Δ V V , taken with the opposite sign):
∆ p = - B ∆ V V .
Thus, the propagation velocity of longitudinal waves in an infinite medium is determined by the formula:
Example 1
At a temperature of 20 ° C, the propagation velocity of longitudinal waves in water is υ ≈ 1480 m / s, in various grades of steel υ ≈ 5 - 6 km / s.
If it's about longitudinal waves, which are distributed in elastic rods, the formula for the wave velocity contains not the modulus of compression, but Young's modulus:
For steel difference E from B insignificantly, but for other materials it can be 20 - 30% or more.
Figure 2. 6. 5 . Model of longitudinal and transverse waves.
Suppose that a mechanical wave propagating in a certain medium encounters some obstacle on its way: in this case, the nature of its behavior will change dramatically. For example, at the interface between two media with different mechanical properties, the wave is partially reflected, and partially penetrates into the second medium. A wave running along a rubber band or string will be reflected from the fixed end, and a counter wave will arise. If both ends of the string are fixed, complex oscillations will appear, which are the result of the superimposition (superposition) of two waves propagating in opposite directions and experiencing reflections and re-reflections at the ends. This is how the strings of all strings "work" musical instruments fixed at both ends. A similar process occurs with the sound of wind instruments, in particular, organ pipes.
If the waves propagating along the string in opposite directions have a sinusoidal shape, then under certain conditions they form a standing wave.
Suppose a string of length l is fixed in such a way that one of its ends is located at the point x \u003d 0, and the other at the point x 1 \u003d L (Figure 2.6.6). There is tension in the string T.
Picture 2 . 6 . 6 . The emergence of a standing wave in a string fixed at both ends.
Two waves with the same frequency run simultaneously along the string in opposite directions:
- y 1 (x, t) = A cos (ω t + k x) is a wave propagating from right to left;
- y 2 (x, t) = A cos (ω t - k x) is a wave propagating from left to right.
The point x = 0 is one of the fixed ends of the string: at this point the incident wave y 1 creates a wave y 2 as a result of reflection. Reflecting from the fixed end, the reflected wave enters antiphase with the incident one. In accordance with the principle of superposition (which is an experimental fact), the vibrations created by counterpropagating waves at all points of the string are summed up. It follows from the above that the final fluctuation at each point is defined as the sum of the fluctuations caused by the waves y 1 and y 2 separately. In this way:
y \u003d y 1 (x, t) + y 2 (x, t) \u003d (- 2 A sin ω t) sin k x.
The above expression is a description of a standing wave. Let us introduce some concepts applicable to such a phenomenon as a standing wave.
Definition 6
Knots are points of immobility in a standing wave.
antinodes– points located between the nodes and oscillating with the maximum amplitude.
If we follow these definitions, for a standing wave to occur, both fixed ends of the string must be nodes. The above formula meets this condition at the left end (x = 0) . For the condition to be satisfied at the right end (x = L) , it is necessary that k L = n π , where n is any integer. From what has been said, we can conclude that a standing wave does not always appear in a string, but only when the length L string is equal to an integer number of half-wavelengths:
l = n λ n 2 or λ n = 2 l n (n = 1 , 2 , 3 , . . .) .
The set of values λ n of wavelengths corresponds to the set of possible frequencies f
f n = υ λ n = n υ 2 l = n f 1 .
In this notation, υ = T μ is the speed with which transverse waves propagate along the string.
Definition 7
Each of the frequencies f n and the type of string vibration associated with it is called a normal mode. The lowest frequency f 1 is called the fundamental frequency, all others (f 2 , f 3 , ...) are called harmonics.
Figure 2. 6. 6 illustrates the normal mode for n = 2.
A standing wave has no energy flow. The energy of vibrations, "locked" in the segment of the string between two neighboring nodes, is not transferred to the rest of the string. In each such segment, a periodic (twice per period) T) conversion of kinetic energy into potential energy and vice versa, similar to an ordinary oscillatory system. However, there is a difference here: if a weight on a spring or a pendulum has a single natural frequency f 0 = ω 0 2 π , then the string is characterized by the presence of an infinite number of natural (resonant) frequencies f n . Figure 2. 6. 7 shows several variants of standing waves in a string fixed at both ends.
Figure 2. 6. 7. The first five normal vibration modes of a string fixed at both ends.
According to the principle of superposition standing waves various kinds(with different meanings n) are able to simultaneously be present in the vibrations of the string.
Figure 2. 6. eight . Model of normal modes of a string.
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Wave– the process of propagation of oscillations in an elastic medium.
mechanical wave– mechanical disturbances propagating in space and carrying energy.
Wave types:
longitudinal - particles of the medium oscillate in the direction of wave propagation - in all elastic media;
x
oscillation direction
points of the environment
transverse - particles of the medium oscillate perpendicular to the direction of wave propagation - on the surface of the liquid.
X
Types of mechanical waves:
elastic waves - propagation of elastic deformations;
waves on the surface of a liquid.
Wave characteristics:
Let A oscillate according to the law: 
.
Then B oscillates with a delay by an angle 
, where 
, i.e.
Wave energy.
is the total energy of one particle. If particlesN, then where 
- epsilon, V - volume.
Epsilon– energy per unit volume of the wave – volumetric energy density.
The wave energy flux is equal to the ratio of the energy transferred by waves through a certain surface to the time during which this transfer is carried out: 
, watt; 1 watt = 1J/s.
Energy Flux Density - Wave Intensity- energy flow through a unit area - a value equal to the average energy transferred by a wave per unit time per unit area of the cross section.
[W/m2]
.
Umov vector– vector I showing the direction of wave propagation and equal to the flow wave energy passing through a unit area perpendicular to this direction:
.
Physical characteristics of the wave:
amplitude
wavelength
wave speed
intensity
Vibrational:
Wave:
Complex oscillations (relaxation) - different from sinusoidal.
Fourier transform- any complex periodic function can be represented as the sum of several simple (harmonic) functions, the periods of which are multiples of the period of the complex function - this is harmonic analysis. Occurs in parsers. The result is the harmonic spectrum of a complex oscillation:
BUT
0 
Sound - vibrations and waves that act on the human ear and cause an auditory sensation.
Sound vibrations and waves are a special case of mechanical vibrations and waves. Types of sounds:
simple - harmonic - tuning fork
complex - anharmonic - speech, music
tones- sound, which is a periodic process:
A complex tone can be decomposed into simple ones. The lowest frequency of such decomposition is the fundamental tone, the remaining harmonics (overtones) have frequencies equal to 2 
and others. A set of frequencies indicating their relative intensity is the acoustic spectrum.
Noise - sound with a complex non-repeating time dependence (rustle, creak, applause). The spectrum is continuous.
Physical characteristics of sound:
Hearing sensation characteristics:
Height is determined by the frequency of the sound wave. The higher the frequency, the higher the tone. The sound of greater intensity is lower.
Timbre– determined by the acoustic spectrum. The more tones, the richer the spectrum.
Volume- characterizes the level of auditory sensation. Depends on sound intensity and frequency. Psychophysical Weber-Fechner law: if you increase irritation in geometric progression(in the same number of times), then the feeling of this irritation will increase in arithmetic progression(by the same amount).
, where E is loudness (measured in phons); 
- intensity level (measured in bels). 1 bel - change in intensity level, which corresponds to a change in sound intensity by 10 times. K - proportionality coefficient, depends on frequency and intensity.
The relationship between loudness and intensity of sound is equal loudness curves, built on experimental data (they create a sound with a frequency of 1 kHz, change the intensity until an auditory sensation arises similar to the sensation of the volume of the sound under study). Knowing the intensity and frequency, you can find the background.
Audiometry- a method for measuring hearing acuity. The instrument is an audiometer. The resulting curve is an audiogram. The threshold of hearing sensation at different frequencies is determined and compared.
Noise meter - noise level measurement.
In the clinic: auscultation - stethoscope / phonendoscope. A phonendoscope is a hollow capsule with a membrane and rubber tubes.
Phonocardiography - graphic registration of backgrounds and heart murmurs.
Percussion.
Ultrasound– mechanical vibrations and waves with a frequency above 20 kHz up to 20 MHz. Ultrasound emitters are electromechanical emitters based on the piezoelectric effect ( alternating current to the electrodes, between which - quartz).
The wavelength of ultrasound is less than the wavelength of sound: 1.4 m - sound in water (1 kHz), 1.4 mm - ultrasound in water (1 MHz). Ultrasound is well reflected at the border of the bone-periosteum-muscle. Ultrasound will not penetrate into the human body if it is not lubricated with oil (air layer). The speed of propagation of ultrasound depends on the environment. Physical processes: microvibrations, destruction of biomacromolecules, restructuring and damage of biological membranes, thermal effect, destruction of cells and microorganisms, cavitation. In the clinic: diagnostics (encephalograph, cardiograph, ultrasound), physiotherapy (800 kHz), ultrasonic scalpel, pharmaceutical industry, osteosynthesis, sterilization.
infrasound– waves with a frequency less than 20 Hz. Adverse action - resonance in the body.
vibrations. Beneficial and harmful action. Massage. vibration disease.
Doppler effect– change in the frequency of the waves perceived by the observer (wave receiver) due to the relative motion of the wave source and the observer.
Case 1: N approaches I.
Case 2: And approaches N.
Case 3: approach and distance of I and H from each other:
System: ultrasonic generator - receiver - is motionless relative to the medium. The object is moving. It receives ultrasound with a frequency 
, reflects it, sending it to the receiver, which receives an ultrasonic wave with a frequency 
. Frequency difference - doppler frequency shift:
. It is used to determine the speed of blood flow, the speed of movement of the valves.