Lecture - 14. Mechanical waves.

2. Mechanical wave.

3. Source of mechanical waves.

4. Point source of waves.

5. Transverse wave.

6. Longitudinal wave.

7. Wave front.

9. Periodic waves.

10. Harmonic wave.

11. Wavelength.

12. Speed ​​of distribution.

13. Dependence of the wave velocity on the properties of the medium.

14. Huygens' principle.

15. Reflection and refraction of waves.

16. The law of wave reflection.

17. The law of refraction of waves.

18. Equation of a plane wave.

19. Energy and intensity of the wave.

20. The principle of superposition.

21. Coherent vibrations.

22. Coherent waves.

23. Interference of waves. a) interference maximum condition, b) interference minimum condition.

24. Interference and the law of conservation of energy.

25. Diffraction of waves.

26. Huygens-Fresnel principle.

27. Polarized wave.

29. Sound volume.

30. Pitch of sound.

31. Sound timbre.

32. Ultrasound.

33. Infrasound.

34. Doppler effect.

1.Wave - this is the process of propagation of oscillations of any physical quantity in space. For example, sound waves in gases or liquids represent the propagation of pressure and density fluctuations in these media. electromagnetic wave- this is the process of propagation in space of fluctuations in the intensity of electric magnetic fields.

Energy and momentum can be transferred in space by transferring matter. Any moving body has kinetic energy. Therefore, it transfers kinetic energy by transferring matter. The same body, being heated, moving in space, transfers thermal energy, transferring matter.

Particles of an elastic medium are interconnected. Perturbations, i.e. deviations from the equilibrium position of one particle are transferred to neighboring particles, i.e. energy and momentum are transferred from one particle to neighboring particles, while each particle remains near its equilibrium position. Thus, energy and momentum are transferred along the chain from one particle to another, and there is no transfer of matter.

So, the wave process is the process of transfer of energy and momentum in space without the transfer of matter.

2. Mechanical wave or elastic wave is a disturbance (oscillation) propagating in elastic medium. The elastic medium in which mechanical waves propagate is air, water, wood, metals and other elastic substances. Elastic waves are called sound waves.

3. Source of mechanical waves- a body that performs an oscillatory motion, being in an elastic medium, for example, vibrating tuning forks, strings, vocal cords.

4. Point source of waves - a source of a wave whose dimensions can be neglected compared to the distance over which the wave propagates.

5. transverse wave - a wave in which the particles of the medium oscillate in a direction perpendicular to the direction of wave propagation. For example, waves on the surface of water are transverse waves, because vibrations of water particles occur in a direction perpendicular to the direction of the water surface, and the wave propagates along the surface of the water. A transverse wave propagates along a cord, one end of which is fixed, the other oscillates in a vertical plane.

A transverse wave can propagate only along the interface between the spirit of different media.

6. Longitudinal wave - a wave in which vibrations occur in the direction of wave propagation. A longitudinal wave occurs in a long helical spring if one of its ends is subjected to periodic perturbations directed along the spring. The elastic wave running along the spring is a propagating sequence of compression and tension (Fig. 88)

A longitudinal wave can propagate only inside an elastic medium, for example, in air, in water. In solids and liquids, both transverse and longitudinal waves can propagate simultaneously, because a solid body and a liquid are always limited by a surface - the interface between two media. For example, if a steel rod is hit on the end with a hammer, then elastic deformation will begin to propagate in it. A transverse wave will run along the surface of the rod, and a longitudinal wave will propagate inside it (compression and rarefaction of the medium) (Fig. 89).

7. Wave front (wave surface) is the locus of points oscillating in the same phases. On the wave surface, the phases of the oscillating points at the considered moment of time have the same value. If a stone is thrown into a calm lake, then transverse waves in the form of a circle will begin to propagate along the surface of the lake from the place of its fall, with the center at the place where the stone fell. In this example, the wavefront is a circle.

In a spherical wave, the wave front is a sphere. Such waves are generated by point sources.

At very large distances from the source, the curvature of the front can be neglected and the wave front can be considered flat. In this case, the wave is called a plane wave.

8. Beam - straight line is normal to the wave surface. In a spherical wave, the rays are directed along the radii of the spheres from the center, where the wave source is located (Fig.90).

In a plane wave, the rays are directed perpendicular to the surface of the front (Fig. 91).

9. Periodic waves. When talking about waves, we meant a single perturbation propagating in space.

If the source of waves performs continuous oscillations, then elastic waves traveling one after one arise in the medium. Such waves are called periodic.

10. harmonic wave- a wave generated by harmonic oscillations. If the wave source makes harmonic vibrations, then it generates harmonic waves - waves in which particles oscillate according to a harmonic law.

11. Wavelength. Let a harmonic wave propagate along the OX axis and oscillate in it in the direction of the OY axis. This wave is transverse and can be represented as a sinusoid (Fig.92).

Such a wave can be obtained by causing vibrations in the vertical plane of the free end of the cord.

Wavelength is the distance between two nearest points. A and B oscillating in the same phases (Fig. 92).

12. Wave propagation speed – physical quantity numerically equal to the speed of propagation of oscillations in space. From Fig. 92 it follows that the time for which the oscillation propagates from point to point BUT to the point AT, i.e. by a distance of a wavelength equal to the period of oscillation. Therefore, the propagation speed of the wave is

13. Dependence of the wave propagation velocity on the properties of the medium. The frequency of oscillations when a wave occurs depends only on the properties of the wave source and does not depend on the properties of the medium. The speed of wave propagation depends on the properties of the medium. Therefore, the wavelength changes when crossing the interface between two different media. The speed of the wave depends on the bond between the atoms and molecules of the medium. The bond between atoms and molecules in liquids and solids is much more rigid than in gases. Therefore, the speed of sound waves in liquids and solids is much greater than in gases. In air, the speed of sound at normal conditions equal to 340, in water 1500, and in steel 6000.

The average speed of thermal motion of molecules in gases decreases with decreasing temperature, and as a result, the speed of wave propagation in gases decreases. In a denser medium, and therefore more inert, the wave speed is lower. If sound propagates in air, then its speed depends on the density of the air. Where the density of air is higher, the speed of sound is lower. Conversely, where the density of air is less, the speed of sound is greater. As a result, when sound propagates, the wave front is distorted. Over a swamp or over a lake, especially in evening time the density of air near the surface due to water vapor is greater than at a certain height. Therefore, the speed of sound near the surface of the water is less than at a certain height. As a result, the wave front turns in such a way that top part The front curves more and more towards the surface of the lake. It turns out that the energy of a wave traveling along the lake surface and the energy of a wave traveling at an angle to the lake surface add up. Therefore, in the evening, the sound is well distributed over the lake. Even a quiet conversation can be heard standing on the opposite bank.

14. Huygens principle- each point of the surface that the wave has reached at a given moment is a source of secondary waves. Drawing a surface tangent to the fronts of all secondary waves, we get the wave front at the next time.

Consider, for example, a wave propagating over the surface of water from a point O(Fig.93) Let at the moment of time t the front had the shape of a circle of radius R centered on a point O. At the next moment of time, each secondary wave will have a front in the form of a circle of radius , where V is the speed of wave propagation. Drawing a surface tangent to the fronts of the secondary waves, we get the wave front at the moment of time (Fig. 93)

If the wave propagates in a continuous medium, then the wave front is a sphere.

15. Reflection and refraction of waves. When a wave falls on the interface between two different media, each point of this surface, according to the Huygens principle, becomes a source of secondary waves propagating on both sides of the section surface. Therefore, when crossing the interface between two media, the wave is partially reflected and partially passes through this surface. Because different media, then the speed of the waves in them is different. Therefore, when crossing the interface between two media, the direction of wave propagation changes, i.e. wave breaking occurs. Consider, on the basis of the Huygens principle, the process and the laws of reflection and refraction are complete.

16. Wave reflection law. Let a plane wave fall on a flat interface between two different media. Let's select in it the area between the two rays and (Fig. 94)

The angle of incidence is the angle between the incident beam and the perpendicular to the interface at the point of incidence.

Reflection angle - the angle between the reflected beam and the perpendicular to the interface at the point of incidence.

At the moment when the beam reaches the interface at the point , this point will become a source of secondary waves. The wave front at this moment is marked by a straight line segment AC(Fig.94). Consequently, the beam still has to go to the interface at this moment, the path SW. Let the beam travel this path in time . The incident and reflected rays propagate on the same side of the interface, so their velocities are the same and equal v. Then .

During the time the secondary wave from the point BUT will go the way. Consequently . right triangles and are equal, because - common hypotenuse and legs. From the equality of triangles follows the equality of angles . But also , i.e. .

Now we formulate the law of wave reflection: incident beam, reflected beam , the perpendicular to the interface between two media, restored at the point of incidence, lie in the same plane; the angle of incidence is equal to the angle of reflection.

17. Wave refraction law. Let a plane wave pass through a plane interface between two media. And the angle of incidence is different from zero (Fig.95).

The angle of refraction is the angle between the refracted beam and the perpendicular to the interface, restored at the point of incidence.

Denote and the wave propagation velocities in media 1 and 2. At the moment when the beam reaches the interface at the point BUT, this point will become a source of waves propagating in the second medium - the ray , and the ray still has to go the way to the surface of the section. Let be the time it takes the beam to travel the path SW, then . During the same time in the second medium, the beam will travel the path . Because , then and .

Triangles and right angles with a common hypotenuse , and = , are like angles with mutually perpendicular sides. For the angles and we write the following equalities

.

Taking into account that , , we get

Now we formulate the law of wave refraction: The incident beam, the refracted beam and the perpendicular to the interface between two media, restored at the point of incidence, lie in the same plane; the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant value for two given media and is called the relative refractive index for the two given media.

18. Plane wave equation. Particles of the medium that are at a distance S from the source of the waves begin to oscillate only when the wave reaches it. If a V is the speed of wave propagation, then the oscillations will begin with a delay for a time

If the wave source oscillates according to the harmonic law, then for a particle located at a distance S from the source, we write the law of oscillations in the form

.

Let's introduce the value called the wave number. It shows how many wavelengths fit into the distance units length. Now the law of oscillations of a particle of a medium located at a distance S from the source we write in the form

.

This equation defines the displacement of the oscillating point as a function of time and distance from the wave source and is called the plane wave equation.

19. Wave Energy and Intensity. Each particle that the wave has reached oscillates and therefore has energy. Let a wave propagate in some volume of an elastic medium with an amplitude BUT and cyclic frequency. This means that the average energy of oscillations in this volume is equal to

Where m- the mass of the allocated volume of the medium.

The average energy density (average over volume) is the wave energy per unit volume of the medium

, where is the density of the medium.

Wave intensity is a physical quantity numerically equal to the energy that a wave transfers per unit of time through a unit area of ​​a plane perpendicular to the direction of wave propagation (through a unit area of ​​the wave front), i.e.

.

The average power of a wave is the average total energy transferred by a wave per unit time through a surface with an area S. We obtain the average wave power by multiplying the wave intensity by the area S

20.The principle of superposition (overlay). If waves from two or more sources propagate in an elastic medium, then, as observations show, the waves pass one through the other without affecting each other at all. In other words, the waves do not interact with each other. This is explained by the fact that within the limits of elastic deformation, compression and tension in one direction in no way affect the elastic properties in other directions.

Thus, each point of the medium where two or more waves come takes part in the oscillations caused by each wave. In this case, the resulting displacement of a particle of the medium at any time is equal to geometric sum displacements caused by each of the folding oscillatory processes. This is the essence of the principle of superposition or superposition of oscillations.

The result of the addition of oscillations depends on the amplitude, frequency and phase difference of the emerging oscillatory processes.

21. Coherent oscillations - oscillations with the same frequency and a constant phase difference in time.

22.coherent waves- waves of the same frequency or the same wavelength, the phase difference of which at a given point in space remains constant in time.

23.Wave interference- the phenomenon of an increase or decrease in the amplitude of the resulting wave when two or more coherent waves are superimposed.

a) . interference maximum conditions. Let waves from two coherent sources and meet at a point BUT(Fig.96).

Displacements of medium particles at a point BUT, caused by each wave separately, we write according to the wave equation in the form

where and , , - amplitudes and phases of oscillations caused by waves at a point BUT, and - point distances, - the difference between these distances or the difference in the course of the waves.

Due to the difference in the course of the waves, the second wave is delayed compared to the first. This means that the phase of oscillations in the first wave is ahead of the phase of oscillations in the second wave, i.e. . Their phase difference remains constant over time.

To the point BUT particles oscillated with maximum amplitude, the crests of both waves or their troughs should reach the point BUT simultaneously in identical phases or with a phase difference equal to , where n- integer, and - is the period of the sine and cosine functions,

Here , therefore, the condition of the interference maximum can be written in the form

Where is an integer.

So, when coherent waves are superimposed, the amplitude of the resulting oscillation is maximum if the difference in the path of the waves is equal to an integer number of wavelengths.

b) Interference minimum condition. The amplitude of the resulting oscillation at a point BUT is minimal if the crest and trough of two coherent waves arrive at this point simultaneously. This means that one hundred waves will come to this point in antiphase, i.e. their phase difference is equal to or , where is an integer.

The interference minimum condition is obtained by performing algebraic transformations:

Thus, the amplitude of oscillations when two coherent waves are superimposed is minimal if the difference in the path of the waves is equal to an odd number of half-waves.

24. Interference and the law of conservation of energy. When waves interfere in places of interference minima, the energy of the resulting oscillations is less than the energy of the interfering waves. But in the places of interference maxima, the energy of the resulting oscillations exceeds the sum of the energies of the interfering waves by as much as the energy has decreased in the places of interference minima.

When waves interfere, the energy of oscillations is redistributed in space, but the conservation law is strictly observed.

25.Wave diffraction- the phenomenon of wave wrapping around the obstacle, i.e. deviation from rectilinear wave propagation.

Diffraction is especially noticeable when the size of the obstacle is less than or comparable to the wavelength. Let a screen with a hole, the diameter of which is comparable with the wavelength (Fig. 97), be located on the path of propagation of a plane wave.

According to the Huygens principle, each point of the hole becomes a source of the same waves. The size of the hole is so small that all sources of secondary waves are located so close to each other that they can all be considered one point - one source of secondary waves.

If an obstacle is placed in the path of the wave, the size of which is comparable to the wavelength, then the edges, according to the Huygens principle, become a source of secondary waves. But the size of the gap is so small that its edges can be considered coinciding, i.e. the obstacle itself is a point source of secondary waves (Fig.97).

The phenomenon of diffraction is easily observed when waves propagate over the surface of water. When the wave reaches the thin, motionless stick, it becomes the source of the waves (Fig. 99).

25. Huygens-Fresnel principle. If the size of the hole significantly exceeds the wavelength, then the wave, passing through the hole, propagates in a straight line (Fig. 100).

If the size of the obstacle significantly exceeds the wavelength, then a shadow zone is formed behind the obstacle (Fig. 101). These experiments contradict Huygens' principle. The French physicist Fresnel supplemented Huygens' principle with the idea of ​​the coherence of secondary waves. Each point at which a wave has arrived becomes a source of the same waves, i.e. secondary coherent waves. Therefore, waves are absent only in those places where the conditions of the interference minimum are satisfied for the secondary waves.

26. polarized wave is a transverse wave in which all particles oscillate in the same plane. If the free end of the filament oscillates in one plane, then a plane-polarized wave propagates along the filament. If the free end of the filament oscillates in different directions, then the wave propagating along the filament is not polarized. If an obstacle in the form of a narrow slit is placed on the path of an unpolarized wave, then after passing through the slit the wave becomes polarized, because the gap allows the vibrations of the cord occurring along it.

If a second slot parallel to the first one is placed on the path of a polarized wave, then the wave will freely pass through it (Fig. 102).

If the second slot is placed at right angles to the first, then the wave will stop spreading. A device that separates vibrations occurring in one specific plane is called a polarizer (first slot). The device that determines the plane of polarization is called an analyzer.

27.Sound - this is the process of propagation of compressions and rarefactions in an elastic medium, for example, in a gas, liquid or metals. The propagation of compressions and rarefaction occurs as a result of the collision of molecules.

28. Sound volume is the force of the impact of a sound wave on the eardrum of the human ear, which is from sound pressure.

Sound pressure - This is the additional pressure that occurs in a gas or liquid when a sound wave propagates. Sound pressure depends on the amplitude of the oscillation of the sound source. If we make the tuning fork sound with a light blow, then we get one volume. But, if the tuning fork is hit harder, then the amplitude of its oscillations will increase and it will sound louder. Thus, the loudness of the sound is determined by the amplitude of the oscillation of the sound source, i.e. amplitude of sound pressure fluctuations.

29. Sound pitch determined by the oscillation frequency. The higher the frequency of the sound, the higher the tone.

Sound vibrations occurring according to the harmonic law are perceived as a musical tone. Usually sound is a complex sound, which is a combination of vibrations with close frequencies.

The root tone of a complex sound is the tone corresponding to the lowest frequency in the set of frequencies of the given sound. Tones corresponding to other frequencies of a complex sound are called overtones.

30. Sound timbre. Sounds with the same basic tone differ in timbre, which is determined by a set of overtones.

Each person has his own unique timbre. Therefore, we can always distinguish the voice of one person from the voice of another person, even if their fundamental tones are the same.

31.Ultrasound. The human ear perceives sounds whose frequencies are between 20 Hz and 20,000 Hz.

Sounds with frequencies above 20,000 Hz are called ultrasounds. Ultrasounds propagate in the form of narrow beams and are used in sonar and flaw detection. Ultrasound can determine the depth of the seabed and detect defects in various parts.

For example, if the rail has no cracks, then the ultrasound emitted from one end of the rail, reflected from its other end, will give only one echo. If there are cracks, then the ultrasound will be reflected from the cracks and the instruments will record several echoes. With the help of ultrasound, submarines, schools of fish are detected. The bat navigates in space with the help of ultrasound.

32. infrasound– sound with a frequency below 20 Hz. These sounds are perceived by some animals. They often come from fluctuations. earth's crust during earthquakes.

33. Doppler effect- this is the dependence of the frequency of the perceived wave on the movement of the source or receiver of the waves.

Let a boat rest on the surface of the lake and waves beat against its side with a certain frequency. If the boat starts moving against the direction of wave propagation, then the frequency of wave impacts on the side of the boat will become greater. Moreover, the greater the speed of the boat, the greater the frequency of wave impacts on board. Conversely, when the boat moves in the direction of wave propagation, the frequency of impacts will become less. These considerations are easy to understand from Fig. 103.

The greater the speed of the oncoming movement, the less time is spent on passing the distance between the two nearest ridges, i.e. the shorter the period of the wave and the greater the frequency of the wave relative to the boat.

If the observer is motionless, but the source of waves is moving, then the frequency of the wave perceived by the observer depends on the movement of the source.

Let a heron walk along a shallow lake towards the observer. Every time she puts her foot in the water, waves ripple out from that spot. And each time the distance between the first and last waves decreases, i.e. fit at a shorter distance more ridges and depressions. Therefore, for a stationary observer towards which the heron is walking, the frequency increases. And vice versa for a motionless observer who is in a diametrically opposite point at a greater distance, there are as many ridges and troughs. Therefore, for this observer, the frequency decreases (Fig. 104).

You can imagine what mechanical waves are by throwing a stone into the water. The circles that appear on it and are alternating troughs and ridges are an example of mechanical waves. What is their essence? Mechanical waves are the process of propagation of vibrations in elastic media.

Waves on liquid surfaces

Such mechanical waves exist due to the influence of intermolecular forces and gravity on the particles of the liquid. People have been studying this phenomenon for a long time. The most notable are the oceanic and sea ​​waves. As the wind speed increases, they change and their height increases. The shape of the waves themselves also becomes more complicated. In the ocean, they can reach frightening proportions. One of the most obvious examples of force is the tsunami, sweeping away everything in its path.

Energy of sea and ocean waves

Reaching the shore, sea waves increase with a sharp change in depth. They sometimes reach a height of several meters. At such moments, a colossal mass of water is transferred to coastal obstacles, which are quickly destroyed under its influence. The strength of the surf sometimes reaches grandiose values.

elastic waves

In mechanics, not only oscillations on the surface of a liquid are studied, but also the so-called elastic waves. These are perturbations that propagate in different media under the action of elastic forces in them. Such a perturbation is any deviation of the particles of a given medium from the equilibrium position. good example elastic waves is a long rope or rubber tube attached at one end to something. If you pull it tight, and then create a disturbance at the second (unfixed) end of it with a lateral sharp movement, you can see how it “runs” along the entire length of the rope to the support and is reflected back.

The initial perturbation leads to the appearance of a wave in the medium. It is caused by the action of some foreign body, which in physics is called the source of the wave. It can be the hand of a person swinging a rope, or a pebble thrown into the water. In the case when the action of the source is short-lived, a solitary wave often appears in the medium. When the “disturber” makes long waves, they begin to appear one after another.

Conditions for the occurrence of mechanical waves

Such oscillations are not always formed. Necessary condition for their appearance is the occurrence at the moment of perturbation of the medium of forces preventing it, in particular, elasticity. They tend to bring neighboring particles closer together when they move apart, and push them away from each other when they approach each other. Elastic forces, acting on particles far from the source of perturbation, begin to unbalance them. Over time, all particles of the medium are involved in one oscillatory motion. The propagation of such oscillations is a wave.

Mechanical waves in an elastic medium

In an elastic wave, there are 2 types of motion simultaneously: particle oscillations and perturbation propagation. A longitudinal wave is a mechanical wave whose particles oscillate along the direction of its propagation. A transverse wave is a wave whose medium particles oscillate across the direction of its propagation.

Properties of mechanical waves

Perturbations in a longitudinal wave are rarefaction and compression, and in a transverse wave they are shifts (displacements) of some layers of the medium relative to others. The compression deformation is accompanied by the appearance of elastic forces. In this case, it is associated with the appearance of elastic forces exclusively in solids. In gaseous and liquid media, the shift of the layers of these media is not accompanied by the appearance of the mentioned force. Due to their properties, longitudinal waves are able to propagate in any medium, and transverse waves - only in solid ones.

Features of waves on the surface of liquids

Waves on the surface of a liquid are neither longitudinal nor transverse. They have a more complex, so-called longitudinal-transverse character. In this case, the fluid particles move in a circle or along elongated ellipses. particles on the surface of the liquid, and especially with large fluctuations, are accompanied by their slow but continuous movement in the direction of wave propagation. It is these properties of mechanical waves in the water that cause the appearance of various seafood on the shore.

Frequency of mechanical waves

If in an elastic medium (liquid, solid, gaseous) vibration of its particles is excited, then due to the interaction between them, it will propagate with a speed u. So, if an oscillating body is in a gaseous or liquid medium, then its movement will begin to be transmitted to all particles adjacent to it. They will involve the next ones in the process and so on. In this case, absolutely all points of the medium will begin to oscillate with the same frequency, equal to the frequency of the oscillating body. It is the frequency of the wave. In other words, this quantity can be characterized as points in the medium where the wave propagates.

It may not be immediately clear how this process occurs. Mechanical waves are associated with the transfer of energy of oscillatory motion from its source to the periphery of the medium. As a result, so-called periodic deformations arise, which are carried by the wave from one point to another. In this case, the particles of the medium themselves do not move along with the wave. They oscillate near their equilibrium position. That is why the spread mechanical wave is not accompanied by the transfer of a substance from one place to another. Mechanical waves have different frequencies. Therefore, they were divided into ranges and created a special scale. Frequency is measured in hertz (Hz).

Basic Formulas

Mechanical waves, whose calculation formulas are quite simple, are an interesting object for study. The wave speed (υ) is the speed of movement of its front (geometrical place of all points to which the oscillation of the medium has reached at a given moment):

where ρ is the density of the medium, G is the modulus of elasticity.

When calculating, you should not confuse the speed of a mechanical wave in a medium with the speed of movement of the particles of the medium that are involved in. So, for example, a sound wave in air propagates with average speed vibrations of its molecules at 10 m/s, while the speed of a sound wave under normal conditions is 330 m/s.

The wave front happens different types, the simplest of which are:

Spherical - caused by fluctuations in a gaseous or liquid medium. In this case, the wave amplitude decreases with distance from the source in inverse proportion to the square of the distance.

Flat - is a plane that is perpendicular to the direction of wave propagation. It occurs, for example, in a closed piston cylinder when it performs oscillatory movements. A plane wave is characterized by an almost constant amplitude. Its slight decrease with distance from the disturbance source is associated with the degree of viscosity of the gaseous or liquid medium.

Wavelength

Under understand the distance over which its front will move in a time that is equal to the period of oscillation of the particles of the medium:

λ = υT = υ/v = 2πυ/ ω,

where T is the oscillation period, υ is the wave speed, ω is the cyclic frequency, ν is the oscillation frequency of the medium points.

Since the propagation velocity of a mechanical wave is completely dependent on the properties of the medium, its length λ changes during the transition from one medium to another. In this case, the oscillation frequency ν always remains the same. Mechanical and similar in that during their propagation, energy is transferred, but no matter is transferred.

With waves of any origin, under certain conditions, four phenomena listed below can be observed, which we will consider using the example of sound waves in air and waves on the surface of water.

Reflection of waves. Let's do an experiment with an audio frequency current generator to which a loudspeaker (speaker) is connected, as shown in Fig. "a". We will hear a whistling sound. At the other end of the table, we put a microphone connected to an oscilloscope. Since a sine wave with a small amplitude appears on the screen, it means that the microphone perceives a weak sound.

Let us now place a board on top of the table, as shown in Fig. "b". Since the amplitude on the oscilloscope screen has increased, it means that the sound reaching the microphone has become louder. This and many other experiments suggest that mechanical waves of any origin have the ability to be reflected from the interface between two media.

Refraction of waves. Let's turn to the figure, which shows the waves running on the coastal shallows (top view). Gray-yellow color depicts the sandy shore, and blue - the deep part of the sea. Between them there is a sandbank - shallow water.

Waves traveling through deep water propagate in the direction of the red arrow. In the place of running aground, the wave is refracted, that is, it changes the direction of propagation. Therefore, the blue arrow indicating the new direction of wave propagation is positioned differently.

This and many other observations show that mechanical waves of any origin can be refracted when the propagation conditions change, for example, at the interface between two media.

Diffraction of waves. Translated from the Latin "diffractus" means "broken". In physics diffraction is the deviation of waves from rectilinear propagation in the same medium, leading to their rounding of obstacles.

Now take a look at another pattern of waves on the surface of the sea (view from the shore). Waves running towards us from afar are obscured by a large rock on the left, but at the same time they partially go around it. The smaller rock on the right is not at all an obstacle to the waves: they completely go around it, spreading in the same direction.

Experiences show that diffraction is most clearly manifested if the incident wavelength more sizes obstacles. Behind him, the wave spreads as if there was no obstacle.

Wave interference. We have considered the phenomena associated with the propagation of a single wave: reflection, refraction and diffraction. Consider now the propagation with the superposition of two or more waves on each other - interference phenomenon(from the Latin “inter” - mutually and “ferio” - I hit). Let's study this phenomenon experimentally.

Connect two speakers connected in parallel to the audio frequency current generator. The sound receiver, as in the first experiment, will be a microphone connected to an oscilloscope.

Let's start moving the microphone to the right. The oscilloscope will show that the sound gets weaker and stronger, despite the fact that the microphone moves away from the speakers. Bring the microphone back middle line between the speakers, and then we will move it to the left, moving away from the speakers again. The oscilloscope will again show us the attenuation, then the amplification of the sound.

This and many other experiments show that in space where several waves propagate, their interference can lead to the appearance of alternating regions with amplification and attenuation of oscillations.

mechanical waves

If oscillations of particles are excited in any place of a solid, liquid or gaseous medium, then due to the interaction of atoms and molecules of the medium, oscillations begin to be transmitted from one point to another with a finite speed. The process of propagation of oscillations in a medium is called wave .

mechanical waves are of different types. If in a wave the particles of the medium experience a displacement in a direction perpendicular to the direction of propagation, then the wave is called transverse . An example of a wave of this kind can be waves running along a stretched rubber band (Fig. 2.6.1) or along a string.

If the displacement of the particles of the medium occurs in the direction of wave propagation, then the wave is called longitudinal . Waves in an elastic rod (Fig. 2.6.2) or sound waves in a gas are examples of such waves.

Waves on the liquid surface have both transverse and longitudinal components.

Both in transverse and longitudinal waves, there is no transfer of matter in the direction of wave propagation. In the process of propagation, the particles of the medium only oscillate around the equilibrium positions. However, waves carry the energy of oscillations from one point of the medium to another.

characteristic feature mechanical waves is that they propagate in material media (solid, liquid or gaseous). There are waves that can also propagate in a vacuum (for example, light waves). For mechanical waves, a medium is required that has the ability to store kinetic and potential energy. Therefore, the environment must have inert and elastic properties. In real environments, these properties are distributed throughout the volume. So, for example, any small element solid body has mass and elasticity. In the simplest one-dimensional model a solid body can be represented as a collection of balls and springs (Fig. 2.6.3).

Longitudinal mechanical waves can propagate in any media - solid, liquid and gaseous.

If in a one-dimensional model of a rigid body one or more balls are displaced in a direction perpendicular to the chain, then a deformation will occur shear. The springs deformed under such a displacement will tend to return the displaced particles to the equilibrium position. In this case, elastic forces will act on the nearest undisplaced particles, tending to deflect them from the equilibrium position. As a result, a transverse wave will run along the chain.

In liquids and gases, elastic shear deformation does not occur. If one layer of liquid or gas is displaced by some distance relative to the neighboring layer, then no tangential forces will appear at the boundary between the layers. The forces acting 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 applies to gaseous media. Consequently, transverse waves cannot exist in liquid or gaseous media.

Of considerable interest for practice are simple harmonic or sine waves . They are characterized amplitudeA particle vibrations, frequencyf and wavelengthλ. Sinusoidal waves propagate in homogeneous media with some constant speed υ.

Bias y (x, t) particles of the medium from the equilibrium position in a sinusoidal wave depends on the coordinate x on axle OX, along which the wave propagates, and from time t in law.