1. Mechanical waves, wave frequency. Longitudinal and transverse waves.

2. Wave front. Velocity and wavelength.

3. Equation of a plane wave.

4. Energy characteristics of the wave.

5. Some special types of waves.

6. Doppler effect and its use in medicine.

7. Anisotropy during the propagation of surface waves. Effect of shock waves on biological tissues.

8. Basic concepts and formulas.

9. Tasks.

2.1. Mechanical waves, wave frequency. Longitudinal and transverse waves

If in any place of an elastic medium (solid, liquid or gaseous) oscillations of its particles are excited, then due to the interaction between particles, this oscillation will begin to propagate in the medium from particle to particle with a certain speed v.

For example, if an oscillating body is placed in a liquid or gaseous medium, then oscillating motion body will be transmitted to adjacent particles of the environment. They, in turn, involve neighboring particles in oscillatory motion, and so on. In this case, all points of the medium oscillate with the same frequency, equal to the frequency of the vibration of the body. This frequency is called wave frequency.

wave is the process of propagation of mechanical vibrations in an elastic medium.

wave frequency called the frequency of oscillations of the points of the medium in which the wave propagates.

The wave is associated with the transfer of vibration energy from the source of vibrations to the peripheral parts of the medium. At the same time, in the environment there are

periodic deformations that are carried by a wave from one point of the medium to another. The particles of the medium themselves do not move along with the wave, but oscillate around their equilibrium positions. Therefore, the propagation of the wave is not accompanied by the transfer of matter.

according to frequency mechanical waves are divided into different ranges, which are indicated in Table. 2.1.

Table 2.1. Scale of mechanical waves

Depending on the direction of particle oscillations in relation to the direction of wave propagation, longitudinal and transverse waves are distinguished.

Longitudinal waves- waves, during the propagation of which the particles of the medium oscillate along the same straight line along which the wave propagates. In this case, the areas of compression and rarefaction alternate in the medium.

Longitudinal mechanical waves can occur in all media (solid, liquid and gaseous).

transverse waves- waves, during the propagation of which particles oscillate perpendicular to the direction of propagation of the wave. In this case, periodic shear deformations occur in the medium.

In liquids and gases, elastic forces arise only during compression and do not arise during shear, so transverse waves do not form in these media. The exception is waves on the surface of a liquid.

2.2. wave front. Velocity and wavelength

In nature, there are no processes that propagate at an infinitely high speed, therefore, a disturbance created by an external influence at one point in the environment will reach another point not instantly, but after some time. In this case, the medium is divided into two regions: the region, the points of which are already involved in the oscillatory motion, and the region, the points of which are still in equilibrium. The surface separating these regions is called wave front.

Wave front - the locus of points to which the oscillation (perturbation of the medium) has reached a given moment.

When a wave propagates, its front moves at a certain speed, which is called the speed of the wave.

Wave speed (v) is the speed of movement of its front.

The speed of a wave depends on the properties of the medium and the type of wave: transverse and longitudinal waves in a solid propagate at different speeds.

The propagation velocity of all types of waves is determined under the condition of weak wave attenuation by the following expression:

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

The speed of a wave in a medium should not be confused with the speed of movement of the particles of the medium involved in wave process. For example, when a sound wave propagates in air, the average vibration velocity of its molecules is about 10 cm/s, and the velocity sound wave under normal conditions about 330 m/s.

The wavefront shape determines the geometric type of the wave. The simplest types of waves on this basis are flat And spherical.

flat A wave is called a wave whose front is a plane perpendicular to the direction of propagation.

Plane waves arise, for example, in a closed piston cylinder with gas when the piston oscillates.

The amplitude of the plane wave remains practically unchanged. Its slight decrease with distance from the wave source is associated with the viscosity of the liquid or gaseous medium.

spherical called a wave whose front has the shape of a sphere.

Such, for example, is a wave caused in a liquid or gaseous medium by a pulsating spherical source.

The amplitude of a spherical wave decreases with distance from the source inversely proportional to the square of the distance.

To describe a number of wave phenomena, such as interference and diffraction, use a special characteristic called the wavelength.

Wavelength called the distance over which its front moves in a time equal to the period of oscillation of the particles of the medium:

Here v- wave speed, T - oscillation period, ν - frequency of oscillations of medium points, ω - cyclic frequency.

Since the speed of wave propagation depends on the properties of the medium, the wavelength λ when moving from one medium to another, it changes, while the frequency ν stays the same.

This definition of wavelength has an important geometric interpretation. Consider Fig. 2.1a, which shows the displacements of the points of the medium at some point in time. The position of the wave front is marked by points A and B.

After a time T equal to one period of oscillation, the wave front will move. Its positions are shown in Fig. 2.1, b points A 1 and B 1. It can be seen from the figure that the wavelength λ is equal to the distance between adjacent points oscillating in the same phase, for example, the distance between two adjacent maxima or minima of the perturbation.

Rice. 2.1. Geometric interpretation of the wavelength

2.3. Plane wave equation

The wave arises as a result of periodic external influences on the medium. Consider the distribution flat wave created by harmonic oscillations of the source:

where x and - displacement of the source, A - amplitude of oscillations, ω - circular frequency of oscillations.

If some point of the medium is removed from the source at a distance s, and the wave speed is equal to v, then the perturbation created by the source will reach this point in time τ = s/v. Therefore, the phase of the oscillations at the considered point at the time t will be the same as the phase of the source oscillations at the time (t - s/v), and the amplitude of the oscillations will remain practically unchanged. As a result, the fluctuations of this point will be determined by the equation

Here we have used the formulas for the circular frequency (ω = 2π/T) and wavelength (λ = v T).

Substituting this expression into the original formula, we get

Equation (2.2), which determines the displacement of any point of the medium at any time, is called plane wave equation. The argument at cosine is the magnitude φ = ωt - 2 π s /λ - called wave phase.

2.4. Energy characteristics of the wave

The medium in which the wave propagates has mechanical energy, which is made up of the energies of the oscillatory motion of all its particles. The energy of one particle with mass m 0 is found by formula (1.21): E 0 = m 0 Α 2 w 2/2. The volume unit of the medium contains n = p/m 0 particles (ρ is the density of the medium). Therefore, a unit volume of the medium has the energy w р = nЕ 0 = ρ Α 2 w 2 /2.

Bulk energy density(\¥ p) - the energy of the oscillatory motion of the particles of the medium contained in a unit of its volume:

where ρ is the density of the medium, A is the amplitude of particle oscillations, ω is the frequency of the wave.

As the wave propagates, the energy imparted by the source is transferred to distant regions.

For a quantitative description of the energy transfer, the following quantities are introduced.

Energy flow(Ф) - a value equal to the energy carried by the wave through a given surface per unit time:

Wave intensity or energy flux density (I) - value, equal to the flow energy carried by a wave through a unit area perpendicular to the direction of wave propagation:

It can be shown that the wave intensity is equal to the product of its propagation velocity and the volume energy density

2.5. Some special varieties

waves

1. shock waves. When sound waves propagate, the particle oscillation velocity does not exceed a few cm/s, i.e. it is hundreds of times less than the wave speed. Under strong disturbances (explosion, movement of bodies at supersonic speed, powerful electric discharge), the speed of oscillating particles of the medium can become comparable to the speed of sound. This creates an effect called a shock wave.

During an explosion, products with high density, heated to high temperatures, expand and compress thin layer ambient air.

shock wave - a thin transition region propagating at supersonic speed, in which there is an abrupt increase in pressure, density, and velocity of matter.

The shock wave can have significant energy. So, in a nuclear explosion, the formation of a shock wave in environment about 50% of the total energy of the explosion is expended. The shock wave, reaching objects, is capable of causing destruction.

2. surface waves. Along with body waves in continuous media in the presence of extended boundaries, there can be waves localized near the boundaries, which play the role of waveguides. Such, in particular, are surface waves in a liquid and an elastic medium, discovered by the English physicist W. Strett (Lord Rayleigh) in the 90s of the 19th century. In the ideal case, Rayleigh waves propagate along the boundary of the half-space, decaying exponentially in the transverse direction. As a result, surface waves localize the energy of perturbations created on the surface in a relatively narrow near-surface layer.

surface waves - waves that propagate along the free surface of a body or along the boundary of the body with other media and decay rapidly with distance from the boundary.

An example of such waves is waves in the earth's crust (seismic waves). The penetration depth of surface waves is several wavelengths. At a depth equal to the wavelength λ, the volumetric energy density of the wave is approximately 0.05 of its volumetric density at the surface. The displacement amplitude rapidly decreases with distance from the surface and practically disappears at a depth of several wavelengths.

3. Waves of excitation in active environments.

An actively excitable, or active, environment is a continuous environment consisting of a large number of elements, each of which has an energy reserve.

Moreover, each element can be in one of three states: 1 - excitation, 2 - refractoriness (non-excitability for a certain time after excitation), 3 - rest. Elements can go into excitation only from a state of rest. Excitation waves in active media are called autowaves. Autowaves - these are self-sustaining waves in an active medium, keeping their characteristics constant due to energy sources distributed in the medium.

The characteristics of an autowave - period, wavelength, propagation velocity, amplitude and shape - in the steady state depend only on the local properties of the medium and do not depend on the initial conditions. In table. 2.2 shows the similarities and differences between autowaves and ordinary mechanical waves.

Autowaves can be compared with the spread of fire in the steppe. The flame spreads over an area with distributed energy reserves (dry grass). Each subsequent element (dry blade of grass) is ignited from the previous one. And thus the front of the excitation wave (flame) propagates through the active medium (dry grass). When two fires meet, the flame disappears, as the energy reserves are exhausted - all the grass is burned out.

The description of the processes of propagation of autowaves in active media is used in the study of the propagation of action potentials along nerve and muscle fibers.

Table 2.2. Comparison of autowaves and ordinary mechanical waves

2.6. Doppler effect and its use in medicine

Christian Doppler (1803-1853) - Austrian physicist, mathematician, astronomer, director of the world's first physical institute.

Doppler effect consists in changing the frequency of oscillations perceived by the observer, due to the relative motion of the source of oscillations and the observer.

The effect is observed in acoustics and optics.

We obtain a formula describing the Doppler effect for the case when the source and receiver of the wave move relative to the medium along one straight line with velocities v I and v P, respectively. A source commits harmonic vibrations with frequency ν 0 relative to its equilibrium position. The wave created by these oscillations propagates in the medium at a speed v. Let us find out what frequency of oscillations will fix in this case receiver.

Disturbances created by source oscillations propagate in the medium and reach the receiver. Consider one complete oscillation of the source, which begins at time t 1 = 0

and ends at the moment t 2 = T 0 (T 0 is the source oscillation period). The disturbances of the medium created at these moments of time reach the receiver at the moments t" 1 and t" 2, respectively. In this case, the receiver captures oscillations with a period and frequency:

Let's find the moments t" 1 and t" 2 for the case when the source and receiver are moving towards to each other, and the initial distance between them is equal to S. At the moment t 2 \u003d T 0, this distance will become equal to S - (v I + v P) T 0, (Fig. 2.2).

Rice. 2.2. Mutual position of the source and receiver at the moments t 1 and t 2

This formula is valid for the case when the speeds v and and v p are directed towards each other. In general, when moving

source and receiver along one straight line, the formula for the Doppler effect takes the form

For the source, the speed v And is taken with the “+” sign if it moves in the direction of the receiver, and with the “-” sign otherwise. For the receiver - similarly (Fig. 2.3).

Rice. 2.3. Choice of signs for the velocities of the source and receiver of waves

Consider one special case use of the Doppler effect in medicine. Let the ultrasound generator be combined with the receiver in the form of some technical system that is stationary relative to the medium. The generator emits ultrasound having a frequency ν 0 , which propagates in the medium with a speed v. Towards system with a speed v t moves some body. First, the system performs the role source (v AND= 0), and the body is the role of the receiver (vTl= v T). Then the wave is reflected from the object and fixed by a fixed receiving device. In this case, v AND = v T, and v p \u003d 0.

Applying formula (2.7) twice, we obtain the formula for the frequency fixed by the system after reflection of the emitted signal:

At approach object to the sensor frequency of the reflected signal increases and at removal - decreases.

By measuring the Doppler frequency shift, from formula (2.8) we can find the speed of the reflecting body:

The sign "+" corresponds to the movement of the body towards the emitter.

The Doppler effect is used to determine the speed of blood flow, the speed of movement of the valves and walls of the heart (Doppler echocardiography) and other organs. A diagram of the corresponding setup for measuring blood velocity is shown in Fig. 2.4.

Rice. 2.4. Scheme of an installation for measuring blood velocity: 1 - ultrasound source, 2 - ultrasound receiver

The device consists of two piezocrystals, one of which is used to generate ultrasonic vibrations (inverse piezoelectric effect), and the second - to receive ultrasound (direct piezoelectric effect) scattered by blood.

Example. Determine the speed of blood flow in the artery, if the counter reflection of ultrasound (ν 0 = 100 kHz = 100,000 Hz, v \u003d 1500 m / s) a Doppler frequency shift occurs from erythrocytes ν D = 40 Hz.

Solution. By formula (2.9) we find:

v 0 = v D v /2v0 = 40x 1500/(2x 100,000) = 0.3 m/s.

2.7. Anisotropy during the propagation of surface waves. Effect of shock waves on biological tissues

1. Anisotropy of surface wave propagation. When researching mechanical properties skin with the help of surface waves at a frequency of 5-6 kHz (not to be confused with ultrasound), acoustic anisotropy of the skin is manifested. This is expressed in the fact that the propagation velocities of the surface wave in mutually perpendicular directions - along the vertical (Y) and horizontal (X) axes of the body - differ.

To quantify the severity of acoustic anisotropy, the mechanical anisotropy coefficient is used, which is calculated by the formula:

where v y- speed along the vertical axis, v x- along the horizontal axis.

The anisotropy coefficient is taken as positive (K+) if v y> v x at v y < v x the coefficient is taken as negative (K -). The numerical values ​​of the velocity of surface waves in the skin and the degree of anisotropy are objective criteria for evaluating various effects, including those on the skin.

2. Action of shock waves on biological tissues. In many cases of impact on biological tissues (organs), it is necessary to take into account the resulting shock waves.

So, for example, a shock wave occurs when a blunt object hits the head. Therefore, when designing protective helmets, care is taken to dampen the shock wave and protect the back of the head in a frontal impact. This purpose is served by the internal tape in the helmet, which at first glance seems to be necessary only for ventilation.

Shock waves arise in tissues when exposed to high-intensity laser radiation. Often after that, cicatricial (or other) changes begin to develop in the skin. This is the case, for example, in cosmetic procedures. Therefore, in order to reduce harmful effect shock waves, it is necessary to pre-calculate the dosage of exposure, taking into account the physical properties of both radiation and the skin itself.

Rice. 2.5. Propagation of Radial Shock Waves

Shock waves are used in radial shock wave therapy. On fig. 2.5 shows the propagation of radial shock waves from the applicator.

Such waves are created in devices equipped with a special compressor. A radial shock wave is generated pneumatic method. The piston, located in the manipulator, moves at high speed under the influence of a controlled pulse of compressed air. When the piston hits the applicator installed in the manipulator, its kinetic energy is converted into mechanical energy of the area of ​​the body that was affected. In this case, to reduce losses during the transmission of waves in the air gap located between the applicator and the skin, and to ensure good conductivity of shock waves, a contact gel is used. Normal operating mode: frequency 6-10 Hz, operating pressure 250 kPa, number of pulses per session - up to 2000.

1. On the ship, a siren is turned on, giving signals in the fog, and after t = 6.6 s, an echo is heard. How far away is the reflective surface? speed of sound in air v= 330 m/s.

Solution

In time t, sound travels a path 2S: 2S = vt →S = vt/2 = 1090 m. Answer: S = 1090 m.

2. What minimum size objects whose position can be determined by bats using their sensor, which has a frequency of 100,000 Hz? What is the minimum size of objects that dolphins can detect using a frequency of 100,000 Hz?

Solution

The minimum dimensions of an object are equal to the wavelength:

λ1\u003d 330 m / s / 10 5 Hz \u003d 3.3 mm. This is roughly the size of the insects that bats feed on;

λ2\u003d 1500 m / s / 10 5 Hz \u003d 1.5 cm. A dolphin can detect a small fish.

Answer:λ1= 3.3 mm; λ2= 1.5 cm.

3. First, a person sees a flash of lightning, and after 8 seconds after that he hears a thunderclap. At what distance did the lightning flash from him?

Solution

S \u003d v star t \u003d 330 x 8 = 2640 m. Answer: 2640 m

4. Two sound waves have the same characteristics, except that one has twice the wavelength of the other. Which one carries the most energy? How many times?

Solution

The intensity of the wave is directly proportional to the square of the frequency (2.6) and inversely proportional to the square of the wavelength (ω = 2πv/λ ). Answer: one with a shorter wavelength; 4 times.

5. A sound wave having a frequency of 262 Hz propagates in air at a speed of 345 m/s. a) What is its wavelength? b) How long does it take for the phase at a given point in space to change by 90°? c) What is the phase difference (in degrees) between points 6.4 cm apart?

Solution

but) λ =v /ν = 345/262 = 1.32 m;

in) Δφ = 360°s/λ= 360 x 0.064/1.32 = 17.5°. Answer: but) λ = 1.32 m; b) t = T/4; in) Δφ = 17.5°.

6. Estimate the upper limit (frequency) of ultrasound in air if the speed of its propagation is known v= 330 m/s. Assume that air molecules have a size of the order of d = 10 -10 m.

Solution

In air, a mechanical wave is longitudinal and the wavelength corresponds to the distance between two nearest concentrations (or discharges) of molecules. Since the distance between the clusters cannot be smaller sizes molecules, then d = λ. From these considerations, we have ν =v /λ = 3,3x 10 12 Hz. Answer:ν = 3,3x 10 12 Hz.

7. Two cars are moving towards each other with speeds v 1 = 20 m/s and v 2 = 10 m/s. The first machine gives a signal with a frequency ν 0 = 800 Hz. Sound speed v= 340 m/s. What frequency will the driver of the second car hear: a) before the cars meet; b) after the meeting of the cars?

8. When a train passes by, you hear how the frequency of its whistle changes from ν 1 = 1000 Hz (when approaching) to ν 2 = 800 Hz (when the train is moving away). What is the speed of the train?

Solution

This problem differs from the previous ones in that we do not know the speed of the sound source - the train - and the frequency of its signal ν 0 is unknown. Therefore, a system of equations with two unknowns is obtained:

Solution

Let be v is the speed of the wind, and it blows from the person (receiver) to the source of the sound. Relative to the ground, they are motionless, and relative to the air, both move to the right with a speed u.

By formula (2.7) we obtain the sound frequency. perceived by man. She is unchanged:

Answer: frequency will not change.

A mechanical or elastic wave is the process of propagation of oscillations in an elastic medium. For example, air begins to oscillate around a vibrating string or speaker cone - the string or speaker has become sources of a sound wave.

For the occurrence of a mechanical wave, two conditions must be met - the presence of a wave source (it can be any oscillating body) and an elastic medium (gas, liquid, solid).

Find out the cause of the wave. Why do the particles of the medium surrounding any oscillating body also come into oscillatory motion?

The simplest model of a one-dimensional elastic medium is a chain of balls connected by springs. Balls are models of molecules, the springs connecting them model the forces of interaction between molecules.

Suppose the first ball oscillates with a frequency ω. Spring 1-2 is deformed, an elastic force arises in it, which changes with frequency ω. Under the action of an external periodically changing force, the second ball begins to perform forced oscillations. Since forced oscillations always occur at the frequency of the external driving force, the oscillation frequency of the second ball will coincide with the oscillation frequency of the first. However, the forced oscillations of the second ball will occur with some phase delay relative to the external driving force. In other words, the second ball will begin to oscillate somewhat later than the first ball.

The vibrations of the second ball will cause a periodically changing deformation of the spring 2-3, which will make the third ball oscillate, and so on. Thus, all the balls in the chain will alternately be involved in an oscillatory motion with the oscillation frequency of the first ball.

Obviously, the cause of wave propagation in an elastic medium is the presence of interaction between molecules. The oscillation frequency of all particles in the wave is the same and coincides with the oscillation frequency of the wave source.

According to the nature of particle oscillations in a wave, waves are divided into transverse, longitudinal and surface waves.

IN longitudinal wave particles oscillate along the direction of wave propagation.

The propagation of a longitudinal wave is associated with the occurrence of tensile-compressive deformation in the medium. In the stretched areas of the medium, a decrease in the density of the substance is observed - rarefaction. In compressed areas of the medium, on the contrary, there is an increase in the density of the substance - the so-called thickening. For this reason, a longitudinal wave is a movement in space of areas of condensation and rarefaction.

Tensile-compressive deformation can occur in any elastic medium, therefore longitudinal waves can spread in gases, liquids and solids. An example of a longitudinal wave is sound.

IN shear wave particles oscillate perpendicular to the direction of wave propagation.

The propagation of a transverse wave is associated with the occurrence of shear deformation in the medium. This type of deformation can only exist in solids, so transverse waves can only propagate in solids. An example of a shear wave is the seismic S-wave.

surface waves occur at the interface between two media. Oscillating particles of the medium have both transverse, perpendicular to the surface, and longitudinal components of the displacement vector. During their oscillations, the particles of the medium describe elliptical trajectories in a plane perpendicular to the surface and passing through the direction of wave propagation. An example of surface waves are waves on the water surface and seismic L - waves.

The wave front is the locus of points reached by the wave process. The shape of the wave front can be different. The most common are plane, spherical and cylindrical waves.

Note that the wavefront is always located perpendicular direction of the wave! All points of the wavefront will begin to oscillate in one phase.

To characterize the wave process, the following quantities are introduced:

1. Wave frequencyν is the oscillation frequency of all the particles in the wave.

2. Wave amplitude A is the oscillation amplitude of the particles in the wave.

3. Wave speedυ is the distance over which the wave process (perturbation) propagates per unit time.

Please note that the speed of the wave and the speed of oscillation of the particles in the wave are different concepts! The speed of a wave depends on two factors: the type of wave and the medium in which the wave propagates.

The general pattern is as follows: the speed of a longitudinal wave in a solid is greater than in liquids, and the speed in liquids, in turn, is greater than the speed of a wave in gases.

It is not difficult to understand the physical reason for this regularity. The cause of wave propagation is the interaction of molecules. Naturally, the perturbation propagates faster in the medium where the interaction of molecules is stronger.

In the same medium, the regularity is different - the speed of the longitudinal wave is greater than the speed of the transverse wave.

For example, the speed of a longitudinal wave in a solid, where E is the elastic modulus (Young's modulus) of the substance, ρ is the density of the substance.

Shear wave velocity in a solid, where N is the shear modulus. Since for all substances , then . One of the methods for determining the distance to the source of an earthquake is based on the difference in the velocities of longitudinal and transverse seismic waves.

The speed of a transverse wave in a stretched cord or string is determined by the tension force F and the mass per unit length μ:

4. Wavelength λ - minimum distance between points that oscillate equally.

For waves traveling on the surface of water, the wavelength is easily defined as the distance between two adjacent humps or adjacent depressions.

For a longitudinal wave, the wavelength can be found as the distance between two adjacent concentrations or rarefactions.

5. In the process of wave propagation, sections of the medium are involved in an oscillatory process. An oscillating medium, firstly, moves, therefore, it has kinetic energy. Secondly, the medium through which the wave runs is deformed, therefore, it has potential energy. It is easy to see that wave propagation is associated with the transfer of energy to unexcited parts of the medium. To characterize the energy transfer process, we introduce wave intensity I.

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 water or vibrations earth's crust propagating from the epicenter of the 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.

Create mechanical waves

Let's get pretty long rope, one end of which is attached to vertical surface, and we will move the second one 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.

Transfer of energy without transfer of matter - the most important property 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:

	Physical quantities characterizing oscillations
	Oscillation frequency ν	Oscillation period T	Oscillation amplitude A
Define	number of oscillations per unit of time	time of one oscillation	the maximum distance a point deviates from its equilibrium position
Formula to determine
	N is the number of oscillations per time interval t
Unit in SI		second (s)

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, a wave propagated in the earth's crust 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 this moment time points A, B and C of the cord move; 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.

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 perturbation (oscillation) propagating in an 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 in liquids, both transverse and longitudinal waves can propagate simultaneously, tk. 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 oscillations, 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 IN, 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 under normal conditions is 340, in water 1500, and in steel 6000.

average speed thermal motion molecules in gases decreases with decreasing temperature and, as a consequence, the velocity 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 ABOUT(Fig.93) Let at the moment of time t the front had the shape of a circle of radius R centered on a point ABOUT. 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 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 ​​the 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.

but) . 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 propagation waves.

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 slot passes the oscillations 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. Bat oriented in space with the help of ultrasound.

32. infrasound– sound with a frequency below 20 Hz. These sounds are perceived by some animals. Their source is often vibrations of the 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).