Angles of incidence and reflection of sound from a person. sound reflection

The sound pressure p depends on the speed v of the oscillating particles of the medium. Calculations show that

where p is the density of the medium, c is the speed of the sound wave in the medium. The product pc is called the specific acoustic impedance, for a plane wave it is also called the wave impedance.

Wave resistance is the most important characteristic of a medium, which determines the conditions for reflection and refraction of waves at its boundary.

Imagine that a sound wave hits the interface between two media. Part of the wave is reflected, and part is refracted. The laws of reflection and refraction of a sound wave are similar to the laws of reflection and refraction of light. The refracted wave can be absorbed in the second medium, or it can leave it.

Let us assume that a plane wave is incident normally to the interface, its intensity in the first medium I 1 is the intensity of the refracted (transmitted) wave in the second medium 1 2 . Let's call

sound wave penetration coefficient.

Rayleigh showed that the sound penetration coefficient is given by

If the wave resistance of the second medium is very large compared to the wave resistance of the first medium (с 2 р 2 >> с 1 ρ 1), then instead of (6.7) we have

since с 1 ρ 1 /с 2 р 2 >>1. Let us present the wave resistances of some substances at 20 °C (Table 14).

Table 14

We use (6.8) to calculate the coefficient of penetration of a sound wave from air into concrete and into water:

These data are impressive: it turns out that only a very small part of the energy of the sound wave passes from air to concrete and water.

In any closed room, sound reflected from walls, ceilings, furniture falls on other walls, floors, etc., is again reflected and absorbed, and gradually fades away. Therefore, even after the sound source has ceased, there are still sound waves in the room that create the hum. This is especially noticeable in large spacious halls. The process of gradual attenuation of sound in enclosed spaces after the source is turned off is called reverberation.

Reverberation, on the one hand, is useful, since the perception of sound is enhanced by the energy of the reflected wave, but, on the other hand, excessively long reverberation can significantly impair the perception of speech and music, since each new part of the text overlaps with the previous ones. In this regard, some optimal reverberation time is usually indicated, which is taken into account when building auditoriums, theater and concert halls, etc. For example, the reverberation time of the filled Column Hall in the House of Unions in Moscow is 1.70 s, filled in the Bolshoi Theater - 1, 55 p. For these rooms (empty), the reverberation time is 4.55 and 2.06 s, respectively.

The physics of hearing

Let's consider some questions of the physics of hearing on the example of the outer, middle and inner ear. The outer ear consists of the auricle 1 and the external auditory canal 2 (Fig. 6.8). The auricle in humans does not play a significant role in hearing. It helps to determine the localization of the sound source when it is located in the anterior-posterior direction. Let's explain this. The sound from the source enters the auricle. Depending on the position of the source in the vertical plane

(Fig. 6.9) sound waves will diffract differently on the auricle due to its specific shape. This will also lead to a change in the spectral composition of the sound wave entering the auditory canal (for more details on diffraction issues, see Chapter 19). As a result of experience, a person has learned to associate a change in the spectrum of a sound wave with the direction to the sound source (directions A, B and B in Fig. 6.9).

Having two sound receivers (ears), man and animals are able to set the direction to the sound source and in the horizontal plane (binaural effect; Fig. 6.10). This is due to the fact that the sound from the source to different ears travels different distances and there is a phase difference for the waves that enter the right and left auricles. The relationship between the difference between these distances (5) and the phase difference (∆φ) is derived in § 19.1 when explaining the interference of light [see. (19.9)]. If the sound source is directly in front of the person's face, then δ = 0 and ∆φ = 0, if the sound source is located on the side against one of the auricles, then it will fall into the other auricle with a delay. We will assume approximately that in this case 5 is the distance between the auricles. According to formula (19.9), for v = 1 kHz and δ = 0.15 m, the phase difference can be calculated. It is approximately 180°.

Different directions to the sound source in the horizontal plane will correspond to a phase difference between 0° and 180° (for the above data). It is believed that a person with normal hearing can fix directions to a sound source with an accuracy of 3 °, this corresponds to a phase difference of 6 °. Therefore, it can be assumed that a person is able to distinguish the change in the phase difference of sound waves entering his ears with an accuracy of 6 °.

In addition to the phase difference, the binaural effect is facilitated by the difference in sound intensities in different ears, as well as the "acoustic shadow" from the head for one ear. On fig. 6.10 schematically shows that the sound from the source enters the left

ear as a result of diffraction (ch. 19).

The sound wave passes through the ear canal and is partially reflected from the tympanic membrane 3 (see Fig. 6.8). As a result of the interference of the incident and reflected waves, acoustic resonance can occur. In this case, the wavelength is four times the length of the external auditory canal. The human ear canal is approximately 2.3 cm long; therefore, acoustic resonance occurs at a frequency

The most essential part of the middle ear is the tympanic membrane 3 and the auditory ossicles: the malleus 4, the anvil 5 and the stirrup 6 with the corresponding muscles, tendons and ligaments. Bones carry out the transmission of mechanical vibrations from the air environment of the outer ear to the liquid environment of the inner ear. The liquid medium of the inner ear has a wave resistance approximately equal to the wave resistance of water. As has been shown (see § 6.4), only 0.123% of the incident intensity is transmitted in the direct transition of a sound wave from air to water. This is too little. Therefore, the main purpose of the middle ear is to facilitate the transmission of greater sound intensity to the inner ear. In technical terms, the middle ear matches the impedances of the air and fluid in the inner ear.

The ossicle system (see Fig. 6.8) at one end is connected with the tympanic membrane with a hammer (area S 1 = 64 mm 2), at the other - with a stirrup - with an oval window 7 of the inner ear (area S 2 = 3 mm 2).

At the same time, a force F 2 acts on the oval window of the inner ear, creating Sound pressure p 2 in a liquid medium. The connection between them:
Dividing (6.9) by (6.10) and comparing this relation with (6.11), we obtain

where

or in logarithmic units (see § 1.1)

At this level, the middle ear increases the transmission of external sound pressure to the inner ear.

Another of the functions of the middle ear is the weakening of the transmission of vibrations in the case of a sound of great intensity. This is done by reflex relaxation of the muscles of the ossicles of the middle ear.

The middle ear is connected to the atmosphere through the auditory (Eustachian) tube.

The outer and middle ear are part of the sound-conducting system. The sound-receiving system is the inner ear.

The main part of the inner ear is the cochlea, which converts mechanical vibrations into an electrical signal. In addition to the cochlea, the vestibular apparatus belongs to the inner ear (see § 4.3), which has nothing to do with the auditory function.

The human cochlea is a bony formation about 35 mm long and has the shape of a cone-shaped spiral with 2 3/4 whorls. The diameter at the base is about 9 mm, the height is about 5 mm.

On fig. 6.8 the cochlea (limited by a dashed line) is shown schematically expanded for ease of viewing. Three canals run along the cochlea. One of them, which starts from the oval window 7, is called the vestibular scala 8. The other channel comes from the round window 9, it is called the scala tympani 10. The vestibular and tympanic scala are connected in the dome of the cochlea through a small hole - helicotrema 11. Thus, both these channels in some way represent a single system filled with perilymph. The vibrations of the stirrup 6 are transmitted to the membrane of the oval window 7, from it to the perilymph and "protrude" the membrane of the round window 9. The space between the vestibular and tympanic scala is called the cochlear canal 12, it is filled with endolymph. Between the cochlear canal and the scala tympani, the main (basilar) membrane 13 passes along the cochlea. Corti's organ containing receptor (hair) cells is located on it, and the auditory nerve comes from the cochlea (these details are not shown in Fig. 6.8).

The organ of Corti (spiral organ) is the converter of mechanical vibrations into an electrical signal.

The length of the main membrane is about 32 mm, it expands and thins in the direction from the oval window to the top of the cochlea (from a width of 0.1 to 0.5 mm). The main membrane is a very interesting structure for physics, it has frequency-selective properties. Helmholtz drew attention to this,

represented the main membrane in a similar way to a series of tuned piano strings. The Nobel Prize winner Bekesy established the fallacy of this resonator theory. In the works of Bekesy it was shown that the main membrane is an inhomogeneous line, the transmission of mechanical excitation. When exposed to an acoustic stimulus, a wave propagates along the main membrane. This wave is attenuated differently depending on the frequency. The lower the frequency, the farther away from the oval window the wave propagates along the main membrane before it begins to decay. So, for example, a wave with a frequency of 300 Hz will propagate up to approximately 25 mm from the oval window before attenuation begins, and a wave with a frequency of 100 Hz reaches its maximum near 30 mm. Based on these observations, theories have been developed according to which the perception of pitch is determined by the position of the maximum oscillation of the main membrane. Thus, a certain functional chain can be traced in the inner ear: oscillation of the oval window membrane - oscillation of the perilymph - complex oscillations of the main membrane - complex oscillations of the main membrane - irritation of the hair cells (receptors of the organ of Corti) - generation of an electrical signal.

Some forms of deafness are associated with damage to the receptor apparatus of the cochlea. In this case, the cochlea does not generate electrical signals when subjected to mechanical vibrations. It is possible to help such deaf people by implanting electrodes in the cochlea and giving them electrical signals corresponding to those that arise when exposed to a mechanical stimulus.

Such prosthetics of the main function, the cochlea (cochlear prosthesis) are being developed in a number of countries. In Russia, cochlear prosthetics was developed and implemented at the Russian Medical University. The cochlear prosthesis is shown in Fig. 6.12, here 1 is the main body, 2 is an ear with a microphone, 3 is a plug of the electrical connector for connecting to implantable electrodes.

Each of you is familiar with such a sound phenomenon as an echo. The echo is formed as a result of the reflection of sound from various obstacles - the walls of a large empty room, a forest, the vaults of a high arch in a building.

An echo is heard only when the reflected sound is perceived separately from the spoken one. To do this, it is necessary that the time interval between the impact of these two sounds on the eardrum is at least 0.06 s.

Let's determine how long after you uttered a short exclamation, the sound reflected from the wall will reach your ear if you are standing at a distance of 3 m from this wall.

The sound must travel the distance to the wall and back, i.e. 6 m, propagating at a speed of 340 m/s. This will take time t = s/v, i.e. t \u003d 6m / 340m / s \u003d 0.02 s.

The interval between the two sounds you perceive - spoken and reflected - is much less than what is needed to hear the echo. In addition, the formation of an echo in the room is prevented by the furniture, curtains and other objects located in it, which partially absorb the reflected sound. Therefore, in such a room, the speech of people and other sounds are not distorted by the echo and sound clearly and legibly.

Large, semi-empty rooms with smooth walls, floors, and ceilings tend to reflect sound waves very well. In such a room, due to the incursion of the previous sound waves onto the subsequent ones, an overlay of sounds is obtained, and a rumble is formed. To improve the sound properties of large halls and auditoriums, their walls are often lined with sound-absorbing materials.

The action of a horn is based on the property of sound to be reflected from smooth surfaces - an expanding pipe, usually of a round or rectangular cross section. When using a horn, sound waves do not scatter in all directions, but form a narrow beam, due to which the sound power increases and it spreads over a greater distance.

A few famous multiple echoes: at Woodstock Castle in England, the echo clearly repeats 17 syllables. The ruins of Derenburg Castle near Halberstadt gave a 27-syllable echo, which, however, was silent since one wall was blown up. The rocks, spread out in the form of a circle near Adersbach in Czechoslovakia, repeat in a certain place, three times 7 syllables; but a few steps from this point, even the sound of a gunshot does not give any echo. A very multiple echo was observed in one (now defunct) castle near Milan: a shot fired from an outbuilding window was echoed 40-50 times, and a loud word - 30 times ... In a particular case, the echo is the concentration of sound by reflecting it from concave curved surfaces. So, if the sound source is placed in one of the two foci of the ellipsoidal vault, then the sound waves are collected in its other focus. This explains, for example, the famous " ear of Dionysus"in Syracuse - a grotto or recess in the wall, from which every word uttered by the prisoners in it could be heard in some place remote from it. One church in Sicily had a similar acoustic property, where in a certain place one could hear whispered words in Also known in this regard are the Mormon temple at the Salt Lake in America and the grottoes in the Oliva monastery park near Danzig. In Olympia (Greece) in the temple of Zeus, the "Porch of Echo" has survived to this day. In it, the voice is repeated 5 ... 7 times. In In Siberia, there is an amazing place on the Lena River north of Kirensk.The relief of the rocky shores there is such that the echo of the horns of motor ships going along the river can be repeated up to 10 or even 20 times (under favorable weather conditions).Such an echo is sometimes perceived as a gradually fading sound, and sometimes as sound fluttering from various directions.Multiple echoes can also be heard on Lake Teletskoye in the Altai Mountains.This lake is 80 km long and only a few kilometers trov in width; its banks are high and steep, covered with forests. A shot from a gun or a sharp loud cry generates here up to 10 echo signals that sound for 10 ... 15 s. It is curious that often sound responses appear to the observer as coming from somewhere above, as if the echo were picked up by coastal heights.

Depending on the terrain, the location and orientation of the observer, weather conditions, time of year and day, the echo changes its volume, timbre, and duration; the number of iterations changes. In addition, the frequency of the audio response may also change; it may turn out to be higher or, conversely, lower than the frequency of the original audio signal.

It is not so easy to find a place where the echo is clearly audible even once. In Russia, however, it is relatively easy to find such places. There are many plains surrounded by forests, many clearings in the forests; it is worth shouting loudly in such a clearing so that a more or less distinct echo comes from the wall of the forest.

Definition 1

Echo- a physical phenomenon, which consists in the acceptance by the observer of a wave reflected from obstacles (electromagnetic, sound, etc.)

An echo is the same reflection, only the mirror reflects light, and in the case of an echo, sound. Any obstacle can become a mirror for sound. The sharper, more abrupt the sound, the more distinct the echo. The best way to evoke an echo is by clapping your hands. A low male voice is reflected poorly, and a high voice gives a distinct echo.

Echoes can be heard if the sound is made on the spot, surrounded by hills or large buildings.

acoustic phenomenon

Acoustic waves bounce off walls and other hard surfaces such as mountains. When sound travels through a medium that does not have constant physical properties, it can be refracted.

Figure 1. Explanation of how echo works

The human ear cannot distinguish the echo from the original sound if the delay is less than $1/15$ of a second.

Echo strength is often measured in dB sound pressure levels (SPL) relative to the transmitted wave itself. Echoes can be desirable (as in sonar) or undesirable (such as in telephone systems).

The reflection of sound waves from surfaces also depends on the shape of the surface. Flat surfaces reflect sound waves, such that the angle at which the wave approaches the surface is equal to the angle at which the wave leaves the surface.

Reflection of sound waves from curved surfaces leads to a more interesting phenomenon. Curved surfaces with a parabolic shape have a habit of focusing sound waves to a point. Sound waves reflected from parabolic surfaces concentrate all their energy at one point in space; at this point, the sound is amplified. Scientists have long believed that owls have spherical disks on their faces that can be used to collect and reflect sound.

Using sound reflection

The speed of sound in water is different than in air. Consider the operation of the echo sounder. It makes a sharp sound, which, passing through the water column, reaches the bottom of the sea, is reflected and runs back in the form of an echo. The echo sounder catches it and calculates the distance to the bottom of the sea.

Figure 2. Echo sounder operation

Sound reflection is used in many devices. For example, loudspeaker, horn, stethoscope, hearing aid, etc.

The stethoscope is used to hear the sounds of the patient's internal organs; for diagnostic purposes. It works according to the laws of sound reflection.

Bats use high frequency (short wavelength) ultrasonic waves to enhance their ability to hunt. A typical bat prey is the moth, an object not much larger than the bat itself. Bats use ultrasonic echolocation techniques to locate their relatives in the air. But why ultrasound? The answer to this question lies in the physics of diffraction. As the wavelength becomes shorter than the obstacle it encounters, the wave is no longer able to dissipate around it and is therefore reflected. Bats use ultrasonic waves with wavelengths smaller than the size of their prey. These sound waves will collide with the prey, and instead of being diffracted around the prey, they will bounce off the prey, allowing the mouse to hunt with echolocation.

If a sound wave encounters no obstacles in its path, it propagates uniformly in all directions. But not every obstacle becomes an obstacle for her.

Having met an obstacle in its path, the sound can bend around it, be reflected, refracted or absorbed.

sound diffraction

We can talk to a person standing around the corner of a building, behind a tree, or behind a fence, although we cannot see him. We hear it because the sound is able to bend around these objects and penetrate into the area behind them.

The ability of a wave to go around an obstacle is called diffraction .

Diffraction is possible when the wavelength of the sound wave exceeds the size of the obstacle. Low frequency sound waves are quite long. For example, at a frequency of 100 Hz, it is 3.37 m. As the frequency decreases, the length becomes even longer. Therefore, a sound wave easily bends around objects commensurate with it. The trees in the park do not prevent us from hearing the sound at all, because the diameters of their trunks are much smaller than the wavelength of the sound wave.

Due to diffraction, sound waves penetrate through gaps and holes in an obstacle and propagate behind them.

Let us place a flat screen with a hole in the path of the sound wave.

When the sound wave length ƛ much larger than the hole diameter D , or these values ​​are approximately equal, then behind the hole the sound will reach all points of the area that is behind the screen (the area of ​​​​sound shadow). The outgoing wave front will look like a hemisphere.

If ƛ only slightly smaller than the slot diameter, then the main part of the wave propagates directly, and a small part diverges slightly to the sides. And in the case when ƛ much less D , the whole wave will go in the forward direction.

sound reflection

In the case of a sound wave hitting the interface between two media, various options for its further propagation are possible. The sound can be reflected from the interface, it can go to another medium without changing direction, or it can be refracted, that is, go, changing its direction.

Let's suppose that an obstacle has appeared in the path of the sound wave, the size of which is much larger than the wavelength, for example, a sheer cliff. How will the sound behave? Since it cannot go around this obstacle, it will be reflected from it. Behind the obstacle is acoustic shadow zone .

Sound reflected from an obstacle is called echo .

The nature of the reflection of the sound wave can be different. It depends on the shape of the reflective surface.

reflection called a change in the direction of a sound wave at the interface between two different media. When reflected, the wave returns to the medium from which it came.

If the surface is flat, the sound is reflected from it in the same way as a ray of light is reflected in a mirror.

Sound rays reflected from a concave surface are focused at one point.

The convex surface dissipates sound.

The effect of dispersion is given by convex columns, large moldings, chandeliers, etc.

Sound does not pass from one medium to another, but is reflected from it if the densities of the media differ significantly. So, the sound that appeared in the water does not pass into the air. Reflected from the interface, it remains in the water. A person standing on the river bank will not hear this sound. This is due to the large difference in wave resistance of water and air. In acoustics, wave resistance is equal to the product of the density of the medium and the speed of sound in it. Since the wave resistance of gases is much less than the wave resistance of liquids and solids, when it hits the border of air and water, the sound wave is reflected.

Fish in the water do not hear the sound that appears above the surface of the water, but they clearly distinguish the sound, the source of which is a body vibrating in the water.

refraction of sound

Changing the direction of sound propagation is called refraction . This phenomenon occurs when sound passes from one medium to another, and the speed of its propagation in these media is different.

The ratio of the sine of the angle of incidence to the sine of the angle of reflection is equal to the ratio of the speeds of sound propagation in media.

where i - angle of incidence,

r is the angle of reflection,

v1 is the speed of sound propagation in the first medium,

v2 is the speed of sound propagation in the second medium,

n is the index of refraction.

The refraction of sound is called refraction .

If the sound wave does not fall perpendicular to the surface, but at an angle other than 90°, then the refracted wave will deviate from the direction of the incident wave.

Sound refraction can be observed not only at the interface between media. Sound waves can change their direction in an inhomogeneous medium - the atmosphere, the ocean.

In the atmosphere, refraction is caused by changes in air temperature, the speed and direction of movement of air masses. And in the ocean, it appears due to the heterogeneity of the properties of water - different hydrostatic pressure at different depths, different temperatures and different salinities.

sound absorption

When a sound wave hits a surface, some of its energy is absorbed. And how much energy a medium can absorb can be determined by knowing the sound absorption coefficient. This coefficient shows what part of the energy of sound vibrations is absorbed by 1 m 2 of the obstacle. It has a value from 0 to 1.

The unit of measure for sound absorption is called sabin . It got its name from the American physicist Wallace Clement Sabin, founder of architectural acoustics. 1 sabin is the energy that is absorbed by 1 m 2 of the surface, the absorption coefficient of which is 1. That is, such a surface must absorb absolutely all the energy of the sound wave.

Reverberation

Wallace Sabin

The property of materials to absorb sound is widely used in architecture. While researching the acoustics of the Lecture Hall, part of the Fogg Museum, Wallace Clement Sabin came to the conclusion that there is a relationship between the size of the hall, the acoustic conditions, the type and area of ​​sound-absorbing materials, and reverberation time .

Reverb called the process of reflection of a sound wave from obstacles and its gradual attenuation after turning off the sound source. In an enclosed space, sound can bounce off walls and objects multiple times. As a result, various echo signals appear, each of which sounds as if apart. This effect is called reverb effect .

The most important feature of a room is reverberation time , which was introduced and calculated by Sabin.

where V - the volume of the room,

BUT – general sound absorption.

where a i is the sound absorption coefficient of the material,

Si is the area of ​​each surface.

If the reverberation time is long, the sounds seem to "roam" around the room. They overlap each other, drown out the main source of sound, and the hall becomes booming. With a short reverberation time, the walls quickly absorb sounds, and they become deaf. Therefore, each room must have its own exact calculation.

Based on the results of his calculations, Sabin arranged the sound-absorbing materials in such a way that the "echo effect" was reduced. And the Boston Symphony Hall, on which he was an acoustic consultant, is still considered one of the finest halls in the world.

As in any wave process, when sound waves fall on an obstacle of limited size, in addition to interference, their reflection is observed (Fig. 1.10). In this case, the angles of incidence and reflection are equal to each other. Therefore, flat and convex surfaces scatter sound (Fig. 1.10 a, b and c.), while concave ones focus it and concentrate it at a certain point (Fig. 1.10 d).

Fig. 1.10 Reflection of sound waves from surfaces of various shapes

When waves fall on the boundary of two media (Fig. 1.11), part of the sound energy is reflected, and part passes into the second medium.

Rice. 1.11 Reflection and propagation of waves at the boundary of two media

According to the law of conservation of energy, the sum of the elapsed E past. and reflected E neg. energy is equal to the energy of the incident wave E pad, , i.e.

Epad \u003d Eotr. + Eprosh.

(1.59)

Divide the right and left sides of the formula by E pad .

1 = (E neg./ Epad) +(Eprosh / Epad)

The terms in the above ratio show what proportion of the incident energy was reflected, and what proportion passed on. They are the reflection and transmission coefficients. Introducing for them the notation η and τ, respectively, we obtain

Figure 1.12 shows the change in the reflection and transmission coefficients depending on the ratio of the acoustic impedances of the adjacent media. It can be seen from the graph that the value of the coefficients depends only on the absolute

the absolute value of the ratios of the acoustic impedances of the media, but does not depend on which of these impedances is greater. This can explain the fact that sound propagating in any massive wall undergoes the same reflection from the interface with the air medium as sound propagating in air when reflected from this wall.

Rice. 1.12. Odds η and τ depending on the ratio of acoustic impedances of the adjacent media (Z 1 /Z 2)

In a number of cases, it is of interest to know how the sound pressure or vibrational velocity of particles will change when passing through the boundary of two media. Since the intensity of sound energy is proportional to the squares of sound pressure and vibration velocity, it is obvious that the reflection coefficient for pressure and velocity can be found by the formula

The above formulas for the reflection and transmission coefficients can be used in the calculations of one-dimensional sound guides when their cross section changes (Fig. 1.13), if the cross-sectional area S1 and S2 not too different. At

Fig.1.13. Changing the sections of the sound guide

Sound absorption

Sound absorption (damping, dissipation) - the transformation of sound energy into heat. It is caused both by thermal conductivity and viscosity (classical absorption) and by intramolecular reflection. At very large amplitudes, which occur only near very powerful sound sources or during supersonic impact, nonlinear processes occur, leading to distortion of the waveform and to enhanced absorption.

For sound in gases and liquids, absorption is of practical importance only when the sound propagates over long distances (at least several hundred wavelengths) or when bodies with a very large surface are encountered in the path of the sound.

Consider the process of sound passing through an obstacle (Fig. 1.14). Incident sound energy E pad . is divided into the energy reflected from the obstacle E neg absorbed in it E absorb and the energy passed through the obstacles

According to the law of conservation of energy

Fig.1.14. Distribution of energy during the incidence of sound on an obstacle.

This process can be estimated by the ratios of the transmitted, absorbed and reflected energies to the energy incident on the obstacle:

τ = E past. / E pad; η = E neg. / E pad; α = E absorb. / E pad; (1.67)

As mentioned above, the first two ratios are called transmission coefficients τ and reflections η . The third coefficient characterizes the share of absorbed energy and is called the absorption coefficient α. Obviously, from (1.66) it follows

α + η + τ = 1

(1.68)

Sound absorption is due to the transition of vibrational energy into heat due to frictional losses in the material. Friction losses are high in porous and loose fibrous materials. Structures made of such materials reduce the intensity of sound waves reflected from the surface. Sound absorbers located inside the room can also reduce the intensity of direct sound if they are located in the path of sound waves.

Resonators.

The so-called resonator can serve as an effective absorber of sound waves, and in some cases their amplifier. Under the pony resonator

a system of the "mass-spring" type is being developed, in which the role of the oscillating mass is played by the mass of air in a narrow hole or in the slot of the plate, and the role of the spring

is the elastic volume of air in the cavity behind the plate. A schematic representation of the Helmholtz resonator is shown in Fig. 1.15

Rice. 1.15. Helmholtz resonator

Consider the simplest air resonator, i.e. a vessel with rigid walls and a narrow neck. When a sound wave of a certain frequency falls on it, the air "plug" in the throat of the vessel comes into intense oscillatory motion. The vibrational speed of particles in the throat is several times higher than the vibrational speed in a free sound field. ξ . In the internal volume of the resonator at this time, the pressure correspondingly increases R . If you bring a tube to the inner cavity of the resonator, then the perceived sound will be louder.

At the same time, with sufficiently large friction losses, the resonator can act not as an amplifier, but as an absorber of sound energy. If a layer of sound-absorbing material is introduced into the throat of the resonator, the absorption will noticeably increase.

Natural circular frequency o with mass m on a spring with stiffness s can be found by the well-known formula

edits, the value of which depends on the shape of the neck and the area of ​​​​its cross-section. Thus, the natural frequency of the resonator is defined as

fo=	s o			S	(1.72)
2π			V( l+l i+lα)

In such resonant systems, in the presence of an external sound source, the air enclosed in the cavity oscillates with it in unison with an amplitude that depends on the ratio between the values ​​of the periods of natural and forced oscillations. When the source is turned off, the resonator gives back the oscillations accumulated inside it, becoming for a short time a secondary source.

Depending on the characteristics, the resonator can either amplify or absorb sound vibrations at a particular frequency.

The sound absorption of the resonator is described using the conditional characteristic sound-absorbing section A . It is understood as a conditional cross-sectional area perpendicular to the direction of propagation of the incident wave, through which a free wave (in the absence of a resonator) transmits power equal to that absorbed by the resonator.

Let us assume that the dimensions of the resonator are small compared to the length of the incident wave. Then, in the first approximation, we can neglect the scattering of sound energy on the resonator case. If we take the resonator hole closed acoustically rigidly, then the sound pressure in the neck p h = p l , and the vibrational speed υ = p h / Z h (if the resonator is on the screen, then the multiplier will be added in the above formulas 2 ).

The resonator neck impedance is the sum of the internal losses R i , active radiation resistance R r and reactances of mass and elasticity.

2. INDUSTRIAL ACOUSTIC