School Encyclopedia. Laws of propagation of sound waves

Sound is understood as elastic waves lying within the limits of audibility of the human ear, in the range of oscillations from 16 Hz up to 20 kHz. Oscillations with a frequency below 16 Hz called infrasound, over 20 kHz-ultrasound.

Water is denser and less compressible than air. In this regard, the speed of sound in water is four and a half times greater than in air, and is 1440 m/sec. Sound vibration frequency (nude) is related to the wavelength (lambda) by the relation: c= lambda-nu. Sound propagates in water without dispersion. The speed of sound in water varies depending on two parameters: density and temperature. A change in temperature by 1° entails a corresponding change in the speed of sound by 3.58 m per second. If we follow the speed of sound propagation from the surface to the bottom, it turns out that at first, due to a decrease in temperature, it quickly decreases, reaching a minimum at a certain depth, and then, with depth, it begins to increase rapidly due to an increase in water pressure, which, as is known, increases by approximately 1 atm for every 10 m depths.

Starting from a depth of approximately 1200 m, where the temperature of the water remains practically constant, the change in the speed of sound is due to the change in pressure. “At a depth of approximately 1200 m (for the Atlantic), there is a minimum value for the speed of sound; at greater depths, due to the increase in pressure, the speed of sound increases again. Since sound rays are always bent towards the areas of the medium where their speed is the lowest, they are concentrated in the layer with the minimum speed of sound” (Krasilnikov, 1954). This layer, discovered by Soviet physicists L.D. Rozenberg and L.M. Brekhovskikh, is called the "underwater sound channel". Sound entering the sound channel can propagate over long distances without attenuation. This feature must be kept in mind when considering the acoustic signaling of deep-sea fish.

Sound absorption in water is 1000 times less than in air. Sound source in the air with a power of 100 kW in the water can be heard at a distance of up to 15 km; sound source in water 1 kW heard at a distance of 30-40 km. Sounds of different frequencies are absorbed differently: high-frequency sounds are most strongly absorbed and low-frequency sounds are the least absorbed. The low absorption of sound in water made it possible to use it for sonar and signaling. Water spaces are filled with a large number of different sounds. The sounds of water bodies of the World Ocean, as shown by the American hydroacousticist Wenz (Wenz, 1962), arise in connection with the following factors: tides, currents, wind, earthquakes and tsunamis, industrial human activity and biological life. The nature of the noise created by various factors differs both in the set of sound frequencies and in their intensity. On fig. Figure 2 shows the dependence of the spectrum and pressure level of the sounds of the World Ocean on the factors that cause them.

In different parts of the World Ocean, the composition of noise is determined by different components. Big influence at the same time, the composition of sounds is affected by the bottom and shores.

Thus, the composition and intensity of noise in different parts of the World Ocean are extremely diverse. There are empirical formulas that show the dependence of the intensity of sea noise on the intensity of the factors that cause them. However, in practical purposes Ocean noise is usually measured empirically.

It should be noted that among the sounds of the World Ocean, industrial sounds created by man are the most intense: the noise of ships, trawls, etc. According to Shane (1964), they are 10-100 times more intense than other sounds of the World Ocean. However, as can be seen from Fig. 2, their spectral composition is somewhat different from the spectral composition of sounds caused by other factors.

When propagating in water, sound waves can be reflected, refracted, absorbed, diffracted, and interfered.

Encountering an obstacle on its way, sound waves can be reflected from it in the case when their wavelength (lambda) less than the size of the obstacle, or go around (diffract) it in the case when their wavelength is greater than the obstacle. In this case, one can hear what is happening behind the obstacle without seeing the source directly. Falling on an obstacle, sound waves in one case can be reflected, in another case they can penetrate into it (be absorbed by it). The value of the energy of the reflected wave depends on how strongly the so-called acoustic impedances of the media “p1c1” and “p2c2” differ from each other, on the interface of which sound waves fall. Under the acoustic resistance of the medium is meant the product of the density of the given medium p and the speed of sound propagation With in her. How more difference acoustic impedance of media, the most of energy will be reflected from the separation of two media, and vice versa. In the case of, for example, sound falling from the air, rs which 41, into the water, rs which is 150,000, it is reflected according to the formula:

In connection with the above, sound penetrates much better into a solid body from water than from air. From air to water, sound penetrates well through bushes or reeds protruding above the water surface.

In connection with the reflection of sound from obstacles and its wave nature, the addition or subtraction of the amplitudes of sound pressures of the same frequencies that have come to a given point in space can occur. An important consequence of such addition (interference) is the formation of standing waves upon reflection. If, for example, a tuning fork is brought into oscillation, bringing it closer and further away from the wall, one can hear the increase and decrease in the sound volume due to the appearance of antinodes and nodes in the sound field. Usually standing waves are formed in closed containers: in aquariums, pools, etc. with a relatively long sounding source.

In the real conditions of the sea or other natural reservoir, during the propagation of sound, numerous complex phenomena are observed that arise in connection with the heterogeneity of the aquatic environment. A huge influence on the propagation of sound in natural reservoirs is exerted by the bottom and interfaces (water - air), temperature and salt heterogeneity, hydrostatic pressure, air bubbles and planktonic organisms. The water-air interface and the bottom, as well as the heterogeneity of the water, lead to the phenomena of refraction (curvature of sound rays), or reverberation (multiple reflection of sound rays).

Water bubbles, plankton and other suspended matter contribute to sound absorption in the water. Quantification of these numerous factors has not yet been developed. It is necessary to take them into account when setting up acoustic experiments.

Let us now consider the phenomena that occur in water when sound is emitted in it.

Imagine a sound source as a pulsating sphere in infinite space. The acoustic energy emitted by such a source is attenuated inversely with the square of the distance from its center.

The energy of the resulting sound waves can be characterized by three parameters: speed, pressure and displacement of oscillating water particles. The last two parameters are of particular interest when considering the auditory abilities of fish, so we will dwell on them in more detail.

According to Harris and Bergeldzhik (Harris a. Berglijk, 1962), pressure wave propagation and displacement effects are presented differently in the near (at a distance of less than one wavelength of sound) and far (at a distance of more than one wavelength of sound) acoustic field.

In the far acoustic field, the pressure attenuates inversely with the distance from the sound source. In this case, in the far acoustic field, the displacement amplitudes are directly proportional to the pressure amplitudes and are interconnected by the formula:

where R - acoustic pressure in dynes/cm 2 ;

d- particle displacement value in cm.

In the near acoustic field, the dependence between the pressure and displacement amplitudes is different:

where R-acoustic pressure in dynes/cm 2 ;

d - displacement of water particles in cm;

f - oscillation frequency in hz;

rs- acoustic resistance of water equal to 150,000 g/cm2 sec 2 ;

lambda is the wavelength of sound in m; r - distance from the center of the pulsating sphere;

i= SQR i

It can be seen from the formula that the displacement amplitude in the near acoustic field depends on the wavelength, sound, and distance from the sound source.

At distances smaller than the wavelength of the sound in question, the displacement amplitude decreases inversely with the square of the distance:

where BUT is the radius of the pulsating sphere;

D- increase in the radius of the sphere due to pulsation; r is the distance from the center of the sphere.

Fish, as will be shown below, have two different types of receivers. Some of them perceive pressure, while others perceive the displacement of water particles. The above equations are therefore great importance for the correct assessment of fish responses to underwater sound sources.

In connection with the emission of sound, we note two more phenomena associated with emitters: the phenomenon of resonance and directivity of emitters.

The emission of sound by the body occurs in connection with its vibrations. Each body has its own oscillation frequency, determined by the size of the body and its elastic properties. If such a body is brought into oscillation, the frequency of which coincides with its own frequency, the phenomenon of a significant increase in the amplitude of the oscillation occurs - resonance. The use of the concept of resonance makes it possible to characterize certain acoustic properties of fish emitters and receivers. Sound radiation into water can be directional or non-directional. In the first case, sound energy propagates predominantly in a certain direction. A graph expressing the spatial distribution of the sound energy of a given sound source is called its directivity diagram. The directivity of the radiation is observed in the case when the diameter of the emitter is much larger than the wavelength of the emitted sound.

In the case of omnidirectional radiation, sound energy diverges uniformly in all directions. This phenomenon occurs when the wavelength of the emitted sound exceeds the diameter of the emitter lambda>2A. The second case is most typical for low-frequency underwater radiators. Typically, the wavelengths of low-frequency sounds are significantly more sizes used underwater emitters. The same phenomenon is typical for fish emitters. In these cases, the radiation patterns of the emitters are absent. In this chapter, only some general physical properties sound in aquatic environment in relation to fish bioacoustics. Some more specific questions of acoustics will be considered in the relevant sections of the book.

In conclusion, let us consider the sound measurement systems used by various authors. Sound can be expressed by its intensity, pressure, or level of pressure.

Sound intensity in absolute units is measured either by a number erg / sec-cm 2, or W / cm 2. At the same time 1 erg/sec=10 -7 Tue.

Sound pressure is measured in bars.

There is a relationship between the intensity and pressure of sound:

which can be used to convert these values ​​from one to another.

No less often, especially when considering the hearing of fish, due to the huge range of threshold values, sound pressure is expressed in relative logarithmic decibel units, db. If the sound pressure of one sound R, and the other R o, then they consider that the first sound is louder than the second by kdb and calculate it according to the formula:

In this case, most researchers take the threshold value of human hearing equal to 0.0002 as the zero reading of the sound pressure P o bar for frequency 1000 Hz.

The advantage of such a system is the possibility of a direct comparison of the hearing of humans and fish, the disadvantage is the difficulty of comparing the results obtained by the sound and hearing of fish.

The actual values ​​of sound pressure created by fish are four to six orders of magnitude higher than the accepted zero level (0.0002 bar), and the threshold levels of hearing of various fish lie both above and below the conditional zero count.

Therefore, for the convenience of comparing the sounds and hearing of fish, American authors (Tavolga and Wodinsky, 1963, etc.) use a different frame of reference.

The sound pressure of 1 bar, which is 74 db higher than previously accepted.

Below is an approximate ratio of both systems.

Actual values ​​according to American system references in the text are marked with an asterisk.

Over long distances, sound energy propagates only along gentle rays, which do not touch the ocean floor all the way. In this case, the limitation imposed by the medium on the range of sound propagation is its absorption in sea ​​water. The main mechanism of absorption is associated with relaxation processes that accompany the violation of the thermodynamic equilibrium between ions and molecules of salts dissolved in water by an acoustic wave. It should be noted that the main role in absorption in a wide range of sound frequencies, magnesium sulphide salt MgSO4 belongs, although in percentage terms its content in sea water is quite small - almost 10 times less than, for example, NaCl rock salt, which nevertheless does not play any noticeable role in sound absorption.

Absorption in sea water, generally speaking, is greater the higher the frequency of the sound. At frequencies from 3-5 to at least 100 kHz, where the above mechanism dominates, the absorption is proportional to the frequency to a power of about 3/2. At lower frequencies, a new absorption mechanism is activated (possibly due to the presence of boron salts in water), which becomes especially noticeable in the range of hundreds of hertz; here, the absorption level is anomalously high and decreases much more slowly with decreasing frequency.

To more clearly imagine the quantitative characteristics of absorption in sea water, we note that due to this effect, sound with a frequency of 100 Hz is attenuated by a factor of 10 on a path of 10 thousand km, and with a frequency of 10 kHz - at a distance of only 10 km (Fig. 2). Thus, only low-frequency sound waves can be used for long-range underwater communications, for long-range detection of underwater obstacles, and the like.

Figure 2 - Distances at which sounds of different frequencies attenuate 10 times when propagating in sea water.

In the region of audible sounds for the frequency range of 20-2000 Hz, the range of propagation under water of sounds of medium intensity reaches 15-20 km, and in the region of ultrasound - 3-5 km.

Based on the values ​​of sound attenuation observed in laboratory conditions in small volumes of water, one would expect much greater ranges. However, in vivo In addition to damping due to the properties of water itself (the so-called viscous damping), its scattering and absorption by various inhomogeneities of the medium also affect.

The refraction of sound, or the curvature of the path of the sound beam, is caused by the heterogeneity of the properties of water, mainly along the vertical, due to three main reasons: changes in hydrostatic pressure with depth, changes in salinity, and changes in temperature due to uneven heating of the water mass by the sun's rays. As a result of the combined action of these causes, the speed of sound propagation, which is about 1450 m / s for fresh water and about 1500 m / s for sea water, changes with depth, and the law of change depends on the season, time of day, depth of the reservoir, and a number of other reasons . Sound rays leaving the source at some angle to the horizon are bent, and the direction of the bend depends on the distribution of sound velocities in the medium. In summer, when the upper layers are warmer than the lower ones, the rays bend down and are mostly reflected from the bottom, losing a significant portion of their energy. On the contrary, in winter, when the lower layers of the water maintain their temperature, while the upper layers cool, the rays bend upward and undergo multiple reflections from the surface of the water, during which much less energy is lost. Therefore, in winter, the sound propagation distance is greater than in summer. Due to refraction, so-called. dead zones, i.e. areas located close to the source in which there is no audibility.

The presence of refraction, however, can lead to an increase in the range of sound propagation - the phenomenon of ultra-long propagation of sounds under water. At some depth below the surface of the water there is a layer in which sound propagates at the lowest speed; above this depth, the speed of sound increases due to an increase in temperature, and below this, due to an increase in hydrostatic pressure with depth. This layer is a kind of underwater sound channel. A beam deviated from the axis of the channel up or down, due to refraction, always tends to get back into it. If a sound source and receiver are placed in this layer, then even sounds of medium intensity (for example, explosions of small charges of 1-2 kg) can be recorded at distances of hundreds and thousands of kilometers. A significant increase in the sound propagation range in the presence of an underwater sound channel can be observed when the sound source and receiver are located not necessarily near the channel axis, but, for example, near the surface. In this case, the rays, refracting downwards, enter the deep layers, where they deviate upwards and come out again to the surface at a distance of several tens of kilometers from the source. Further, the pattern of propagation of rays is repeated, and as a result, a sequence of so-called. secondary illuminated zones, which are usually traced to distances of several hundred km.

The propagation of high-frequency sounds, in particular ultrasounds, when the wavelengths are very small, is influenced by small inhomogeneities that are usually found in natural reservoirs: microorganisms, gas bubbles, etc. These inhomogeneities act in two ways: they absorb and scatter the energy of sound waves. As a result, with an increase in the frequency of sound vibrations, the range of their propagation is reduced. This effect is especially noticeable in the surface layer of water, where there are the most inhomogeneities. Scattering of sound by inhomogeneities, as well as by irregularities in the water surface and the bottom, causes the phenomenon of underwater reverberation that accompanies the sending of a sound pulse: sound waves, reflecting from a combination of inhomogeneities and merging, give a tightening of the sound pulse, which continues after its end, similar to reverberation observed in enclosed spaces. Underwater reverberation is a rather significant interference for a number of practical applications of hydroacoustics, in particular for sonar.

The limits of the propagation range of underwater sounds are also limited by the so-called. own noises of the sea, which have a twofold origin. Part of the noise arises from the impact of waves on the surface of the water, from the surf, from the noise of rolling pebbles, etc. The other part is related to the marine fauna; this includes sounds produced by fish and other marine animals.

We perceive sounds at a distance from their sources. Sound usually travels to us through the air. Air is an elastic medium that transmits sound.

Pay attention!

If the sound transmission medium is removed between the source and the receiver, then the sound will not propagate and, therefore, the receiver will not perceive it.

Example:

Let us place an alarm clock under the bell of the air pump (Fig. 1).

As long as there is air in the bell, the sound of the bell is heard clearly. When air is pumped out from under the bell, the sound gradually weakens and finally becomes inaudible. Without a transmission medium, the vibrations of the bell's cymbal cannot propagate, and the sound does not reach our ear. Let the air under the bell and hear the ringing again.

Pay attention!

Elastic substances, such as metals, wood, liquids, gases, conduct sounds well.

Let's put a pocket watch on one end of the wooden board, and we ourselves will move to the other end. Putting your ear to the board, we will hear the clock (Fig. 2).

Tie a string to a metal spoon. Attach the end of the string to the ear. Hitting the spoon, we will hear a strong sound (Fig. 3). We will hear an even stronger sound if we replace the twine with wire.

Pay attention!

Soft and porous bodies are poor conductors of sound.

To protect any room from the penetration of extraneous sounds, the walls, floor and ceiling are laid with layers of sound-absorbing materials. As interlayers, felt, pressed cork, porous stones, various synthetic materials (for example, foam plastic) made on the basis of foamed polymers are used. The sound in such layers quickly attenuates.

Sound propagates in any elastic medium - solid, liquid and gaseous, but cannot propagate in space where there is no substance.

Oscillations of the source create an elastic wave of sound frequency in its environment. The wave, reaching the ear, acts on the eardrum, causing it to vibrate at a frequency corresponding to the frequency of the sound source. Trembling of the tympanic membrane is transmitted through the ossicles to the endings of the auditory nerve, irritate them and thereby cause a sensation of sound (Fig. 4).

In gases and liquids, only longitudinal elastic waves can exist. Therefore, sound in the air is transmitted longitudinal waves, that is, alternating thickening and rarefaction of air coming from the sound source.

A sound wave, like any other mechanical waves, does not propagate in space instantly, but at a certain speed.

Watching the firing of a gun, we first see fire and smoke, and then after a while we hear the sound of a shot.

We know that sound travels through the air. That is why we can hear. No sound can exist in a vacuum. But if sound is transmitted through the air, due to the interaction of its particles, will it not be transmitted by other substances? Will be.

Propagation and speed of sound in different media

Sound is not only transmitted by air. Probably everyone knows that if you put your ear to the wall, you can hear conversations in the next room. In this case, the sound is transmitted by the wall. Sounds propagate in water and in other media. Moreover, the propagation of sound in various environments ah it's different. The speed of sound varies depending on the substance.

Curiously, the speed of sound propagation in water is almost four times higher than in air. That is, fish hear "faster" than we do. In metals and glass, sound travels even faster. This is because sound is a vibration of the medium, and sound waves travel faster in media with better conductivity.

The density and conductivity of water is greater than that of air, but less than that of metal. Accordingly, the sound is transmitted differently. When moving from one medium to another, the speed of sound changes.

The length of a sound wave also changes as it passes from one medium to another. Only its frequency remains the same. But that's why we can distinguish who specifically speaks even through the walls.

Since sound is vibrations, all the laws and formulas for vibrations and waves are well applicable to sound vibrations. When calculating the speed of sound in air, one should also take into account the fact that this speed depends on the air temperature. As the temperature increases, the speed of sound propagation increases. At normal conditions the speed of sound in air is 340,344 m/s.

sound waves

Sound waves, as is known from physics, propagate in elastic media. That is why sounds are well transmitted by the earth. Putting your ear to the ground, you can hear from afar the sound of footsteps, the clatter of hooves, and so on.

In childhood, everyone must have had fun by putting their ear to the rails. The sound of train wheels is transmitted along the rails for several kilometers. To create the reverse effect of sound absorption, soft and porous materials are used.

For example, in order to protect a room from extraneous sounds, or, conversely, in order to prevent sounds from escaping from the room to the outside, the room is treated and soundproofed. The walls, floor and ceiling are upholstered with special materials based on foamed polymers. In such an upholstery, all sounds subside very quickly.

The basic laws of sound propagation include the laws of its reflection and refraction at the boundaries of various media, as well as the diffraction of sound and its scattering in the presence of obstacles and inhomogeneities in the medium and at the interfaces between media.

The sound propagation distance is influenced by the sound absorption factor, that is, the irreversible transfer of sound wave energy into other types of energy, in particular, into heat. An important factor is also the direction of radiation and the speed of sound propagation, which depends on the medium and its specific state.

Acoustic waves propagate from a sound source in all directions. If a sound wave passes through a relatively small hole, then it propagates in all directions, and does not go in a directed beam. For example, street sounds penetrating through an open window into a room are heard at all its points, and not just against the window.

The nature of the propagation of sound waves at an obstacle depends on the ratio between the dimensions of the obstacle and the wavelength. If the dimensions of the obstacle are small compared to the wavelength, then the wave flows around this obstacle, propagating in all directions.

Sound waves, penetrating from one medium to another, deviate from their original direction, that is, they are refracted. The angle of refraction can be greater or less than the angle of incidence. It depends on which medium the sound comes from. If the speed of sound in the second medium is greater, then the angle of refraction will be greater than the angle of incidence, and vice versa.

Encountering an obstacle on its way, sound waves are reflected from it according to a strictly defined rule - the angle of reflection is equal to the angle of incidence - the concept of echo is associated with this. If sound is reflected from several surfaces at different distances, multiple echoes occur.

Sound propagates in the form of a diverging spherical wave that fills an ever larger volume. As the distance increases, the oscillations of the particles of the medium weaken, and the sound dissipates. It is known that in order to increase the transmission distance, sound must be concentrated in a given direction. When we want, for example, to be heard, we put our hands to our mouths or use a mouthpiece.

Diffraction, that is, the bending of sound rays, has a great influence on the range of sound propagation. The more heterogeneous the medium, the more the sound beam is bent and, accordingly, the shorter the sound propagation distance.

sound propagation

Sound waves can travel through air, gases, liquids and solids. Waves do not form in airless space. This can be easily seen from a simple experiment. If an electric bell is placed under an airtight cap from which the air is evacuated, we will not hear any sound. But as soon as the cap is filled with air, sound occurs.

The speed of propagation of oscillatory motions from particle to particle depends on the medium. In ancient times, warriors put their ears to the ground and thus discovered the enemy's cavalry much earlier than it appeared in sight. And the famous scientist Leonardo da Vinci wrote in the 15th century: “If you, being at sea, lower the hole of the pipe into the water, and put the other end to your ear, you will hear the noise of ships very distant from you.”

The speed of sound in air was first measured in the 17th century by the Milan Academy of Sciences. A cannon was installed on one of the hills, and an observation post was located on the other. The time was recorded both at the moment of the shot (by flash) and at the moment of sound reception. From the distance between the observation post and the gun and the time of origin of the signal, the speed of sound propagation was no longer difficult to calculate. It turned out to be equal to 330 meters per second.

In water, the speed of sound propagation was first measured in 1827 on Lake Geneva. Two boats were one from the other at a distance of 13847 meters. On the first, a bell was hung under the bottom, and on the second, a simple hydrophone (horn) was lowered into the water. On the first boat, at the same time as the bell was struck, gunpowder was set on fire, on the second observer, at the moment of the flash, he started the stopwatch and began to wait for the sound signal from the bell to arrive. It turned out that sound travels more than 4 times faster in water than in air, i.e. at a speed of 1450 meters per second.

Sound propagation speed

The higher the elasticity of the medium, the greater the speed: in rubber50, in air330, in water1450, and in steel - 5000 meters per second. If we, who were in Moscow, could shout so loudly that the sound would reach Petersburg, then we would be heard there only in half an hour, and if the sound propagated over the same distance in steel, it would be received in two minutes.

The speed of sound propagation is influenced by the state of the same medium. When we say that sound travels in water at a speed of 1450 meters per second, this does not mean at all that in any water and under any conditions. With an increase in temperature and salinity of water, as well as with an increase in depth, and, consequently, hydrostatic pressure, the speed of sound increases. Or take steel. Here, too, the speed of sound depends both on the temperature and on the qualitative composition of the steel: the more carbon it contains, the harder it is, the faster sound travels in it.

Encountering an obstacle on its way, sound waves are reflected from it in a strictly certain rule: The angle of reflection is equal to the angle of incidence. Sound waves coming from the air are almost completely reflected upwards from the surface of the water, and sound waves coming from a source in the water are reflected downwards from it.

Sound waves, penetrating from one medium to another, deviate from their original position, i.e. are refracted. The angle of refraction can be greater or less than the angle of incidence. It depends on the medium from which the sound penetrates. If the speed of sound in the second medium is greater than in the first, then the angle of refraction will be greater than the angle of incidence and vice versa.

In air, sound waves propagate in the form of a diverging spherical wave, which fills an ever larger volume, as the particle vibrations caused by sound sources are transferred to the air mass. However, as the distance increases, the oscillations of the particles weaken. It is known that in order to increase the transmission distance, the sound must be concentrated in a given direction. When we want to be heard better, we put our palms to our mouths or use a horn. In this case, the sound will be attenuated less, and the sound waves will propagate further.

As the wall thickness increases, sonar at low mid frequencies increases, but the “insidious” coincidence resonance, which causes sonar suffocation, begins to appear at lower frequencies and captures a wider area of ​​them.