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

Most people are well aware of what sound is. It is associated with hearing and is associated with physiological and psychological processes. In the brain, the processing of sensations that come through the hearing organs is carried out. The speed of sound depends on many factors.

Sounds that humans hear

In the general sense of the word, sound is physical phenomenon, which causes an effect on the hearing organs. It has the form of longitudinal waves of different frequencies. Humans can hear sound whose frequency ranges from 16-20,000 Hz. These elastic longitudinal waves, which propagate not only in the air, but also in other media, reaching the human ear, cause sound sensations. People can't hear everything. Elastic waves with a frequency of less than 16 Hz are called infrasound, and above 20,000 Hz - ultrasound. Their human ear cannot hear.

Sound characteristics

There are two main characteristics of sound: loudness and pitch. The first of them is related to the intensity of the elastic sound wave. There is another important indicator. Physical quantity, which characterizes the height, is the oscillation frequency of the elastic wave. In this case, one rule applies: the larger it is, the higher the sound, and vice versa. Another important characteristic is the speed of sound. AT different environments she is different. It represents the speed of propagation of elastic sound waves. In a gaseous environment, this indicator will be less than in liquids. The speed of sound in solids the tallest. Moreover, for longitudinal waves it is always greater than for transverse ones.

Sound Wave Velocity

This indicator depends on the density of the medium and its elasticity. In gaseous media, it is affected by the temperature of the substance. As a rule, the speed of sound does not depend on the amplitude and frequency of the wave. In rare cases, when these characteristics have an influence, one speaks of the so-called dispersion. The speed of sound in vapors or gases ranges from 150-1000 m/s. In liquid media, it is already 750-2000 m/s, and in solid materials - 2000-6500 m/s. Under normal conditions, the speed of sound in air reaches 331 m/s. AT ordinary water- 1500 m/s.

The speed of sound waves in different chemical media

The speed of sound propagation in different chemical media is not the same. So, in nitrogen it is 334 m / s, in air - 331, in acetylene - 327, in ammonia - 415, in hydrogen - 1284, in methane - 430, in oxygen - 316, in helium - 965, in carbon monoxide- 338, in carbonic acid - 259, in chlorine - 206 m/s. The speed of a sound wave in gaseous media increases with increasing temperature (T) and pressure. In liquids, it most often decreases with an increase in T by several meters per second. Sound speed (m/s) in liquid media (at 20°C):

Water - 1490;

Ethyl alcohol - 1180;

Benzene - 1324;

Mercury - 1453;

Carbon tetrachloride - 920;

Glycerin - 1923.

The only exception to this rule is water, in which the speed of sound also increases with increasing temperature. It reaches its maximum when this liquid is heated to 74°C. As the temperature rises further, the speed of sound decreases. With an increase in pressure, it will increase by 0.01% / 1 Atm. in salty sea ​​water as temperature, depth, and salinity increase, so does the speed of sound. In other environments, this indicator varies in different ways. So, in a mixture of liquid and gas, the speed of sound depends on the concentration of its components. In an isotopic solid, it is determined by its density and elastic moduli. Transverse (shear) and longitudinal elastic waves propagate in unbounded dense media. Sound speed (m/s) in solids(longitudinal / transverse wave):

Glass - 3460-4800/2380-2560;

Fused quartz - 5970/3762;

Concrete - 4200-5300/1100-1121;

Zinc - 4170-4200/2440;

Teflon - 1340/*;

Iron - 5835-5950/*;

Gold - 3200-3240/1200;

Aluminum - 6320/3190;

Silver - 3660-3700/1600-1690;

Brass - 4600/2080;

Nickel - 5630/2960.

In ferromagnets, the speed of a sound wave depends on the strength of the magnetic field. In single crystals, the speed of a sound wave (m/s) depends on the direction of its propagation:

• ruby (longitudinal wave) - 11240;
• cadmium sulfide (longitudinal / transverse) - 3580/4500;
• lithium niobate (longitudinal) - 7330.

The speed of sound in a vacuum is 0, because it simply does not propagate in such an environment.

Determining the speed of sound

Everything related to sound signals interested our ancestors thousands of years ago. Almost all prominent scientists worked on the definition of the essence of this phenomenon. ancient world. Even ancient mathematicians found that sound is caused by oscillatory movements body. Euclid and Ptolemy wrote about it. Aristotle established that the speed of sound differs by a finite value. The first attempts to determine this indicator were made by F. Bacon in the 17th century. He tried to establish the speed by comparing the time intervals between the sound of a shot and a flash of light. Based on this method, a group of physicists at the Paris Academy of Sciences determined the speed of a sound wave for the first time. AT various conditions experiment, it was 350-390 m/s. Theoretical justification the speed of sound for the first time in his "Principles" was considered by I. Newton. P.S. succeeded in making the correct determination of this indicator. Laplace.

Formulas for the speed of sound

For gaseous media and liquids, in which sound propagates, as a rule, adiabatically, the temperature change associated with expansions and compressions in a longitudinal wave cannot quickly equalize in a short period of time. Obviously, this figure is influenced by several factors. The speed of a sound wave in a homogeneous gaseous medium or liquid is determined by the following formula:

where β is the adiabatic compressibility, ρ is the density of the medium.

In partial derivatives, this value is calculated according to the following formula:

c 2 \u003d -υ 2 (δρ / δυ) S \u003d -υ 2 Cp / Cυ (δρ / δυ) T,

where ρ, T, υ are the pressure of the medium, its temperature and specific volume; S - entropy; Cp - isobaric heat capacity; Cυ - isochoric heat capacity. For gaseous media, this formula will look like this:

c 2 = ζkT/m= ζRt/M = ζR(t + 273.15)/M = ά 2 T,

where ζ is the adiabat value: 4/3 for polyatomic gases, 5/3 for monatomic gases, 7/5 for diatomic gases (air); R - gas constant (universal); T is the absolute temperature, measured in kelvins; k - Boltzmann's constant; t - temperature in °C; M- molar mass; m- molecular mass; ά 2 = ζR/M.

Determination of the speed of sound in a solid body

In a solid body with homogeneity, there are two types of waves that differ in the polarization of oscillations in relation to the direction of their propagation: transverse (S) and longitudinal (P). The speed of the first (C S) will always be lower than the second (C P):

C P 2 = (K + 4/3G)/ρ = E(1 - v)/(1 + v)(1-2v)ρ;

C S 2 = G/ρ = E/2(1 + v)ρ,

where K, E, G - moduli of compression, Young, shear; v - Poisson's ratio. When calculating the speed of sound in a solid body, adiabatic moduli of elasticity are used.

Speed ​​of sound in multiphase media

In multiphase media, due to the inelastic absorption of energy, the speed of sound is directly dependent on the frequency of vibrations. In a two-phase porous medium, it is calculated using the Biot-Nikolaevsky equations.

Conclusion

The measurement of sound wave speed is used in determining various properties of substances, such as the moduli of elasticity of a solid, the compressibility of liquids and gases. A sensitive method for the determination of impurities is the measurement of small changes in the speed of the sound wave. In solids, the fluctuation of this index makes it possible to study the band structure of semiconductors. The speed of sound is a very important quantity, the measurement of which allows you to learn a lot about a variety of media, bodies and other objects. scientific research. Without the ability to determine it, many scientific discoveries would be impossible.

1.25. 3SONIC WAVES

The concept of a sound wave. The speed of sound in various media. Physical characteristics of sound: intensity, spectrum, pitch, loudness, attenuation. Ultrasound and its applications. Doppler effect. shock waves.

Sound waves.

An important type of longitudinal waves are sound waves . This is the name of waves with frequencies of 17 - 20,000 Hz. The study of sound is called acoustics. In acoustics, waves are studied that propagate not only in air, but also in any other medium. Elastic waves with a frequency below 17 Hz are called infrasound, and those with a frequency above 20,000 Hz are called ultrasound.

Sound waves are elastic vibrations that propagate in the form of a wave process in gases, liquids, solids.

Excessive sound pressure. Sound wave equation.

The elastic wave equation allows you to calculate the displacement of any point in the space through which the wave passes, at any time. But how to talk about the displacement of particles of air or liquid from the equilibrium position? Sound, propagating in a liquid or gas, creates areas of compression and rarefaction of the medium, in which the pressure respectively increases or decreases compared to the pressure of the undisturbed medium.

If is the pressure and density of the unperturbed medium (the medium through which the wave does not pass), and is the pressure and density of the medium during the propagation of the wave process in it, then the quantity is called overpressure . Value there is a maximum overpressure value (overpressure amplitude ).

The change in excess pressure for a plane sound wave (i.e., the plane sound wave equation) is:

where y is the distance from the source of oscillations of the point, the excess pressure in which we determine at the time t.

If we introduce the value of the excess density and its amplitude in the same way as we introduced the value of the excess sound pressure, then the equation of a plane sound wave could be written as follows:

. (30.2)

Sound speed- the speed of propagation of sound waves in the medium. As a rule, the speed of sound in gases is less than in liquids, and in liquids the speed of sound is less than in solids. The greater the density, the greater the speed of sound. The speed of sound in any medium is calculated by the formula: where β is the adiabatic compressibility of the medium; ρ is the density.

Objective and subjective characteristics of sound.

The word “sound” itself reflects two different but related concepts: 1) sound as a physical phenomenon; 2) sound - the perception that the hearing aid (human ear) experiences and the sensations that arise from it. Accordingly, the sound characteristics are divided into objective , that can be measured by physical equipment, and Withsubjective , determined by the perception of a given sound by a person.

The objective (physical) characteristics of sound include characteristics that describe any wave process: frequency, intensity and spectral composition. In table1. comparative data of objective and subjective characteristics are included.

Table 1.

sound frequency is measured by the number of oscillations of the particles of the medium participating in the wave process in 1 second.

Intensity wave is measured by the energy carried by the wave per unit time through a unit area (located perpendicular to the direction of wave propagation).

Spectral composition (spectrum) sound indicates what vibrations this sound consists of and how the amplitudes are distributed between its individual components.

Distinguish continuous and line spectra . For a subjective assessment of loudness, quantities called sound level and loudness level .

Table 2 - Objective characteristics of mechanical wave processes.

To characterize the quantities that determine the perception of sound, it is not so much the absolute values ​​of the sound intensity and sound pressure that are significant, but their relation to certain threshold values. Therefore, the concepts of relative levels of intensity and sound pressure are introduced.

In order for a sound wave to be perceived by ear, it is necessary that its intensity exceed the minimum value called Ploud of hearing . The value is different for different frequencies. For a frequency, the hearing threshold is of the order of magnitude. It has been established by experience that at each frequency there is an upper limit of sound power, when exceeded, a person experiences pain. The value is called pain threshold.

Intensity level (sound intensity level) is equal to the decimal logarithm of the ratio of the sound intensity at a given frequency to the sound intensity at the same frequency at the threshold of hearing:

.

Sound volume - subjective perception of the strength of sound (the absolute value of the auditory sensation). The loudness mainly depends on the sound pressure and the frequency of sound vibrations. Also, the volume of a sound is affected by its timbre, the duration of exposure to sound vibrations, and other factors. Volume level is equal to the decimal logarithm of the ratio of the sound intensity at a given frequency to the sound intensity at a frequency of 1000 Hz at the threshold of hearing:

.

The intensity level unit is bel (B): . One tenth of a bela is called a decibel (dB): 0.1B = 1dB. The formula for determining the intensity level in decibels will take the form:

.

If we write the formula for the volume level in the form , then the unit of measurement in SI with this definition of the quantity is the unit called background. At a frequency of 1000 Hz, the hum and decibel scales are the same, for other frequencies they are different.

Sound pressure level is equal to the product of 20 times the logarithm of the ratio of the sound pressure at a given frequency to the sound pressure at the threshold of hearing. The unit of measurement in this case is the decibel.

.

Ultrasound: Mechanical waves with an oscillation frequency greater than 20,000 Hz are not perceived by a person as sound.

Ultrasound is a wave-like propagating oscillatory motion of the particles of the medium and is characterized by a number of distinctive features compared to the audible range. In the ultrasonic frequency range, it is relatively easy to obtain directional radiation; ultrasonic vibrations lend themselves well to focusing, as a result of which the intensity of ultrasonic vibrations in certain zones of influence increases. When propagating in gases, liquids and solids, ultrasound generates unique phenomena, many of which have found practical application in various fields of science and technology. A little more than a hundred years have passed since the beginning of research in the field of application of ultrasonic vibrations. During this time, dozens of highly efficient, resource-saving and environmentally friendly ultrasonic technologies have appeared in the asset of mankind. These include: technologies for hardening, tinning and soldering of metals, prevention of scale formation on heat exchange surfaces, drilling of brittle and especially hard materials, drying of thermolabile substances, extraction of animal and vegetable raw materials, dissolution, sterilization of liquid substances, fine spraying of drugs, heavy fuels , production of emulsions and ultrafine suspensions, dispersion of dyes, metal welding and polymers, washing, cleaning parts without the use of flammable and toxic solvents.

In recent years, ultrasound has begun to play an increasingly important role in industry and research. Theoretical and experimental studies in the field of ultrasonic cavitation and acoustic flows have been successfully carried out, which made it possible to develop new technological processes that occur under the action of ultrasound in the liquid phase. Currently, a new direction in chemistry is being formed - ultrasonic chemistry, which makes it possible to accelerate many chemical and technological processes and obtain new substances. Scientific research contributed to the emergence of a new section of acoustics - molecular acoustics, which studies the molecular interaction of sound waves with matter. New areas of application of ultrasound have emerged: introscopy, holography, quantum acoustics, ultrasonic phase measurement, acoustoelectronics.

Along with theoretical and experimental research in the field of ultrasound, a lot of practical work has been done. Universal and special ultrasonic machines, installations operating under increased static pressure, ultrasonic mechanized installations for cleaning parts, generators with an increased frequency and a new cooling system, and converters with a uniformly distributed field have been developed.

An echo sounder is a device for determining the depth of the sea. An ultrasonic locator is used to determine the distance to an obstacle on the way. When ultrasound passes through a liquid, the particles of the liquid acquire large accelerations and strongly affect various bodies placed in the liquid. This is used to speed up a wide variety of technological processes (for example, preparing solutions, washing parts, tanning leather, etc.). Ultrasound is used to detect defects in metal parts. In medicine, ultrasound examination of internal organs is performed.

Doppler effect called the change in the frequency of oscillations perceived by the receiver, when the source of these oscillations and the receiver move relative to each other.

To consider the Doppler effect, suppose that the sound source and receiver move along the straight line connecting them; v ist and v pr - respectively, the speed of movement of the source and receiver, and they are positive if the source (receiver) is approaching the receiver (source), and negative if it is moving away. The oscillation frequency of the source is v 0 .

1. Source and receiver are at rest relative to the medium, i.e. v ist = v pr \u003d 0. If a v - the speed of propagation of a sound wave in the medium under consideration, then the wavelength l= vT= v/ v 0 . Propagating in the medium, the wave will reach the receiver and cause oscillations of its sound-sensitive element with a frequency

Therefore, the frequency v the sound that the receiver will register is equal to the frequency v 0 , with which the sound wave is emitted by the source.

2. The receiver approaches the source, and the source is at rest, i.e. v pr >0, v ist =0. In this case, the wave propagation velocity relative to the receiver will be equal to v + v etc. Since the wavelength does not change, then

(30.4)

i.e., the frequency of oscillations perceived by the receiver, in ( v+ v etc) / v times the source frequency.

3. The source approaches the successor, and the receiver is at rest, i.e. v ist >0, v pr \u003d 0.

The speed of propagation of oscillations depends only on the properties of the medium, therefore, in a time equal to the period of oscillations of the source, the wave emitted by it will travel in the direction of the receiver distance vT(equal to the wavelength l) regardless of whether the source is moving or at rest. During the same time, the source will cover the distance in the direction of the wave v ist T(Fig. 224), i.e., the wavelength in the direction of movement will be reduced and become equal to l"=l-v ist T=(v-v ist) T, then

(30.5)

i.e. frequency n vibrations perceived by the receiver will increase in v/(v – v ist) times. In cases 2 and 3, if v ist<0 и v etc<0, знак будет обратным.

4. Source and receiver are moving relative to each other. Using the results obtained for cases 2 and 3, we can write an expression for the frequency of oscillations perceived by the receiver:

(30.6)

moreover, the upper sign is taken if during the movement of the source or receiver they approach each other, the lower sign - in the case of their mutual removal.

It follows from the above formulas that the Doppler effect is different depending on whether the source or the receiver is moving. If the directions of the speeds v at v ist do not coincide with the straight line passing through the source and receiver, then instead of these velocities in formula (30.6) one must take their projections onto the direction of this straight line.

shock wave: discontinuity surface that moves relative to gas/liquid/solid bodies and upon crossing which pressure, density,

temperature and speed experience a jump.

Shock waves arise during explosions, detonations, during supersonic movements of bodies, with powerful electric. discharges, etc. For example, during the explosion of explosives, highly heated explosion products are formed, which have a high density and are under high pressure. Initially, they are surrounded by air at rest at normal density and atmospheric pressure. The expanding products of the explosion compress the surrounding air, and at each moment of time only the air in a certain volume is compressed; outside this volume, the air remains undisturbed. Over time, the volume of compressed air increases. The surface that separates compressed air from undisturbed air is the front of the shock wave. In a number of cases of supersonic motion of bodies in a gas (artillery shells, descent space vehicles), the direction of gas motion does not coincide with the normal to the surface of the shock wave front, and then oblique shock waves arise .

An example of the occurrence and propagation of a shock wave is the compression of a gas in a pipe by a piston. If the piston moves slowly into the gas, then through the gas at the speed of sound a runs acoustic. (elastic) compression wave. If the speed of the piston is not small compared to the speed of sound, a shock wave arises, the speed of which propagates through the unperturbed gas is greater than the speed of movement of gas particles (the so-called mass speed), which coincides with the speed of the piston. The distances between particles in a shock wave are smaller than in an undisturbed gas due to gas compression. If the piston is first pushed into the gas at a low speed and gradually accelerated, then the shock wave does not form immediately. First, a compression wave arises with continuous distributions of density r and pressure R. Over time, the steepness of the front part of the compression wave increases, since the perturbations from the rapidly moving piston catch up with it and intensify it, as a result of which there is a sharp jump in all hydrodynamics. quantities, i.e. shock wave

Shock wave in real gases. In a real gas at high temperatures, excitation of molecular vibrations, dissociation of molecules, chemical reactions, ionization, etc. occur, which is associated with energy costs and a change in the number of particles. In this case, the internal energy e depends in a complicated way on p and ρ and gas parameters behind the front.

To redistribute the energy of a gas compressed and heated in a strong shock wave over various degrees of freedom, usually a lot of molecular collisions are required. Therefore, the width of the layer Dx, in which the transition from the initial to the final thermodynamically equilibrium state occurs, i.e., the width of the shock wave front, in real gases is usually much larger than the width of the viscous shock and is determined by time relaxation the slowest of the processes: excitation of oscillations, dissociation, ionization, etc. Distributions

Rice. 25.1 Distribution of temperature (a) and density (b) in a shock wave propagating in a real gas .

temperature and density in the shock wave in this case have the form shown in Fig. 25.1 where a viscous shock is depicted as an explosion.

Shock wave in solids. Energy and pressure in solids have a dual nature: they are associated with thermal motion and with the interaction of particles (thermal and elastic components). The theory of interparticle forces cannot give a general dependence of the elastic components of pressure and energy on density in a wide range for different substances, and, therefore, it is theoretically impossible to construct a function that connects ( p,ρ) before and behind the shock wave front. Therefore, calculations for solid (and liquid) bodies are determined from experience or semi-empirically. Significant compression of solids requires pressures of millions of atmospheres, which are now achieved in experimental studies. In practice, weak shock waves with pressures of 10 4 -10 5 atm are of great importance. These are pressures that develop during detonation, explosions in water, impacts of explosion products against obstacles, etc. In a number of substances - iron, bismuth and others, phase transitions - polymorphic transformations - occur in a shock wave. At low pressures in solids, elastic waves , the propagation of which, like the propagation of weak compression waves in gases, can be considered on the basis of the laws of acoustics.

Sound propagation requires an elastic medium. Sound waves cannot propagate in a vacuum because there is nothing to vibrate there. This can be verified by a simple experiment. If an electric bell is placed under a glass bell, then as the air is pumped out from under the bell, the sound from the bell will become weaker and weaker until it stops altogether.

It is known that during a thunderstorm we see a flash of lightning and only after a while hear thunder. This delay occurs due to the fact that the speed of sound in air is much less than the speed of light coming from lightning.

The speed of sound in air was first measured in 1636 by the French scientist M. Mersen. At a temperature of 20 ° C, it is equal to 343 m / s, i.e. 1235 km / h. Note that it is to this value that the speed of a bullet fired from a Kalashnikov assault rifle decreases at a distance of 800 m. The muzzle velocity of the bullet is 825 m/s, which is much higher than the speed of sound in air. Therefore, a person who hears the sound of a shot or the whistle of a bullet need not worry: this bullet has already passed him. The bullet outruns the sound of the shot and reaches its victim before the sound arrives.

The speed of sound in gases depends on the temperature of the medium: with an increase in air temperature, it increases, and with a decrease, it decreases. At 0 °C, the speed of sound in air is 332 m/s.

Sound travels at different speeds in different gases. The larger the mass of gas molecules, the lower the speed of sound in it. So, at a temperature of 0 ° C, the speed of sound in hydrogen is 1284 m/s, in helium - 965 m/s, and in oxygen - 316 m/s.

The speed of sound in liquids is generally greater than the speed of sound in gases. The speed of sound in water was first measured in 1826 by J. Colladon and J. Sturm. They conducted their experiments on Lake Geneva in Switzerland. On one boat they set fire to gunpowder and at the same time struck a bell lowered into the water. The sound of this bell, lowered into the water, was caught on another boat, which was located at a distance of 14 km from the first. The speed of sound in water was determined from the time interval between the flash of the light signal and the arrival of the sound signal. At a temperature of 8°C, it turned out to be 1440 m/s.

The speed of sound in solids is greater than in liquids and gases. If you put your ear to the rail, then after hitting the other end of the rail, two sounds are heard. One of them reaches the ear along the rail, the other - through the air.

Earth has good sound conductivity. Therefore, in the old days, during a siege, "hearers" were placed in the fortress walls, who, by the sound transmitted by the earth, could determine whether the enemy was digging to the walls or not. Putting their ear to the ground, they also watched the approach of the enemy cavalry.

Solid bodies conduct sound well. Because of this, people who have lost their hearing are sometimes able to dance to music that reaches the auditory nerves not through the air and outer ear, but through the floor and bones.

The speed of sound can be determined by knowing the wavelength and frequency (or period) of oscillation.

Sound speed- speed of propagation of elastic waves in a medium: both longitudinal (in gases, liquids or solids) and transverse, shear (in solids). It is determined by the elasticity and density of the medium: as a rule, the speed of sound in gases is less than in liquids, and in liquids it is less than in solids. Also, in gases, the speed of sound depends on the temperature of the given substance, in single crystals - on the direction of wave propagation. Usually does not depend on the frequency of the wave and its amplitude; in cases where the speed of sound depends on frequency, one speaks of the dispersion of sound.

Encyclopedic YouTube

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  Already among ancient authors there is an indication that the sound is due to the oscillatory movement of the body (Ptolemy, Euclid). Aristotle notes that the speed of sound is of finite magnitude and correctly imagines the nature of sound. Attempts to experimentally determine the speed of sound date back to the first half of the 17th century. F. Bacon in "New Organon" pointed out the possibility of determining the speed of sound by comparing the time intervals between a flash of light and the sound of a shot. Using this method, various researchers (M. Mersenne, P. Gassendi, W. Derham, a group of scientists from the Paris Academy of Sciences - D. Cassini, J. Picard, Huygens, Römer) determined the value of the speed of sound (depending on the experimental conditions, 350- 390 m/s). Theoretically, the question of the speed of sound was first considered by I. Newton in his "Principles". Newton actually assumed the isothermal propagation of sound, so he got an underestimate. The correct theoretical value for the speed of sound was obtained by Laplace.

  Calculation of velocity in liquid and gas

  The speed of sound in a homogeneous liquid (or gas) is calculated by the formula:

  c = 1 β ρ (\displaystyle c=(\sqrt (\frac (1)(\beta \rho ))))

  In partial derivatives:

  c = − v 2 (∂ p ∂ v) s = − v 2 C p C v (∂ p ∂ v) T (\displaystyle c=(\sqrt (-v^(2)\left((\frac (\ partial p)(\partial v))\right)_(s)))=(\sqrt (-v^(2)(\frac (Cp)(Cv))\left((\frac (\partial p) (\partial v))\right)_(T))))

  where β (\displaystyle \beta )- adiabatic compressibility of the medium; ρ (\displaystyle \rho )- density; Cp (\displaystyle Cp)- isobaric heat capacity; c v (\displaystyle cv)- isochoric heat capacity; p (\displaystyle p), v (\displaystyle v), T (\displaystyle T)- pressure, specific volume and temperature of the medium; s (\displaystyle s)- entropy of the environment.

  For solutions and other complex physical and chemical systems (for example, natural gas, oil), these expressions can give a very large error.

  Solids

  In the presence of interfaces, elastic energy can be transferred through surface waves of various types, the speed of which differs from the speed of longitudinal and transverse waves. The energy of these oscillations can be many times greater than the energy of bulk waves.