SOUND SPEED- speed of propagation of an elastic wave in the medium. Determined by the elasticity and density of the medium. For running without changing shape with speed With in the direction of the axis X, sound pressure R can be represented in the form p = p(x - - ct), Where t- time. For plane harmony, waves in a medium without dispersion and SZ. expressed in terms of frequency w and k Floy c = w/k. With speed With the harmonic phase propagates. waves, so With called also phase S. z. In media in which the shape of an arbitrary wave changes during propagation, harmonic. the waves nevertheless retain their shape, but the phase velocity turns out to be different for different frequencies, i.e. sound dispersion.In these cases the concept is also used group velocity. At large amplitudes, nonlinear effects appear (see. Nonlinear acoustics), leading to a change in any waves, including harmonic ones: the speed of propagation of each point of the wave profile depends on the pressure at this point, increasing with increasing pressure, which leads to distortion of the wave shape.

Speed ​​of sound in gases and liquids. In gases and liquids, sound propagates in the form of volumetric compression-discharge waves. If the propagation process occurs adiabatically (which, as a rule, is the case), i.e., the change in temperature in the sound wave does not have time to level out even after 1 / 2 , period the heat from the heated (compressed) areas does not have time to move to the cold (rarefied) areas, then S. z. equal to , Where R is the pressure in the substance, is its density, and the index s shows that the derivative is taken at constant entropy. This S. z. called adiabatic. Expression for S. z. can also be written in one of the following forms:

Where TO hell - adiabatic. modulus of all-round compression of matter, - adiabatic. compressibility, - isothermal compressibility, = - the ratio of heat capacities at constant pressure and volume.

In bounded solids, in addition to longitudinal and transverse waves, there are other types of waves. Thus, along the free surface of a solid body or along its boundary with another medium, they propagate surface acoustic waves, the speed of which less speed body waves characteristic of a given material. For plates, rods and other solid acoustic materials. waveguides are characteristic normal waves The speed of which is determined not only by the properties of the substance, but also by the geometry of the body. So, for example, S. z. for a longitudinal wave in a rod with a st, the transverse dimensions of which are much smaller than the wavelength of sound, different from the S. z. in an unrestricted environment with l(Table 3):

Methods for measuring S.z. can be divided into resonant, interferometric, pulsed and optical (see. Diffraction of light by ultrasound).Naib. Measurement accuracy is achieved using pulse-phase methods. Optical methods make it possible to measure S. z. at hypersonic frequencies (up to 10 11 -10 12 Hz). Accuracy abs. measurements S. z. on the best equipment approx. 10 -3%, while the accuracy is relative. measurements of the order of 10 -5% (for example, when studying the dependence With on temperature or magnetic fields or the concentration of impurities or defects).

Measurements of S. z. are used to define plurals. properties of matter, such as the ratio of heat capacities for gases, compressibility of gases and liquids, elastic moduli of solids, Debye temperature, etc. (see. Molecular acoustics). Determination of small changes in S. z. is sensitive. method of fixing impurities in gases and liquids. In solids, the measurement of S. z. and its dependence on different factors (temperature, magnetic fields, etc.) allows you to study the structure of matter: the band structure of semiconductors, the structure of the Fermi surface in metals, etc.

Lit.: Landau L. D., L i f sh i c E. M., Theory of Elasticity, 4th ed., M., 1987; them, Hydrodynamics, 4th ed., M., 1988; Bergman L., and its application in science and technology, trans. from German, 2nd ed., M., 1957; Mikhailov I. G., Solovyov V. A., Syrnikov Yu. P., Fundamentals of molecular acoustics, M., 1964; Tables for calculating the speed of sound in sea ​​water, L., 1965; Physical acoustics, ed. W. Mason, trans. from English, vol. 1, part A, M., 1966, ch. 4; t. 4, part B, M., 1970, ch. 7; Kolesnikov A.E., Ultrasonic measurements, 2nd ed., M., 1982; T r u e l l R., E l b a u m Ch., Ch i k B., Ultrasonic methods in solid state physics, trans. from English, M., 1972; Acoustic crystals, ed. M. P. Shaskolskoy, M., 1982; Krasilnikov V.A., Krylov V.V., Introduction to physical acoustics, M., 1984. A. L. Polyakova.

Sound speed

The main characteristics of sound waves include the speed of sound, its intensity - these are the objective characteristics of sound waves, pitch, loudness are classified as subjective characteristics. Subjective characteristics depend to a large extent on the perception of sound by a particular person, and not on physical characteristics sound.

Measuring the speed of sound in solids, liquids and gases indicate that the speed does not depend on the vibration frequency or sound wavelength, i.e., sound waves are not characterized by dispersion. Longitudinal and transverse waves can propagate in solids, the speed of propagation of which is found using the formulas:

where E is Young's modulus, G is shear modulus in solids. In solids, the speed of propagation of longitudinal waves is almost twice as large as the speed of propagation of transverse waves.

In liquids and gases they can only spread longitudinal waves. The speed of sound in water is found using the formula:

K is the bulk modulus of the substance.

In liquids, as the temperature increases, the speed of sound increases, which is associated with a decrease in the volumetric compression ratio of the liquid.

For gases, a formula has been derived that relates their pressure to density:

I. Newton was the first to use this formula to find the speed of sound in gases. From the formula it is clear that the speed of sound propagation in gases does not depend on temperature, it also does not depend on pressure, since as pressure increases, the density of the gas also increases. The formula can also be given a more rational form: based on the Mendeleev-Clapeyron equation:

Then the speed of sound will be equal to:

The formula is called Newton's formula. The speed of sound in air calculated with its help is 280 m/s at 273K. The actual experimental speed is 330 m/s.

This result differs significantly from the theoretical one, and the reason for this was established by Laplace.

He showed that sound propagates adiabatically in air. Sound waves in gases propagate so quickly that the created local changes in volume and pressure in the gaseous medium occur without heat exchange with environment. Laplace derived an equation for finding the speed of sound in gases:

Propagation of sound waves

As sound waves propagate through the medium, they attenuate. The amplitude of vibrations of particles of the medium gradually decreases with increasing distance from the sound source.

One of the main reasons for wave attenuation is the action of internal friction forces on particles of the medium. To overcome these forces, the mechanical energy of oscillatory motion, which is transferred by the wave, is continuously used. This energy turns into the energy of chaotic thermal movement of molecules and atoms of the environment. Since the wave energy is proportional to the square of the oscillation amplitude, as the waves propagate from the sound source, along with a decrease in the energy reserve of the oscillatory motion, the oscillation amplitude also decreases.

The propagation of sounds in the atmosphere is influenced by many factors: temperature at different heights, air flows. Echo is sound reflected from a surface. Sound waves can be reflected from solid surfaces, from layers of air in which the temperature is different from the temperature of neighboring layers.

Sound speed- the 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 a 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, we speak of sound dispersion.

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  Already in ancient authors there is an indication that sound is caused by oscillatory movement bodies (Ptolemy, Euclid). Aristotle notes that the speed of sound has a finite value, 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 the 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 gunshot. 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, Roemer) 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 that sound propagation is isothermal, and therefore received an underestimate. The correct theoretical value for the speed of sound was obtained by Laplace.

  Calculation of speed 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 (C_(p))(C_(v)))\left((\ frac (\partial p)(\partial v))\right)_(T))))

  Where β (\displaystyle \beta )- adiabatic compressibility of the medium; ρ (\displaystyle \rho )- density; C p (\displaystyle C_(p))- isobaric heat capacity; C v (\displaystyle C_(v))- 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 medium.

  For solutions and other complex physicochemical 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 via surface waves 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 body waves.

  The article examines the characteristics of sound phenomena in the atmosphere: the speed of sound propagation in the air, the influence of wind and fog on the propagation of sound.
  Longitudinal vibrations of matter particles, propagating through the material medium (air, water and solids) and reaching the human ear, cause sensations called sound.
  IN atmospheric air There are always sound waves of different frequencies and strengths. Some of these waves are created artificially by humans, and some of the sounds are of meteorological origin.
  To the sounds meteorological origin include thunder, the howling of the wind, the hum of wires, the noise and rustling of trees, the “voice” of the sea, sounds when falling on earth's surface solid and liquid precipitation, sounds of surf off the coast of seas and lakes and others.
  The speed of sound propagation in the atmosphere is affected by air temperature and humidity, as well as wind (direction and its strength). On average, the speed of sound in the atmosphere is 333 m/s. As air temperature increases, the speed of sound increases slightly. Changes in absolute air humidity have less effect on the speed of sound.
  The speed of sound in air is determined by Laplace's formula:

  (1),
  where p is pressure; ? - air density; c? - heat capacity of air at constant pressure; cp is the heat capacity of air at constant volume.
  Using the gas equation of state, it is possible to obtain a number of dependences of the speed of sound on meteorological parameters.
  The speed of sound in dry air is determined by the formula:
  c0 = 20.1 ?T m/s, (2)
  and in humid air:
  с0 = 20.1 ?ТВ m/s, (3)
  where TV = so-called acoustic virtual temperature, which is determined by the formula TV = T (1+ 0.275 e/p).
  When the air temperature changes by 1°, the speed of sound changes by 0.61 m/s. The speed of sound depends on the value of the ratio e/p (the ratio of humidity to pressure), but this dependence is small, and, for example, when the elasticity of water vapor is less than 7 mm, neglecting it gives an error in the speed of sound not exceeding 0.5 m/sec.
  At normal pressure and T = 0 °C, the speed of sound in dry air is 333 m/sec. In humid air, the speed of sound can be determined by the formula:
  c = 333 + 0.6t + 0.07e (4)
  In the temperature range (t) from -20° to +30°, this formula gives an error in the speed of sound of no more than ± 0.5 m/sec. From the above formulas it is clear that the speed of sound increases with increasing temperature and air humidity.
  The wind has a strong influence: the speed of sound in the direction of the wind increases, against the wind it decreases. The presence of wind in the atmosphere causes the sound wave to drift, which gives the impression that the sound source has shifted. The speed of sound in this case (c1) is determined by the expression:
  c1 = c + U cos ?, (1)
  where U is the wind speed; ? — the angle between the wind direction at the observation point and the observed direction of sound arrival.
  Knowing the speed of sound propagation in the atmosphere has great importance when solving a number of problems in studying upper layers atmosphere using the acoustic method. Taking advantage average speed sound in the atmosphere, you can find out the distance from your location to the place where thunder occurs. To do this, you need to determine the number of seconds between the visible flash of lightning and the moment the sound of thunder arrives. Then you need to multiply the average speed of sound in the atmosphere - 333 m/sec. for the resulting number of seconds.

  Today, when setting up an apartment, many new residents are forced to spend additional work, including soundproofing your home, because The standard materials used make it possible to only partially hide what is going on in your own home, and not to be interested in the communication of your neighbors against your will.

  In solids, it is affected at least by the density and elasticity of the substance resisting the wave. Therefore, when equipping premises, the layer adjacent to the load-bearing wall is made soundproof with “overlaps” at the top and bottom. It allows you to reduce decibels sometimes by more than 10 times. Then basalt mats are laid, and plasterboard sheets are placed on top, which reflect the sound outward from the apartment. When a sound wave “flies up” to such a structure, it is attenuated in the insulator layers, which are porous and soft. If the sound has great strength, then the materials that absorb it can even heat up.

  Elastic substances, such as water, wood, metals, transmit well, so we hear beautiful “singing” musical instruments. And some peoples in the past determined the approach of, for example, horsemen, by putting their ear to the ground, which is also quite elastic.

  

  The speed of sound in km depends on the characteristics of the medium in which it propagates. In particular, the process can be affected by its pressure, chemical composition, temperature, elasticity, density and other parameters. For example, in a steel sheet a sound wave travels at a speed of 5100 meters per second, in glass - about 5000 m/s, in wood and granite - about 4000 m/s. To convert speed to kilometers per hour, you need to multiply the figures by 3600 (seconds per hour) and divide by 1000 (meters per kilometer).

  Speed ​​of sound in km in aquatic environment different for substances with different salinities. For fresh water at a temperature of 10 degrees Celsius it is about 1450 m/s, and at a temperature of 20 degrees Celsius and the same pressure it is already about 1490 m/s.

  A salty environment is characterized by a obviously higher speed of sound vibrations.

  The propagation of sound in air also depends on temperature. With a value of 20 for this parameter, sound waves travel at a speed of about 340 m/s, which is about 1200 km/h. And at zero degrees the speed slows down to 332 m/s. Returning to our apartment insulators, we can learn that in a material such as cork, which is often used to reduce external noise levels, the speed of sound in km is only 1800 km/h (500 meters per second). This is ten times lower than this characteristic in steel parts.

  

  A sound wave is a longitudinal vibration of the medium in which it propagates. When, for example, the melody of a piece of music passes through some obstacle, its volume level decreases, because changes. At the same time, the frequency remains the same, thanks to which we hear a woman’s voice as a woman’s, and a man’s as a man’s. The most interesting place is where the speed of sound in km is close to zero. This is a vacuum in which waves of this type almost do not propagate. To demonstrate how this works, physicists place a ringing alarm clock under a hood from which the air is pumped out. The thinner the air, the quieter the bell is heard.