History of sound speed measurements. Now we know what speed is and what sound is, so let's put these concepts together

4800 17280.0 Carbon dioxide 259 932.4 Chlorine 206 741.6

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.

History of sound speed measurements

Already in ancient authors there is an indication that sound is caused by the oscillatory movement of the body (Ptolemy, Euclid). Aristotle notes that the speed of sound has a finite value, and correctly imagines the nature of sound. Attempts experimental determination sound speeds date back to the first half of the 17th century. F. Bacon in his “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, 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

Check information.

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

$c\; =\; \backslash sqrt(\backslash frac(1)(\backslash beta\; \backslash rho))$

In partial derivatives:

$c\; =\; \backslash sqrt(-v^2\; \backslash left(\backslash frac(\backslash partial\; p)(\backslash partial\; v)\backslash right)\_s)\; =\; \backslash sqrt(-v^2\; \backslash frac(Cp)(Cv)\; \backslash left(\backslash frac\; (\backslash partial\; p)(\backslash partial\; v)\backslash right)\_T)$

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

Solids

In multiphase media, due to the phenomena of inelastic energy absorption, the speed of sound, generally speaking, depends on the oscillation frequency (that is, velocity dispersion is observed). For example, estimating the velocity of elastic waves in a two-phase porous medium can be performed using the equations of the Bio-Nikolaevsky theory. At sufficiently high frequencies (above Bio frequencies ) in such a medium not only longitudinal and transverse waves arise, but also a longitudinal wave of the second kind. At oscillation frequency below Bio frequencies , the speed of elastic waves can be approximately estimated using the much simpler Gassmann equations.

In the presence of interfaces, elastic energy can be transferred through 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.

Speed ​​of sound in water

Sometimes they also use the simplified Leroy formula:

$c\; =\; 1492.9\; +\; 3(T-10)\; -\; 0.006(T-10)^2\; -\; 0.04(T-18)^2\; +\; 1.2(S-35)\; -\; 0.01(T-18)\; (S-35)\; +\; z/61$,

Where z- depth in meters. This formula provides an accuracy of about 0.1 m/s for T < 20 °C и z < 8 000 м.

At a temperature of 24 °C, a salinity of 35 ppm and zero depth, the speed of sound is about 1,532.3 m/s. At T= 4 °C, a depth of 100 m and the same salinity, the speed of sound is 1,468.5 m/s.

see also

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Notes

Literature

• Landau L. D., Lifshits E. M., Mechanics continuum, 2nd ed., M., 1953;
• Mikhailov I. G., Solovyov V. A., Syrnikov Yu. P., Fundamentals of molecular acoustics, M., 1964;
• Kolesnikov A.E., Ultrasonic measurements, M., 1970;
• Isakovich M. A., General acoustics, M., 1973.

Links

An excerpt characterizing the speed of sound

“God willing, God willing,” said Anna Pavlovna. L "homme de beaucoup de merite, still a newcomer to court society, wanting to flatter Anna Pavlovna, shielding her previous opinion from this judgment, said.
- They say that the sovereign reluctantly transferred this power to Kutuzov. On dit qu"il rougit comme une demoiselle a laquelle on lirait Joconde, en lui disant: “Le souverain et la patrie vous dekernent cet honneur.” [They say that he blushed like a young lady to whom Joconde would be read, while told him: “The sovereign and the fatherland reward you with this honor.”]
“Peut etre que la c?ur n"etait pas de la partie, [Perhaps the heart was not fully involved],” said Anna Pavlovna.
“Oh no, no,” Prince Vasily interceded hotly. Now he could no longer give up Kutuzov to anyone. According to Prince Vasily, not only was Kutuzov himself good, but everyone adored him. “No, this cannot be, because the sovereign knew how to value him so much before,” he said.
“God only grant that Prince Kutuzov,” said Anpa Pavlovna, “takes real power and does not allow anyone to put a spoke in his wheels - des batons dans les roues.”
Prince Vasily immediately realized who this nobody was. He said in a whisper:
- I know for sure that Kutuzov, as an indispensable condition, ordered that the heir to the crown prince not be with the army: Vous savez ce qu"il a dit a l"Empereur? [Do you know what he said to the sovereign?] - And Prince Vasily repeated the words that Kutuzov allegedly said to the sovereign: “I cannot punish him if he does something bad, and reward him if he does something good.” ABOUT! This the smartest person, Prince Kutuzov, et quel caractere. Oh je le connais de longue date. [and what a character. Oh, I've known him for a long time.]
“They even say,” said l “homme de beaucoup de merite, who did not yet have court tact, “that His Serene Highness made it an indispensable condition that the sovereign himself should not come to the army.
As soon as he said this, in an instant Prince Vasily and Anna Pavlovna turned away from him and sadly, with a sigh about his naivety, looked at each other.

While this was happening in St. Petersburg, the French had already passed Smolensk and were moving closer and closer to Moscow. The historian of Napoleon Thiers, just like other historians of Napoleon, says, trying to justify his hero, that Napoleon was drawn to the walls of Moscow involuntarily. He is right, as are all historians who seek an explanation of historical events in the will of one person; he is just as right as Russian historians who claim that Napoleon was attracted to Moscow by the art of Russian commanders. Here, in addition to the law of retrospectivity (recurrence), which represents everything that has passed as preparation for an accomplished fact, there is also reciprocity, which confuses the whole matter. A good player who has lost at chess is sincerely convinced that his loss was due to his mistake, and he looks for this mistake at the beginning of his game, but forgets that in every step of his, throughout the entire game, there were the same mistakes that none his move was not perfect. The error to which he draws attention is noticeable to him only because the enemy took advantage of it. How much more complex than this is the game of war, taking place in certain conditions of time, and where it is not one will that guides lifeless machines, but where everything stems from countless collisions of various arbitrarinesses?
After Smolensk, Napoleon sought battles beyond Dorogobuzh at Vyazma, then at Tsarev Zaymishche; but it turned out that due to countless conflicts of circumstances, the Russians could not accept the battle before Borodino, one hundred and twenty versts from Moscow. Napoleon ordered from Vyazma to move directly to Moscow.
Moscou, la capitale asiatique de ce grand empire, la ville sacree des peuples d "Alexandre, Moscou avec ses innombrables eglises en forme de pagodes chinoises! [Moscow, the Asian capital of this great empire, the sacred city of the peoples of Alexander, Moscow with its countless churches, in the form of Chinese pagodas!] This Moscou haunted the imagination of Napoleon. On the transition from Vyazma to Tsarev Zaimishche, Napoleon rode on his nightingale anglicized pacer, accompanied by guards, guards, pages and adjutants. The chief of staff, Berthier, fell behind in order to interrogate a Russian prisoner taken by the cavalry. He galloped, accompanied by the translator Lelorgne d'Ideville, caught up with Napoleon and stopped his horse with a cheerful face.
- Eh bien? [Well?] - said Napoleon.
– Un cosaque de Platow [Platov Cossack] says that Platov’s corps is united with big army that Kutuzov was appointed commander-in-chief. Tres intelligent et bavard! [Very smart and talkative!]
Napoleon smiled and ordered to give this Cossack a horse and bring him to him. He himself wanted to talk to him. Several adjutants galloped off, and an hour later Denisov’s serf, whom he had given over to Rostov, Lavrushka, in a batman’s jacket on a French cavalry saddle, with a roguish and drunken, cheerful face, rode up to Napoleon. Napoleon ordered him to ride next to him and began to ask:
-Are you a Cossack?
- Cossack s, your honor.
“Le cosaque ignorant la compagnie dans laquelle il se trouvait, car la simplicite de Napoleon n"avait rien qui put reveler a une imagination orientale la presence d"un souverain, s"entretint avec la plus extreme familiarite des affaires de la guerre actuelle" , [The Cossack, not knowing the society in which he found himself, because Napoleon’s simplicity had nothing that could reveal to the Eastern imagination the presence of the sovereign, spoke with extreme familiarity about the circumstances real war.] says Thiers, narrating this episode. Indeed, Lavrushka, who got drunk and left the master without dinner, was flogged the day before and sent to the village to get chickens, where he became interested in looting and was captured by the French. Lavrushka was one of those rude, insolent lackeys who have seen all sorts of things, who consider it their duty to do everything with meanness and cunning, who are ready to do any service for their master and who cunningly guess the master's bad thoughts, especially vanity and pettiness.
Once in the company of Napoleon, whose personality he recognized very well and easily. Lavrushka was not at all embarrassed and only tried with all his heart to serve the new masters.
He knew very well that it was Napoleon himself, and the presence of Napoleon could not confuse him more than the presence of Rostov or the sergeant with rods, because he had nothing that neither the sergeant nor Napoleon could deprive him of.
He lied about everything that was said between the orderlies. Much of this was true. But when Napoleon asked him how the Russians thought, whether they would defeat Bonaparte or not, Lavrushka squinted and thought.
He saw subtle cunning here, as people like Lavrushka always see cunning in everything, he frowned and was silent.
“It means: if there is a battle,” he said thoughtfully, “and in speed, then it’s so accurate.” Well, if three days pass after that very date, then it means that this very battle will be delayed.
It was translated to Napoleon as follows: “Si la bataille est donnee avant trois jours, les Francais la gagneraient, mais que si elle serait donnee plus tard, Dieu seul sait ce qui en arrivrait” [“If the battle occurs before three days, the French will win him, but if after three days, then God knows what will happen.”] - smilingly conveyed Lelorgne d "Ideville. Napoleon did not smile, although he was apparently in the most cheerful mood, and ordered these words to be repeated to himself.
Lavrushka noticed this and, to cheer him up, said, pretending that he did not know who he was.
“We know, you have Bonaparte, he beat everyone in the world, well, that’s another story about us...” he said, not knowing how and why in the end, boastful patriotism slipped into his words. The translator conveyed these words to Napoleon without ending, and Bonaparte smiled. “Le jeune Cosaque fit sourire son puissant interlocuteur,” [The young Cossack made his powerful interlocutor smile.] says Thiers. Having walked a few steps in silence, Napoleon turned to Berthier and said that he wanted to experience the effect that would have sur cet enfant du Don [on this child of the Don] the news that the person with whom this enfant du Don was speaking was the Emperor himself , the same emperor who wrote the immortally victorious name on the pyramids.
The news was transmitted.
Lavrushka (realizing that this was done to puzzle him, and that Napoleon thought that he would be afraid), in order to please the new gentlemen, immediately pretended to be amazed, stunned, bulged his eyes and made the same face that he was accustomed to when he was led around flog. “A peine l"interprete de Napoleon," says Thiers, "avait il parle, que le Cosaque, saisi d"une sorte d"ebahissement, no profera plus une parole et marcha les yeux constamment attaches sur ce conquerant, dont le nom avait penetre jusqu"a lui, a travers les steppes de l"Orient. Toute sa loquacite s"etait subitement arretee, pour faire place a un sentiment d"admiration naive et silencieuse, apres l"avoir recompense, lui fit donner la liberte. , comme a un oiseau qu"on rend aux champs qui l"ont vu naitre". [As soon as Napoleon’s translator said this to the Cossack, the Cossack, overcome by some kind of stupor, did not utter a single word and continued to ride, not taking his eyes off the conqueror, whose name had reached him through the eastern steppes. All his talkativeness suddenly stopped and was replaced by a naive and silent feeling of delight. Napoleon, having rewarded the Cossack, ordered him to be given freedom, like a bird that is returned to its native fields.]

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.

Encyclopedic YouTube

• 1 / 5

  Already in ancient authors there is an indication that sound is caused by the oscillatory movement of the body (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 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, 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 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 body waves.

  Most people understand perfectly well what sound is. It is associated with hearing and is associated with physiological and psychological processes. The brain processes sensations that come through the hearing organs. The speed of sound depends on many factors.

  Sounds distinguished by people

  IN in a general sense words sound is physical phenomenon, which causes effects on the hearing organs. It has the form of longitudinal waves of different frequencies. People can hear sound whose frequency ranges from 16-20,000 Hz. These elastic longitudinal waves, which propagate not only in 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 those above 20,000 Hz are called ultrasound. Their human ear can't hear.

  Sound characteristics

  

  There are two main characteristics of sound: volume and pitch. The first of them is related to the intensity of the elastic sound wave. There is another important indicator. Physical size, 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. It varies in different environments. It represents the speed of propagation of elastic sound waves. In a gaseous environment this figure will be less than in liquids. Speed ​​of sound in solids the tallest. Moreover, for longitudinal waves it is always greater than for transverse ones.

  Speed ​​of propagation of sound waves

  This indicator depends on the density of the medium and its elasticity. IN gas media ah, 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 in rare cases When these characteristics have an influence, we speak of 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 hard materials- 2000-6500 m/s. IN normal conditions the speed of sound in air reaches 331 m/s. In ordinary water - 1500 m/s.

  Speed ​​of sound waves in different chemical media

  

  The speed of sound propagation in different chemical environments 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 carbon dioxide - 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 as T increases by several meters per second. Speed ​​of sound (m/s) in liquid media (at a temperature of 20°C):

  Water - 1490;

  Ethyl alcohol - 1180;

  Benzene - 1324;

  Mercury - 1453;

  Carbon tetrachloride - 920;

  Glycerin - 1923.

  The only exception to the above rule is water, in which the speed of sound increases with increasing temperature. It reaches its maximum when this liquid is heated to 74°C. With a further increase in temperature, the speed of sound decreases. As the pressure increases, it will increase by 0.01%/1 Atm. In the salty sea ​​water As temperature, depth and salinity increase, the speed of sound will also increase. In other environments, this indicator changes differently. Thus, 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 unconfined dense media. Speed ​​of sound (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 the 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, since it simply does not propagate in such a medium.

  Determination of the speed of sound

  

  Everything related to sound signals interested our ancestors thousands of years ago. Almost all outstanding scientists worked to determine the essence of this phenomenon. ancient world. Even ancient mathematicians established that sound is determined by oscillatory movements bodies. Euclid and Ptolemy wrote about this. Aristotle established that the speed of sound has a finite value. First attempts to define this indicator were undertaken by F. Bacon in the 17th century. He tried to establish the speed by comparing the time intervals between the sound of the gunshot and the flash of light. Based on this method, a group of physicists Paris Academy Sciences first determined the speed of a sound wave. IN different conditions experiment it was 350-390 m/s. Theoretical background the speed of sound was first considered by I. Newton in his Principia. Produce correct definition P.S. achieved this indicator. Laplace.

  Sound speed formulas

  For gaseous media and liquids in which sound propagates, as a rule, adiabatically, the temperature change associated with tension and compression in a longitudinal wave cannot quickly equalize over a short period of time. Obviously, this indicator 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 adiabatic compressibility, ρ is the density of the medium.

  

  In partial derivatives given value is calculated using the following formula:

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

  where ρ, T, υ - the pressure of the medium, its temperature and specific volume; S - entropy; Cp - isobaric heat capacity; Cυ - isochoric heat capacity. For gas 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 adiabatic value: 4/3 for polyatomic gases, 5/3 for monatomic gases, 7/5 for diatomic gases (air); R - gas constant (universal); T- absolute temperature, measured in kelvins; k- Boltzmann constant; t - temperature in °C; M- molar mass; m- molecular mass; ά 2 = ζR/ M.

  Determination of the speed of sound in a solid

  In a solid body that is homogeneous, there are two types of waves that differ in the polarization of vibrations 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 - compression, Young, shear moduli; v - Poisson's ratio. When calculating the speed of sound in a solid, adiabatic elastic moduli are used.

  Speed ​​of sound in multiphase media

  

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

  Conclusion

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

  Numerous measurements of the speed of sound in various gaseous, liquid and homogeneous solids show that it does not depend on frequency (or wavelength), i.e. there is no dispersion for sound waves. Dispersion was found only for polyatomic gases and liquids at ultrasonic frequencies. We will limit ourselves to studying the propagation of sound waves in media without dispersion. Then, to calculate the speed of propagation of a sound wave, we can use the dependencies we obtained for the speeds of propagation of individual pulses in elastic media. For solid media:

  (1)

  In liquid and gaseous media, sound propagation occurs adiabatically, since due to rapid changes in compression and rarefaction, heat exchange between the disturbed and undisturbed parts of the medium does not have time to establish itself.

  For liquid media:

  (2)

  Where k - volumetric compression modulus, - adiabatic volumetric compression ratio. For gaseous media:

  WITH=
  (3)

  -adiabatic bulk modulus. In liquid and gaseous bodies, the speed of sound changes with temperature.

  For gas, the law of Boyle - Mariotte and Gay-Lussac, known from elementary physics, holds:

  Vp=
  

  V-- gas volume, p - pressure, - coefficient of thermal expansion.

  If the mass of a gas remains constant when its volume changes, then its density is inversely proportional to the volume. And then

  

  Instead of relation (3) we get:

  C=
  (4)

  The dependence of the speed of sound on temperature for liquids is more complex.

  The speed of sound in solids for longitudinal and transverse waves differs sharply. (This circumstance is used, in particular, when processing seismograms, to find the epicenter of an earthquake and to study the internal structure of the Earth.)

  Measuring the speed of sound in air can be done using echo. To do this, measure the time interval t between sending a signal (scream, shot, etc.) and its return after reflection from an obstacle (mountain, edge of a dense forest, river bank, etc.).

  Knowing the distance from the point where the signal is sent to the obstacle, it is easy to calculate the speed of sound:

  C= (5)

  The speed of sound in air and water is determined quite accurately if simultaneously with sound it is sent from the point A and a light signal - a flash visible from point B, where sound is received. Since the speed of light is of the order of 3-10 8 m/sec, and speed of sound 3-10 2 m/sec, i.e., it is 0.0001% of the speed of light, then in such an experiment light can be considered to propagate instantly. Then, measuring at point IN time t between the arrival of light and sound signals and knowing the distance
  It's easy to calculate the speed of sound:

  C=(6)

  If we have a sound source sending waves with a known frequency , and we can somehow measure the wavelength in the medium, then the speed of sound propagation can be easily calculated using the formula:

  C=
  (7)

  The speed of sound in air can be measured using the setup shown in Figure 1.

  

  Part of the glass cylinder connected to the tank is filled with water, the level of which can be changed. A telephone receiver is brought to the open end of the cylinder, the membrane of which vibrates at a known frequency. The oscillation frequency of the membrane is set by an electric sound frequency generator (a tube device that produces alternating currents with frequencies in the audio range). The wave coming from the membrane and the wave reflected from the surface of the water interfere in the air column above the water. If the height of the air column is such that an odd number of quarter waves fit on it, then standing waves arise in it with a node at the surface of the water and with an antinode at the open end of the cylinder. At this moment, the column in the cylinder sounds most intensely, since at the open end there is an antinode of displacements and velocities of particles and the conditions for the release of energy into the surrounding space are the most favorable. As the water level in the tube changes, the sound decreases. The sound again intensifies to its maximum when the water level shifts by a distance of half a wave and an odd number of quarter waves again fits into the air column. Knowing the vibration frequency of the membrane set by the generator and the length

  half waves
  we find from equation (7) the speed C=2
  

  The field of sound waves can be made visible using the so-called Toepler's method. The installation for these purposes is shown in Figure 2.

  

  The slit S is illuminated by a light source I through a lens L, the focus of which coincides with S. The lens , whose focus also coincides with S, sends a parallel beam of rays; in the plane A using the lens obtain an image of the slit. The image of the gap is covered with a curtain D so that the light does not hit the screen. If now in a ditch TO create heterogeneity in the medium, then the rays, passing through it, will deviate from the original path and, passing by the curtain, will give an image of heterogeneity on the screen. If the inhomogeneity of the medium is created by alternating compression and rarefaction in a standing sound wave, then light and dark stripes are clearly visible in the image of the sound field.

  Measuring the speed of sound using echo is used in one of the so-called pulse methods. For the first time, ultraacoustic pulses were used in research practice by S. Ya. Sokolov to study the propagation of sound in solids. The quartz vibration is excited by a generator that sends not a continuous wave, but a short-term pulse consisting of several quickly decaying electromagnetic waves. The pulse applied to the quartz is simultaneously applied to the vertical plates of the oscilloscope E, and at the moment quartz oscillations occur, a sharp “spike” appears on the oscilloscope screen. The pulse propagates from the quartz through the medium under study to the reflector (Fig. 2) and returns back to the quartz. The operation of the generator is calculated so that by the time the reflected pulse returns, the quartz is at rest. Then the returning pulse excites oscillations of the quartz, which at this moment is connected to the oscilloscope, and a second “burst” appears on the screen. Thus, two “bursts” are visible on the screen: one corresponding to the moment the impulse was sent, the other to the moment it returned after reflection. High-frequency pulses are supplied to the oscilloscope plates from a special generator, creating low “bursts” on the oscilloscope screen, spaced from each other by equal distances. They serve as time stamps. Knowing their frequency, you can count the time t impulse path. Then the speed of sound is calculated using formula (5), where - distance between quartz and reflector.

  Thus, the elastic properties of a metal rod are not the same during torsion, compression and bending. And corresponding wave vibrations spread at different speeds.

  Elastic is a medium in which deformation, be it torsion, compression or bending, is proportional to the force causing the deformation.

  Sound speed V For of this type elastic deformation is given by

  Where WITH- modulus of elasticity, depending on the material and type of deformation.
  r- density of the material (mass per unit volume).

  Speed ​​of sound in a solid rod

  A long rod can be stretched or compressed by a force applied to the end. Let the length of the rod be L, applied tensile force - F, and the increase in length - D.L.. Size DL/L we will call the relative deformation, and the force per unit area cross section rod - tension. So the voltage is F/A, Where A- cross-sectional area of ​​the rod. When applied to such a rod, Hooke's law has the form

  Where Y- Young's modulus, i.e. modulus of elasticity of a rod for tension or compression, characterizing the material of the rod. Young's modulus is small for easily stretchable materials, such as rubber, and large for rigid materials, such as steel.

  If we now excite a compression wave in it by hitting the end of the rod with a hammer, it will propagate at a speed where r, as before, is the density of the material from which the rod is made. Wave speed values ​​for some standard materials are given in the table.

  Speed ​​of sound for different types waves in solid materials
  Material	Longitudinal waves in extended solid samples (m/s)	Shear and torsion waves (m/s)	Compression waves in rods (m/s)
  Aluminum	6420	3040	5000
  Brass	4700	2110	3480
  Lead	5950	3240	5120
  Iron	1960	690	1210
  Silver	3650	1610	2680
  Stainless steel	5790	3100	5000
  Flintglass	3980	2380	3720
  Crown glass	5100	2840	4540
  Plexiglas	2680	1100	1840
  Polyethylene	1950	540	920
  Polystyrene	2350	1120	2240

  The considered wave in the rod is a compression wave. But it cannot be considered strictly longitudinal, since the movement of the lateral surface of the rod is associated with compression.

  

  Types of wave motion

  Two other types of waves are also possible in a rod - a bending wave and a torsion wave. Bending deformations correspond to a wave that is neither purely longitudinal nor purely transverse. Torsional deformations, i.e. rotation around the axis of the rod gives a purely transverse wave.

  The speed of the bending wave in the rod depends on the wavelength. Such a wave is called "dispersive".

  Torsion waves in the rod are purely transverse and non-dispersive. Their speed is given by the formula

  Where m- shear modulus, characterizing the elastic properties of the material with respect to shear. Some typical shear wave velocities are given in the table.

  Speed ​​in extended solid media

  In large-volume solid media, where the influence of boundaries can be neglected, elastic waves of two types are possible: longitudinal and transverse.

  Deformation in a longitudinal wave- this is a plane deformation, i.e. one-dimensional compression (or rarefaction) in the direction of wave propagation. Deformation corresponding transverse wave, is the shear displacement perpendicular to the direction of wave propagation.

  The velocity of longitudinal waves in solid materials is given by

  Where C L- modulus of elasticity for simple plane strain. It is related to the bulk modulus IN(defined below) and shear modulus m material ratio C L = B + 4/3m. The table shows the velocities of longitudinal waves for various solid materials.

  The speed of shear waves in extended solid media is the same as the speed of torsion waves in a rod of the same material. Therefore it is given by expression. Its values ​​for ordinary solid materials are given in the table above.

  Gas speed

  In gases, only one type of deformation is possible: compression - rarefaction. Corresponding modulus of elasticity IN called the bulk modulus. It is determined by the relation

  -DP = B(DV/V)

  Here D.P.- pressure change, DV/V- relative change in volume. The minus sign indicates that as pressure increases, volume decreases.

  Velocity in liquids

  Sound waves in liquids are compression-rarefaction waves, as in gases. The speed is given by the same formula. However, a liquid is much less compressible than a gas, and therefore many times larger value IN, more and density r. The speed of sound in liquids is closer to the speed in solids than in gases. It is much less than in gases and depends on temperature. For example, the speed in fresh water is 1460 m/s at 15.6°C. In sea water of normal salinity it is 1504 m/s at the same temperature. The speed of sound increases with increasing