speed of sound [′spēd əv ′sau̇nd]
Speed of Sound
the speed of propagation of the phase of a sound wave. It thus represents a phase velocity, in contrast to a group velocity. The speed of sound is usually a constant for a given substance under specified external conditions and usually does not depend on the frequency and amplitude of the wave. When the speed of sound is dependent on the frequency, we speak of the dispersion of sound.
In gases and liquids, sound usually propagates adiabati-cally—that is, the temperature changes associated with compressions and rarefactions in the sound wave do not even out in one period. The speed of sound in this case can be expressed as follows:
Here, Kad is the adiabatic bulk modulus, ρ is the density, βad is the adiabatic compressibility, βis = γβad is the isothermal compressibility, and γ = cp/cv is the ratio of the specific heat at constant pressure cp to the specific heat at constant volume cv.
The speed of sound in an ideal gas is given by Laplace’s formula:
where p0 is the average pressure in the medium, R is the universal gas constant, T is the absolute temperature, and μ is the molecular weight of the gas. Newton’s formula for the speed of sound is obtained when γ = 1; this formula is based on the assumption that the propagation process has an isothermal character. The difference between adiabatic and isothermal processes can usually be ignored in the case of liquids.
| Table 1. Speed of sound in gases at 0°C and a pressure of 1 atmosphere | |
|---|---|
| Gas | c (m/sec) |
| Nitrogen..................................... | 334 |
| Oxygen .................................. | 316 |
| Air..................... | 331 |
| Helium .................... | 965 |
| Hydrogen ............................. | 1,284 |
| Methane.................................. | 430 |
| Ammonia ................................... | 415 |
The speed of sound is lower in gases than in liquids and is generally lower in liquids than in solids. For this reason, the speed of sound increases when a gas undergoes liquefaction. Tables 1 and 2 give the values of the speed of sound for some gases and liquids. For cases where acoustic dispersion occurs, the tables give the speed of sound at low frequencies, where the period of the sound wave is longer than the relaxation time.
| Table 2. Speed of sound in liquids at 20°C | |
|---|---|
| Liquid | c (m/sec) |
| Water..................................... | 1,490 |
| Benzene .................................... | 1,324 |
| Ethyl alcohol ................................ | 1,180 |
| Carbon tetrachloride ....................... | 920 |
| Mercury .................................... | 1,453 |
| Glycerol .................................... | 1,923 |
In gases, the speed of sound increases as the temperature and pressure increase. In liquids, the speed of sound generally decreases as the temperature increases. Water is an exception to this rule. The speed of sound in water increases as the temperature rises to 74°C; with a further increase in temperature, the speed of sound decreases. In seawater, the speed of sound depends on the temperature, salinity, and depth. This dependence determines the paths of sound beams in seawater and is the reason for the existence of underwater sound channels.
In mixtures of gases or liquids, the speed of sound depends on the concentrations of the components of the mixture.
The speed of sound in isotropic solids is determined by the moduli of elasticity and the density of the substance. In an unbounded solid medium, both longitudinal waves and shear (transverse) waves are propagated. In this case, the longitudinal wave has the speed
and the shear wave has the speed
Here, E is Young’s modulus, G is the shear modulus, ν is Pois-son’s ratio, and K is the bulk modulus. The speed of propagation of longitudinal waves is always higher than the speed of shear waves (see Table 3).
The speed of sound in single crystal solids depends on the direction of wave propagation relative to the crystallographic axes. In many substances, the speed of sound depends on the presence of impurities. In metals and alloys, the speed of sound strongly depends on the processing to which the metal has been subjected—for example, rolling, forging, or annealing.
Measurements of the speed of sound are used in determining many properties of materials. The measurement of small changes in the speed of sound is a sensitive method for detecting the presence of impurities in gases and liquids. In solids, measurements of the speed of sound and of the speed’s dependence on various factors permit investigation of, for example, the band structure of semiconductors and the structure of Fermi surfaces in metals. A number of industrial applications of ultrasound in the areas of measurement and inspection are based on measurements of the speed of sound.
The above discussion pertains to the propagation of sound in a continuous medium—that is, the speed of sound is a macroscopic characteristic of the medium. In actuality, materials are not continuous; their discreteness makes it necessary to consider elastic vibrations of other types. In a solid, the concept of the speed of sound pertains only to the acoustical branch of the lattice vibrations.
REFERENCES
Landau, L. D., and E. M. Lifshits. Mekhanika sploshnykh sred, 2nd ed. Moscow, 1953.Mikhailov, I. G., V. A. Solov’ev, and Iu. P. Syrnikov. Osnovy molekuliarnoi akustiki. Moscow, 1964.
Kolesnikov, A. E. Ultrazvukovye izmereniia. Moscow, 1970.
Isakovich, M. A. Obshchaia akustika. Moscow, 1973.
A. L. POLIAKOVA
Want to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit the webmaster's page for free fun content.
| ?Page tools | ||
|---|---|---|
|