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Speed of sound

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The speed of sound c (mostly in air) varies depending on the medium through which the sound waves pass. It is usually quoted in describing properties of substances (e.g. see the article on sodium). Velocity of sound is not speed of sound.

More commonly the term refers to the speed of sound in air. The humidity affects very little the speed of sound nor does it the static sound pressure, but most important is the temperature. Sound travels slower with an increased altitude (elevation if you're on solid earth). This is primarily a function of temperature and humidity changes and not the sound pressure. An approximate speed (in metres/second) can be calculated from:

c a i r = ( 331 . 5 + 0 . 6   ⋅ ϑ )   m / s {\displaystyle c_{\mathrm {air} }=(331{.}5+0{.}6\ \cdot \vartheta )\ \mathrm {m/s} }

where ϑ {\displaystyle \vartheta } (theta) is the temperature in degrees Celsius.

A more accurate expression is

c = γ R T {\displaystyle c={\sqrt {\gamma RT}}}

where R is the gas constant (287 J/kgK for air), γ is the adiabatic index (1.4 for air), and T is the absolute temperature in kelvin. In the standard atmosphere, T0 is 298.15 K, giving a value of 346 m/s (25°C = 77°F).

In fact, assuming a perfect gas the speed of sound depends on temperature only. Air is almost a perfect gas.

In fluids, using the theory of compressible flow, the speed of sound can be calculated using

c = γ p ρ {\displaystyle c={\sqrt {{\gamma p} \over \rho }}}

This is correct for adiabatic flow; Newton famously used isothermal calculations and omitted the γ from the numerator.

The speed of sound is typically measured given a "standard atmosphere". Under these conditions the speed of sound is approximately 346 m/s at 25°C, or 750 miles/hour. Speed of sound is not dependent on the air pressure.

In solids the speed of sound is given by:

c = E ρ {\displaystyle c={\sqrt {\frac {E}{\rho }}}}

where E is Young's modulus and ρ is density. Thus in steel the speed of sound is approximately 5100 m/s.
For air, see density of air.

The speed of sound in water is of interest to those mapping the ocean floor. In saltwater, sound travels at about 1500 m/s and in freshwater 1435 m/s. These speeds vary due to pressure, depth, temperature, salinity and other factors.

See also Mach number.

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