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Speed of sound

The speed of sound 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).

More commonly the term refers to the speed of sound in air. In this case the physical properties of the air, its pressure and humidity for instance, affect the speed. An approximate speed (in metres/second) can be calculated from:

where T is the temperature in degrees Celsius

A more accurate expression is

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 288.2 K, giving a value of 340 m/s.

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

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 343 m/s, or 750 miles/hour.

In solids the speed of sound is given by:

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

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.