Speed of Sound (air, ideal gases)

Description

The speed of sound is the distance travelled per unit time by a sound wave propagating through an elastic medium. The SI unit of the speed of sound is the metre per second (m/s). In dry air at 20 °C, the speed of sound is 343.2 metres per second (1,126 ft/s). This is 1,236 kilometres per hour (768 mph; 667 kn), or a kilometre in 2.914 s or a mile in 4.689 s.

The speed of sound in an ideal gas is independent of frequency, but does vary slightly with frequency in a real gas. It is proportional to the square root of the absolute temperature, but is independent of pressure or density for a given ideal gas. Sound speed in air varies slightly with pressure only because air is not quite an ideal gas. Although (in the case of gases only) the speed of sound is expressed in terms of a ratio of both density and pressure, these quantities cancel in ideal gases at any given temperature, composition, and heat capacity. This leads to a velocity formula for ideal gases which includes only the latter independent variables.

In common everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies from substance to substance. Sound travels faster in liquids and non-porous solids than it does in air. It travels about 4.3 times as fast in water (1,484 m/s), and nearly 15 times as fast in iron (5,120 m/s), as in air at 20 °C. Sound waves in solids are composed of compression waves (just as in gases and liquids), but there is also a different type of sound wave called a shear wave, which occurs only in solids. These different types of waves in solids usually travel at different speeds, as exhibited in seismology. The speed of a compression sound wave in solids is determined by the medium’s compressibility, shear modulus and density. The speed of shear waves is determined only by the solid material’s shear modulus and density.

In fluid dynamics, the speed of sound in a fluid medium (gas or liquid) is used as a relative measure for the speed of an object moving through the medium. The speed of an object divided by the speed of sound in the fluid is called the Mach number. Objects moving at speeds greater than Mach1 are travelling at supersonic speeds.

Related formulas

Variables

cSpeed of sound (m/s)
γRatio of specific heats(adiabatic index) (dimensionless)
pPressure (Pa)
ρDensity (kg/m3)