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speed of sound

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Symbol c or cs. The speed at which sound waves are propagated through a material medium. In air at 20°C sound travels at 344 m s−1, in water at 20°C it travels at 1461 m s−1, and in steel at 20°C at 5000 m s−1. The speed of sound in a medium depends on the medium's modulus of elasticity (E) and its density (ρ) according to the relationship c = √(E/ρ). For longitudinal waves in a narrow solid specimen, E is the Young modulus; for a liquid E is the bulk modulus (see elastic modulus); and for a gas E = γp, where γ is the ratio of the principal specific heat capacities and p is the pressure of the gas. For an ideal gas the relationship takes the form c = √(γrT), where r is the gas constant per unit mass and T is the thermodynamic temperature. This equation shows how the speed of sound in a gas is related to its temperature. This relationship can be written c = c0√(1 + t/273), where c0 is the speed of sound in a particular gas at 0°C and t is the temperature in °C.

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