Sound Speed in GasesThe speed of sound in an ideal gas is given by the relationship
For air, the adiabatic constant γ = 1.4 and the average molecular mass for dry air is 28.95 gm/mol. This leads to Doing this calculation for air at 0°C gives v_{sound} = 331.39 m/s and at 1°C gives v_{sound} = 332.00 m/s. This leads to a commonly used approximate formula for the sound speed in air: For temperatures near room temperature, the speed of sound in air can be calculated from this convenient approximate relationship, but the more general relationship is needed for calculations in helium or other gases. The calculation above was done for dry air, and moisture content in the air would be expected to increase the speed of sound slightly because the molecular weight of water vapor is 18 compared to 28.95 for dry air. A revised average molecular weight could be calculated based on the vapor pressure of water in the air. However, the assumption of an adiabatic constant of γ = 1.4 used in the calculation is based upon the diatomic molecules N_{2} and O_{2} and does not apply to water molecules. So the detailed modeling of the effect of water vapor on the speed of sound would have to settle on an appropriate value of γ to use.

Index Traveling wave concepts Sound propagation concepts  

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Sound Speed in an Ideal GasThe speed of sound for a uniform medium is determined by its elastic property (bulk modulus) and its density When a sound travels through an ideal gas, the rapid compressions and expansions associated with the longitudinal wave can reasonably be expected to be adiabatic and therefore the pressure and volume obey the relationship The adiabatic assumption for sound waves just means that the compressions associated with the sound wave happen so quickly that there is no opportunity for heat transfer in or out of the volume of air. The bulk modulus can therefore be reformulated by making use of the adiabatic condition in the form so that the derivative of pressure P with respect to volume V can be taken. Since the gas density is the speed of sound can be expressed as Using the ideal gas law PV = nRT leads to

Index Traveling wave concepts Sound propagation concepts  

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