390 Table 112 



VELOCITY OF SOUND IN AIR* 



Symbols referring to given gas: 



A aa (T) = second virial coefficient of dry air, a pure temperature function 

 AaaaiT) = third virial coefficient of dry air, a pure temperature function 

 Aaw (T) = interaction coefficient of dry air and water vapor, a pure temperature 



function 

 A W v>(T) = second virial coefficient of water vapor, a pure temperature function 

 AvwviT) = third virial coefficient of water vapor, a pure temperature function 

 c = velocity of sound under existing conditions 

 Co = velocity of sound at temperature To (and usually at one. atmosphere 



pressure) 

 C P = specific heat at constant pressure 

 Cv = specific heat at constant volume 

 C„ ao = specific heat at constant volume as the volume approaches infinity 

 e = aqueous vapor pressure 



Ea = — V i -^ I = adiabatic elasticity 



\dvj. 



Et = — V ( -^- ) = isothermal elasticity 



M = molecular weight 

 p =z pressure (barometric) 

 R = universal gas constant 

 J = entropy 



T = absolute temperature (°K.) 



To = absolute temperature of the ice point (273.16 °K.) 

 V = volume of one mol 

 x = mol fraction of water vapor in moist air 



n 

 v — =^ = ratio of specific heats 



7 Cv 



p = density 



Subscript o denotes standard conditions of pressure and temperature. (The algebraic 

 sign convention used here for the virial and interaction coefficients is opposite to that 

 found in many texts; it is consistent with that adopted by Goff and Gratch, see 

 reference 3, p. 391.) 



Basic Formula: 



When the amplitude of sound vibrations is not too large, the velocity of sound in a 

 gas is given by the relation (Laplace, 1816) 



P 

 From the definition of Et it follows that 



C = V : 7 = V 7 ^ 



=V*(S) 



(2) 



If the medium through which the sound propagated were a perfect gas (so that 

 the equation of state is pV = RT), then equation (2) would become 



<=^¥=V(^)(£) 



* Prepared especially for the Smithsonian Meteorological Tables by L. P. Harrison, U. S. Weather 

 Bureau. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



