Sound in air
For an ideal gas, the bulk modulus, B, is simply equal to the pressure, P. Thus, the speed of sound in air is: v = [B/r]1/2 = [P/r]1/2 . But from the ideal gas law,
PV = nRT, P = nRT/V; by definition,
r = m/V. Thus, v = [P/r]1/2 = [nRT/m]1/2 . We can replace the m/n (total mass per total moles) by M, the molar mass):
v = [gRT/M]1/2 , where g = CP/CV = 1.4 for a diatomic gas like air has to be introduced due to thermodynamic considerations.