Any general method of determining changes in speed of sound with pressure? I need to correct speed of sound measurements in various gases for changes in ambient pressure, typically 700-1100 mBar. Is there any general theoretical model available for this? Especially something I could code in C
 A: The very famous Newton-Laplace equation is a relation between the speed of sound and the pressure of an ideal gas. It can be written as:
$$
 v = \sqrt{\gamma P / \rho} 
$$
where v is the velocity of sound in the given medium, P is the pressure, γ is the ratio of the heat capacities for the medium and ρ is the density of the medium. 
The Newton-Laplace was first given by Sir Issac Newton in his most famous work Principia Mathematica as:
$$
 v = \sqrt{ P / \rho} 
$$
But the not so obvious flaw in this formula was that he assumed that the process of sound propagation was isothermic. The great French Mathematician Pierre-Simon Laplace, in the same century, identified this flaw, made corrections for the influence of heat transfer on speed of sound and gave the above Newton-Laplace formula. 
Additionally, this formula makes it really simple to code in any language for that matter.
A: There is a model described in Main's Vibrations and Waves in Physics dealing with the speed of sound variations you might consider useful. Sorry, I would just comment that, but I don't have enough reputation.
The other way might be to derive the speed of sound not from the ideal gas laws but from van der Waals equation, but to be honest, I've never tried that. You would need to eliminate the density as the function of pressure with the fit parameters and then those parameters should appear in the resulting equation for c0 (using continuity equation and momentum equation from Euler's system).
