Velocity of sound in a multicomponent medium at rest

The Kuropatenko model is considered, as applied to a multicomponent medium where the number of the sought functions coincides with the number of equations. The velocities of sound in a multicomponent medium at rest are determined. A formula of a polynomial of power $N$ whose positive roots are squared velocities of sound in a medium with $N$ components is derived. For $N=2$, the values of two velocities of sound are determined in explicit form. It is demonstrated that the thus-found maximum value of the velocity of sound in a two-component medium containing nitrogen and oxygen with volume concentrations corresponding to air differs (in dimensionless form) from the velocity of sound in air by less than $0.3\%$. Numerical calculations predict the existence of three velocities of sound in a three-component medium. If the velocity of sound in all $N$ components is identical, it is proved that the maximum velocity of sound in such a medium equals this velocity, and there is only one more velocity of sound in the medium, which has a lower value.