Speed of sound

The speed of sound ($c$) can be written as:

$c={\sqrt {\left.{\frac {\partial p}{\partial \rho }}\right\vert _{S}}}={\sqrt {\frac {B_{S}}{\rho }}}$

where $B$ is the adiabatic bulk modulus, given by

$B_{S}={\frac {C_{p}}{C_{V}}}B_{T}$

where $C$ is the heat capacity and $B_{T}$ is the isothermal bulk modulus, leading to

$c={\sqrt {\frac {C_{p}B_{T}}{C_{V}\rho }}}$

See also

• Cole equation of state