$$ c = – \frac{1}{v} \left. \frac{\partial v}{\partial p} \right|_{T} $$
For water, \( c \approx 1 \times 10^{-5} \text{/psi} \)
For an isothermal ideal gas
$$ c \propto \frac{1}{p} $$
For an adiabatic ideal gas, where \( k \) is the taio of specific heats (1.4 for air)
$$ c \propto \frac{1}{k p } $$
From this can be derived the speed of sound in an ideal gas
$$ a = \sqrt{\frac{k R T}{MW} } $$