The speed of sound in a gas c depends on the gas pressure p

The speed of sound in a gas, c, depends on the gas pressure p and on the gas mass density . Use dimensional analysis to determine how c, p, and are related.

Solution

speed dimension = LT^{-1}

Pressure dimension = M L^{-1} T^{-2}

mass density dimension = M L^{-3}

So Pressure = mass density * speed^2