The velocities of sound at the same temperature in two monoatomic gases of densities $\rho_1$ and $\rho_2$…
The velocities of sound at the same temperature in two monoatomic gases of densities $\rho_1$ and $\rho_2$ are $v_1$ and $v_2$ respectively. If $\rho_1 / \rho_2=4$, then the value of $v_1 / v_2$ is
$1 / 4$
2
$1 / 2$
4.
Solution
Velocity of sound in the gas of density $\rho_1$ is $v_1$ and velocity of sound in the gas of density $\rho_2$ is $v_2$.
Velocity of sound in gas, $v=\sqrt{\frac{\gamma P}{\rho}} \propto \sqrt{\frac{1}{\rho}}$.
Therefore $\frac{v_1}{v_2}=\sqrt{\frac{\rho_2}{\rho_1}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$.