Question

If $v_{rms}$ is the rms speed of molecules in a gas and $v$ is the speed of sound waves in the gas, then the ratio $\frac{v_{rms}}{v}$

• A. $\sqrt{\frac{3}{\gamma}}$
• B. $\sqrt{\frac{\gamma}{3}}$
• C. $\sqrt{3\gamma}$
• D. $\frac{\sqrt{3}}{\gamma}$

Answer 1

Answer: (A)

$rms$ speed of gas molecules is
$v_{rms} = \sqrt{\frac{3P}{\rho}}\quad\ldots\left(i\right)$
Speed of sound in the gas is
$v = \sqrt{\frac{\gamma P}{\rho}} \quad \ldots \left(ii\right)$
Divide $\left(i\right)$ by $\left(ii\right)$, we get, $\frac{v_{rms}}{v} = \sqrt{\frac{3}{\gamma}}$