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