Question

If $V_{rms}$ is $rms$ speed of molecules in a gas and $V$ is the speed of sound wave in the gas, then the ratio $\frac{V_{rms}}{V}$ is:

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

Answer 1

The correct option is A $\sqrt{\frac{3}{\gamma }}$

$rms$ speed of gas molecules is
$V_{rms}=\sqrt{\frac{3P}{\rho }}$ .....(i)
Speed of sound in the gas is
$V=\sqrt{\frac{\gamma P}{\rho }}$ .....(ii)
Divide (i) by (ii), we get, $\frac{V_{rms}}{V}=\sqrt{\frac{3}{\gamma }}$