Q. Speed of sound in a gas is $v$ and $r.m.s.$ velocity of the gas molecules is $c.$ The ratio of $v$ to $c$ is
A) $\frac{3}{\gamma}$
B) $\frac{\gamma}{3}$
C) $\sqrt{\frac{3}{\gamma}}$
D) $\sqrt{\frac{\gamma}{3}}$
Explanation
(d) We know $v_{s} = \sqrt{\frac{\gamma P}{\rho}}\ and\ v_{rms} = \sqrt{\frac{3P}{\rho}}$
$\therefore\frac{v_{rms}}{v_{s}} = \sqrt{\frac{\gamma}{3}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.