Q. Two monoatomic ideal gases 1 and 2 of molecular masses $m_{1}$ and $m_{2}$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by
A) $\sqrt{\frac{m_{1}}{m_{2}}\ }$
B) $\sqrt{\frac{m_{2}}{m_{1}}}$
C) $\frac{m_{1}}{m_{2}}$
D) $\frac{m_{2}}{m_{1}}$
Explanation
(b) Speed of sound in gases is given by
$v = \sqrt{\frac{\gamma RT}{M}} \Rightarrow v \propto \frac{1}{\sqrt{M}} \Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.