Q. The ratio of the velocity of sound in hydrogen (γ=7/5) to that helium $\left( \gamma = \frac{5}{3} \right)$ at the same temperature is
A) $\sqrt{\frac{5}{42}}$
B) $\sqrt{\frac{5}{21}}$
C) $\frac{\sqrt{42}}{5}$
D) $\sqrt{\frac{21}{5}}$
Explanation
(c) Velocity of sound in a gas
$v = \sqrt{\frac{\gamma p}{d}}\ $
$\therefore\ \ \ \ \frac{v_{H_{2}}}{v_{H_{2}}} = \ \sqrt{\frac{\gamma_{H_{2}} \times d_{He}}{d_{H_{2}} \times \gamma_{He\ }}}$
$\frac{v_{H_{2}}}{v_{He}} = \sqrt{\frac{7 \times 3 \times 2}{5 \times 5}}\ \ \ \ \ \ \ \ \ \left\lbrack As\frac{d_{He}}{d_{H_{2}}} = 2 \right\rbrack$
$\therefore\frac{v_{H_{2}}}{v_{He}} = \frac{\sqrt{42}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.