Question

The speed of sound in air under ordinary conditions is around $330 \,m \,s ^{-1}$. The speed of sound in hydrogen under similar conditions will be $\left(\right.$ in $\left. m s ^{-1}\right)$ nearest to

• A. 330
• B. 1200
• C. 600
• D. 900

Answer 1

Answer: (B)

$v \propto \sqrt{\frac{\gamma R T}{M}}$
In air, the majority component is nitrogen $(\sim 74 \%)$.
Hence we take molecular mass of air $=(14 \times 2)=28$
$\frac{v_{ H _{2}}}{v_{ air }}=\sqrt{\frac{M_{ air }}{M_{ H _{2}}}}=\sqrt{\frac{28}{2}} $
$\Rightarrow v_{ H _{2}}=v_{ air } \times \sqrt{14}$
$=330 \times \sqrt{14}=1234 m / s \approx 1200\, m / s$