Question

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

• A. 330
• B. 1200
• C. 600
• D. 900

Answer 1

Answer: (B)

$v\propto \sqrt{\frac{\gamma RT}{M}}$
In air, the majority component is nitrogen $(\sim 74\%)$.
Hence we take molecular mass of air $=(14\times 2)=28$
$\frac{v_{H_2}}{v_{air}}=\sqrt{\frac{M_{air}}{M_{H_2}}}=\sqrt{\frac{28}{2}}$
$\Rightarrow v_{H_2}=v_{air}\times \sqrt{14}$
$=330\times \sqrt{14}=1234m/s\approx 1200m/s$