Question

The speed of sound in hydrogen gas at $N.T.P$ is $1328 \, m \, s^{- 1}$ . If the density of hydrogen is $\frac{1}{16}^{th}$ of that of air, then the speed of sound in air at $N.T.P$ is

• A. $340 \, m s^{- 1}$
• B. $332 \, m s^{- 1}$
• C. $320 \, m s^{- 1}$
• D. $280 \, m s^{- 1}$

Answer 1

Answer: (B)

Here, $v _{ H _{2}}=1328 m s ^{-1} ; \rho_{ H _{2}}=\frac{\rho_{\text {air }}}{16} ; v =\sqrt{\frac{\gamma P }{8}}$
Let $v _{\text {air }}$ be the velocity of sound in air at N.T.P
Now, $\frac{v_{\text {air }}}{v_{ H _{2}}}=\sqrt{\frac{\rho_{ H _{2}}}{\rho_{\text {air }}}} \quad\left\{\begin{array}{l}\text { Since } \\ \gamma_{ H _{2}}=\gamma_{\text {air }}\end{array}\right\}$
or $\quad v _{ air }= v _{ H _{2}} \sqrt{\frac{\rho_{ H _{2}}}{\rho_{ air }}}$
$=332 m s ^{-1}$