Question

The speed of sound in hydrogen gas at $N.T.P$ is $1328m{s}^{-1}$ . 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. $340m{s}^{-1}$
• B. $332m{s}^{-1}$
• C. $320m{s}^{-1}$
• D. $280m{s}^{-1}$

Answer 1

Answer: (B)

Here, $v_{H_2}=1328m{s}^{-1};{\rho }_{H_2}=\frac{{\rho }_{\text{air }}}{16};v=\sqrt{\frac{\gamma P}{8}}$
Let $v_{\text{air }}$ be the velocity of sound in air at N.T.P
Now, $\frac{v_{\text{air }}}{v_{H_2}}=\sqrt{\frac{{\rho }_{H_2}}{{\rho }_{\text{air }}}}\left\{\begin{array}{l}\text{ Since }\\ {\gamma }_{H_2}={\gamma }_{\text{air }}\end{array}\right\}$
or $v_{air}=v_{H_2}\sqrt{\frac{{\rho }_{H_2}}{{\rho }_{air}}}$
$=332m{s}^{-1}$