Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixe(d)The ratio of speed of sound in the mixture to that in hydrogen is

The velocity of sound in a gas at a fixed temperature is given by $$ v=\sqrt{\frac{\gamma R T}{M}} $$ where, $\gamma=\left(\frac{C_{p}}{C_{V}}\right)$ is specific heat ratio and $M$ is the molecular mass of the gas. Let, velocity of sound in hydrogen, $v_{1}=\sqrt{\frac{\gamma R T}{M_{1}}}$ Velocity of sound in oxygen, $v_{2}=\sqrt{\frac{\gamma R T}{M_{2}}}$ Let, $M_{1}$ and $M_{2}$ be the molecular mass of hydrogen and oxygen respectively $n_{1}$ and $n_{2}$ be the moles of hydrogen and oxygen, respectively. Molecular mass of the mixture, $$ M_{\text {mix }}=\frac{n_{1} M_{1}+n_{2} M_{2}}{n_{1}+n_{2}} $$ According to the question, $n_{1}=n_{2}$ at given NTP. (given) $$ \rightarrow \quad \ddot{u}_{\text {aix }}=\sqrt{\frac{2 \gamma R T}{17 M_{1}}} $$ $\therefore$ The ratio of velocity of sound in mixture to that of hydrogen $$ \begin{aligned} \frac{v_{1}}{v_{\operatorname{mix}}} &=\frac{\sqrt{\frac{\gamma R T}{M_{1}}}}{\sqrt{\frac{\gamma 2 R T}{17 M_{1}}}} \\ \Rightarrow \quad \frac{v_{\text {mix }}}{v_{1}} &=\sqrt{\frac{2}{17}} \end{aligned} $$