Question

Oxygen is 16 times heavier than hydrogen. Equal volume of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is

• A. $\sqrt{8}$
• B. $\sqrt{\frac{1}{8}}$
• C. $\sqrt{\frac{32}{17}}$
• D. $\sqrt{\frac{17}{32}}$

Answer 1

Answer: (C)

$\sqrt{\frac{32}{17}}$

velocity of sound is given as $c=\sqrt{\frac{\gamma RT}{M}}$.

where $\gamma$ is specific heat ratio and $M$ is molecular mass of the gas mixture.

velocity of sound in hydrogen $c=\sqrt{\frac{\gamma RT}{M_1}}$

$M_{mixture}=\frac{n_1{M}_1+n_2{M}_2}{n_1+n_2}$

$n_1=n_2$ as equal volumes at NTP are used

$M_2=16M_1$

$M_{mixture}=\frac{M_1+16M_1}{2}=\frac{17M_1}{2}$

velocity of sound in mixture $c=\sqrt{\frac{\gamma RT}{M_{mixure}}}$

ratio of velocity of sound in mixture that of hydrogen $\sqrt{\frac{M_1}{M_{mixure}}}=\sqrt{\frac{2}{17}}$

Hence correct option is C