Question

The velocity of sound in air is 332 m$s^{-1}$. If the air consist of nitrogen and oxygen in the ratio 4 : 1, the velocity of sound in oxygen is

• A. 278 m$s^{-1}$
• B. 315 m$s^{-1}$
• C. 372 m$s^{-1}$
• D. 418 m$s^{-1}$

Answer 1

Answer: (B)

315 m$s^{-1}$

$v\propto \frac{1}{\sqrt{M_{gas}}}$

Here$,v$ is the velocity of sound in the medium, $M_{gas}$ is the

molecular weight of the gas.

$M_{air}=\frac{M_{N_2}\times 4+M_{O_2}\times 1}{4+1}=M_{air}=\frac{28\times 4+32\times 1}{5}=28.8$

Therefore,

$\frac{v_{O_2}}{v_{air}}=\sqrt{\frac{M_{air}}{M_{O_2}}}=\sqrt{\frac{28.8}{32}}=0.9486$

$v_{O_2}=v_{air}\times 0.9486=314.96\approx 315{\text{ms}}^{-1}$

Option "B" is correct.