Physics - Sound Wave Question with Solution | TestHub

The velocity of sound in a gas is given by $v=\sqrt{\frac{\gamma P}{\rho }}$.

For oxygen and hydrogen, both being diatomic gases, the ratio of specific heats $\gamma$ is the same. Assuming they are at the same pressure $P$, the velocity of sound is inversely proportional to the square root of the density of the gas.

$v\propto \frac{1}{\sqrt{\rho }}$

$\frac{v_O}{v_H}=\sqrt{\frac{{\rho }_H}{{\rho }_O}}$

Given ${\rho }_O=16{\rho }_H$,

$\frac{v_O}{v_H}=\sqrt{\frac{{\rho }_H}{16{\rho }_H}}=\sqrt{\frac{1}{16}}=\frac{1}{4}$

The ratio of the velocity of sound in oxygen to that in hydrogen is $1:4$.

Answer: $1:4$