The density of oxygen is 16 times that of hydrogen. The ratio of...

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

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.

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

$\dfrac{v_{O}}{v_{H}} = \sqrt{\dfrac{\rho_{H}}{\rho_{O}}}$

Given $\rho_{O} = 16 \rho_{H}$,

$\dfrac{v_{O}}{v_{H}} = \sqrt{\dfrac{\rho_{H}}{16 \rho_{H}}} = \sqrt{\dfrac{1}{16}} = \dfrac{1}{4}$

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

Answer: $1:4$