Speed Of Sound In Gases

The speed of sound in an ideal gas is given by Laplace's relation $v=\sqrt{\gamma RT/M}$, where $M$ is the molar mass and $\gamma$ is the ratio of specific heats. At the same temperature, and treating both as diatomic gases with the same $\gamma$, the speed depends only on molar mass through $v\propto 1/\sqrt{M}$. Hydrogen and oxygen are both diatomic, so the factor $\gamma$ cancels exactly, and the ratio of the two sound speeds is $\frac{v_H}{v_O}=\sqrt{M_O/M_H}=\sqrt{16}=4$. The option of 16 times forgets to take the square root of the mass ratio. The option of 2 times would correspond to a mass ratio of only 4, not 16. The option of 8 times has no basis in the inverse-square-root dependence. This applies the NCERT Laplace correction for sound speed in gases, including the role of molar mass. As a plausibility check, lighter molecules move faster at a given temperature and transmit pressure disturbances more quickly, so hydrogen must carry sound faster, and the factor of 4 follows directly from the square root of the sixteen-fold mass difference.