Q167 / 200 · MHT CET - Medical 2026 (24 April Shift 1) · Physics
The density of oxygen is 16 times that of hydrogen. The ratio of the velocity of sound in oxygen to that in hydrogen is
- Correct answerA$1:4$
- B$4:1$
- C$1:2$
- D$2:1$
Solution
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: $1:4$
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: $1:4$
Hence, the correct answer is option: 'A'.