Q96 / 100 · BITSAT 2023 (Memory Based Paper 1) · Physics
The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:
- Correct answerA$4: 1$
- B$1: 2$
- C$1: 4$
- D$1: 1$
Solution
Given $\mathrm{M}_{\mathrm{H}_2}=2 ; \mathrm{M}_{\mathrm{O}_2}=32$
Speed of sound, $\mathrm{v}=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}}$
$\Rightarrow \quad v \propto \frac{1}{\sqrt{M}}$
$\therefore \quad \frac{\mathrm{v}_{\mathrm{H}_2}}{\mathrm{v}_{\mathrm{O}_2}}=\sqrt{\frac{\mathrm{M}_{\mathrm{O}_2}}{\mathrm{M}_{\mathrm{H}_2}}}=\sqrt{\frac{32}{2}}=4: 1$
Speed of sound, $\mathrm{v}=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}}$
$\Rightarrow \quad v \propto \frac{1}{\sqrt{M}}$
$\therefore \quad \frac{\mathrm{v}_{\mathrm{H}_2}}{\mathrm{v}_{\mathrm{O}_2}}=\sqrt{\frac{\mathrm{M}_{\mathrm{O}_2}}{\mathrm{M}_{\mathrm{H}_2}}}=\sqrt{\frac{32}{2}}=4: 1$
Hence, the correct answer is option: 'A'.