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The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:
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$4: 1$
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, $\mathrm{v}=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}}$
$\Rightarrow \quad v \propto \frac{1}{\sqrt{M}}$
$\therefore \quad \frac{\mathrm{v}_{\mathrm{H}_2}}{\mathrm{v}_{\mathrm{O}_2}}=\sqrt{\frac{\mathrm{M}_{\mathrm{O}_2}}{\mathrm{M}_{\mathrm{H}_2}}}=\sqrt{\frac{32}{2}}=4: 1$
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