Waves

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133 of 142

Question 133 of 142

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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Answer: (B) 4:14:1

The formula to calculate the speed of sound in hydrogen gas is given by
vH2=γRTMH2...(1){v}_{{H}_{2}}=\sqrt{\dfrac{\gamma RT}{{M}_{{H}_{2}}}}...\left(1\right)
The formula to calculate the speed of sound in oxygen is given by
vO2=γRTMO2...(2){v}_{{O}_{2}}=\sqrt{\dfrac{\gamma RT}{{M}_{{O}_{2}}}}...\left(2\right)
Divide equation (1) by (2) and simplify to obtain the required ratio.
vH2vO2=MO2MH2...(3)\dfrac{{v}_{{H}_{2}}}{{v}_{{O}_{2}}}=\sqrt{\dfrac{{M}_{{O}_{2}}}{{M}_{{H}_{2}}}}...\left(3\right)
Substitute the values of the known parameters into equation (3) to calculate the required ratio.
vH2vO2=322=4:1\begin{matrix}\dfrac{{v}_{{H}_{2}}}{{v}_{{O}_{2}}} & = & \sqrt{\dfrac{32}{2}} \\ & = & 4:1\end{matrix}

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