Waves

JEE Main level, single correct, medium

140 of 142

Question 140 of 142

The speed of sound in oxygen (O2)\left(\mathrm{O}_2\right) at a certain temperature is 460 ms−1460 \mathrm{~ms}^{-1}. The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

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Answer: (D) None of these

v=γRTMV1V2=γ1M2γ2M1=75×453×32460V2=2125×8⇒v2=460×5×2221=1420\begin{aligned} & v=\sqrt{\frac{\gamma R T}{M}} \\ & \frac{V_1}{V_2}=\sqrt{\frac{\gamma_1 M_2}{\gamma_2 M_1}}=\sqrt{\frac{\frac{7}{5} \times 4}{\frac{5}{3} \times 32}} \\ & \frac{460}{V_2}=\sqrt{\frac{21}{25 \times 8}} \Rightarrow \quad v_2=\frac{460 \times 5 \times 2 \sqrt{2}}{\sqrt{21}}=1420 \end{aligned}

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