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JEE Main 2008
Exam
JEE Main
Year
2008
Subject
Physics
Chapter
Waves and Sound

JEE Main 2008 · Physics · Waves and Sound

The speed of sound in oxygen (O_2) at a certain temperature is 460...

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)

Options

  1. A460 ms−1460 \mathrm{~ms}^{-1}
  2. B500 ms−1500 \mathrm{~ms}^{-1}
  3. C650 ms−1650 \mathrm{~ms}^{-1}
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

v=γRTMV1V2=γ1M2γ2M1=75×453×32460V2=2125×8⇒\quadv2=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 \quadv_2=\frac{460 \times 5 \times 2 \sqrt{2}}{\sqrt{21}}=1420 \end{aligned}
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