The speed of sound in oxygen (O₂) at a certain temperature is 460 m s⁻¹. The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal) (a) 1421 m s⁻¹ (b) 500 m s⁻¹ (c) 650 m s⁻¹ (d) 300 m s⁻¹

Answer: (a). Speed of sound in a gas: v = √((γ RT)/(M)), so at the same T, v ∝ √(γ/M). O ₂: γ = 1.4, M = 32; He: γ = 5/3, M = 4. vHevO₂ = √((5/3)/(1.4)×32/4) = √(9.52) ≈ 3.09 vHe = 460 × 3.09 ≈ 1421 m s⁻¹ So the answer is (a) 1421 m s⁻¹.

The speed of sound in oxygen (O₂) at a certain temperature is 460 m… | JEE Main 2008 (AIEEE)

Q88JEE Main 2008 · AIEEEMedium

Molecular Speeds & Maxwell Distribution

The speed of sound in oxygen $(\text{O}_2)$ at a certain temperature is $460\text{ m s}^{-1}.$ The speed of sound in helium $(\text{He})$ at the same temperature will be (assume both gases to be ideal)

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Answer: (a)

Speed of sound in a gas: $v = \sqrt{\dfrac{\gamma RT}{M}}$ , so at the same $T$ , $v \propto \sqrt{\gamma/M}$ .
O $_2$ : $\gamma = 1.4,\ M = 32$ ; He: $\gamma = 5/3,\ M = 4$ .
$\dfrac{v_{He}}{v_{O_2}} = \sqrt{\dfrac{5/3}{1.4}\times\dfrac{32}{4}} = \sqrt{9.52} \approx 3.09$
$v_{He} = 460 \times 3.09 \approx 1421\text{ m s}^{-1}$
So the answer is (a) $1421\text{ m s}^{-1}$ .

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