The speed of sound waves in an atmosphere of helium at $0^{o} C$ and $1 a t m$ pressure is ( $4 g$ helium under STP has a volume of $22.4$ litre and $γ$ $= 1.67$ for $H e$ )

1073 m / s e c

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973 m / s e c

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873 m / s e c

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773 m / s e c

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Solution

The correct option is B $973 m / s e c$
The speed of sound in a medium with pressure P and density $ρ$ having a adiabatic index $γ$ is given by:

$v = \sqrt{γ P / ρ} = \sqrt{γ P V / M}$

Using this here, $= \sqrt{\frac{1.67 \times (1.013 \times 10^{5}) (22.4 \times 10^{- 3})}{4 \times 10^{- 3}}} = 973 m / s$

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