The speed of sound in oxygen $\left( O _{2}\right)$ at a certain temperature is $460 \;ms ^{-1}$. The speed of sound in helium $(He)$ at the same temperature will be (asume both gases to be ideal)
AIEEE 2008, Medium
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Speed of sound is given by : $\mathrm{v}=\sqrt{\frac{\gamma \mathrm{RT}}{\mathrm{M}}}$
${V_{{O_2}}} = \sqrt {\frac{{\frac{7}{5}RT}}{{32}}} \,and\,{V_{He}} = \sqrt {\frac{{\frac{5}{3}RT}}{4}} $
$\frac{v_{O_{2}}}{v_{H e}}=\sqrt{\frac{7 \times 3 \times 4}{5 \times 32 \times 5}}$
$or\,\,\,{V_{He}} = 460 \times 10 \times \sqrt {\frac{2}{{21}}} \simeq 1420\,m/s.$
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