Question

The speed of sound in oxygen $\left(O_2\right)$ at a certain temperature is $460m/s$. The speed in helium $\left(He\right)$ at the same temperature will be [assume both gases to be ideal]

• A. $460m/s$
• B. $500m/s$
• C. $650m/s$
• D. $1420m/s$

Answer 1

The correct option is D $1420m/s$

Speed of sound is given by $V=\sqrt{\frac{\gamma RT}{M}}$

As
${\gamma }_{O_2}=\frac{7}{5},M_{O_2}=32$ and ${\gamma }_{He}=\frac{5}{3},M_{He}=4$

$V_{O_2}=\sqrt{\frac{\frac{7}{5}RT}{32}}$ and
$V_{He}=\sqrt{\frac{\frac{5}{3}RT}{4}}$

$\frac{V_{O_2}}{V_{He}}=\sqrt{\frac{7\times 3\times 4}{5\times 5\times 32}}$

$V_{He}=460\times 10\times \sqrt{\frac{2}{21}}=1420m/s$