Question

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 (assume both gases to be ideal).

• A. $1421\, ms ^{-1}$
• B. $500 \, ms ^{-1}$
• C. $650\, ms ^{-1}$
• D. $330\, ms ^{-1}$

Answer 1

Answer: (A)

The speed of sound in a gas is given by $v=\sqrt{\frac{\gamma R T}{M}}$
$\therefore \frac{v_{ O _2}}{v_{ He }}=\sqrt{\frac{\gamma_{ O _2}}{M_{ O _2}} \times \frac{M_{ He }}{\gamma_{ He }}}=\sqrt{\frac{1.4}{32} \times \frac{4}{1.67}}=0.3237$
$\therefore v_{ He }=\frac{v_{ O _2}}{0.3237}=\frac{460}{0.3237}=1421 \,m / s$