Wave Motion 3 Question 5
5. Two monoatomic ideal gases 1 and 2 of molecular masses $m _1$ and $m _2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to the gas 2 is given by
$(2000,2 M)$
(a) $\sqrt{\frac{m _1}{m _2}}$
(b) $\sqrt{\frac{m _2}{m _1}}$
(c) $\frac{m _1}{m _2}$
(d) $\frac{m _2}{m _1}$
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Answer:
Correct Answer: 5. (b)
Solution:
- Speed of sound in a gas is given by
$$ \begin{array}{rlrl} v & =\sqrt{\frac{\gamma R T}{M}}, v \propto \frac{1}{\sqrt{M}} \\ \therefore \quad & \frac{v _1}{v _2} & =\sqrt{\frac{M _2}{M _1}}=\sqrt{\frac{m _2}{m _1}} \end{array} $$
Here, $\gamma=\frac{C _p}{C _V}=\frac{5}{3}$ for both the gases $\left(\gamma _{\text {monoatomic }}=\frac{5}{3}\right)$
