Wave Motion 3 Question 6
6. The ratio of the speed of sound in nitrogen gas to that in helium gas, at $300 K$ is
(1999, 2M)
(a) $\sqrt{(2 / 7)}$
(b) $\sqrt{(1 / 7)}$
(c) $(\sqrt{3}) / 5$
(d) $(\sqrt{6}) / 5$
True / False
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Answer:
Correct Answer: 6. (c)
Solution:
- Speed of sound in an ideal gas is given by $v=\sqrt{\frac{\gamma R T}{M}} \Rightarrow \therefore v \propto \sqrt{\frac{\gamma}{M}} \quad$ ( $T$ is same for both the gases) $\therefore \quad \frac{v _{N _2}}{v _{He}}=\sqrt{\frac{\gamma _{N _2}}{\gamma _{He}} \cdot \frac{M _{He}}{M _{N _2}}}=\sqrt{\frac{7 / 5}{5 / 3}\left(\frac{4}{28}\right)}=\sqrt{3} / 5$
$$ \gamma _{N _2}=\frac{7}{5} $$
(Diatomic)
$$ \gamma _{He}=\frac{5}{3} $$
(Monoatomic)
