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) $(\sqrt{6}) / 5$

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Answer:

Correct Answer: 6. (c)

Solution:

  1. 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) $\therefore \quad \frac{v _{N _2}}{v _{He}}=\sqrt{\frac{\gamma _{N _2}}{\gamma _{He}} \cdot \frac{M _{He}}{M _{N _2}}}=\sqrt{\frac{7 / 5}{5 / 3}\left(\frac{4}{28}\right)}=\sqrt{3} / 5$

$$ \gamma _{N _2}=\frac{7}{5}(Diatomic) $$

$$ \gamma _{He}=\frac{5}{3}(Monoatomic) $$



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