SATHEE: Wave Motion 3 Question 6

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

Show Answer

Answer:

Correct Answer: 6. (c)

Solution:

Speed of sound in an ideal gas is given by $v = \sqrt{\frac{γ R T}{M}} \Rightarrow∴ v \propto \sqrt{\frac{γ}{M}}$ ( $T$ is same for both the gases) $∴ \frac{v_{N_{2}}}{v_{H e}} = \sqrt{\frac{γ_{N_{2}}}{γ_{H e}} \cdot \frac{M_{H e}}{M_{N_{2}}}} = \sqrt{\frac{7 / 5}{5 / 3} (\frac{4}{28})} = \sqrt{3} / 5$

$γ_{N_{2}} = \frac{7}{5} (D i a t o m i c)$

$γ_{H e} = \frac{5}{3} (M o n o a t o m i c)$

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