Wave Mechanics Question 811
Question: The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is
[IIT 1999]
Options:
A) $ \sqrt{2/7} $
B) $ \sqrt{1/7} $
C) $ \sqrt{3}/5 $
D) $ \sqrt{6}/5 $
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Answer:
Correct Answer: C
Solution:
Velocity of sound in gas $ v=\sqrt{\frac{\gamma RT}{M}} $
Therefore $ v\propto \sqrt{\frac{\gamma T}{M}} $
Therefore $ \frac{{v _{N _{2}}}}{v _{He}}=\sqrt{\frac{{\gamma _{N _{2}}}}{{\gamma _{He}}}\times \frac{M _{He}}{{M _{H _{2}}}}}=\sqrt{\frac{\frac{7}{5}R\times 4}{\frac{5}{3}R\times 28}}=\frac{\sqrt{3}}{5} $
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