Wave Mechanics Question 829
Question: Two monoatomic ideal gases 1 and 2 of molecular masses m1 and m2 respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas 1 to that in gas 2 is given by
[IIT-JEE Screening 2000]
Options:
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: B
Solution:
Speed of sound in gases is given by $ v=\sqrt{\frac{\gamma RT}{M}}\Rightarrow v\propto \frac{1}{\sqrt{M}} $
Therefore $ \frac{v _{1}}{v _{2}}=\sqrt{\frac{m _{2}}{m _{1}}} $
BETA
