wave_mechanics critical_thinking Question 19
Question: Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is
[KCET 2004]
Options:
A) $ \sqrt{\frac{1}{8}} $
B) $ \sqrt{\frac{32}{17}} $
C) $ \sqrt{8} $
D) $ \sqrt{\frac{2}{17}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Density of mixture $ ={\rho _{mix}}=\frac{{V _{O _{2}}}{\rho _{O _{2}}}+{V _{H _{2}}}{\rho _{H _{2}}}}{{V _{O _{2}}}+{V _{H _{2}}}} $
$ =\frac{V( {\rho _{O _{2}}}+{\rho _{H _{2}}} )}{2V}=\frac{{\rho _{O _{2}}}+{\rho _{H _{2}}}}{2} $ (since$ {V _{O _{2}}}={V _{H _{2}}}=V $ ) $ =\frac{{\rho _{H _{2}}}+16{\rho _{H _{2}}}}{2}=8.5{\rho _{H _{2}}} $
Therefore $ v\propto \frac{1}{\sqrt{\rho }} $
Therefore $ \frac{V _{mix}}{{V _{H _{2}}}}=\sqrt{\frac{{\rho _{H _{2}}}}{{\rho _{mxn}}}}=\sqrt{\frac{{\rho _{H _{2}}}}{8.5{\rho _{H _{2}}}}}\approx \sqrt{\frac{1}{8}} $
BETA
