Kinetic Theory - Result Question 17
17. If $C_s$ be the velocity of sound in air and $C$ be the r.m.s velocity, then
(a) $C_s<C$
(b) $C_s=C$
(c) $C_s=C(\gamma / 3)^{1 / 2}$
(d) none of these
[1994]
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Answer:
Correct Answer: 17. (c)
Solution:
- (c) Velocity of sound $(C_S)=\sqrt{\frac{\gamma P}{\rho}}$
R.M.S. velocity of gas molecules $(C)=\sqrt{\frac{3 P}{\rho}}$
$\frac{C_S}{C}=\sqrt{\frac{\gamma P}{\rho} \times \frac{\rho}{3 P}}=\sqrt{\frac{\gamma}{3}} \Rightarrow C_s=C \times \sqrt{\frac{\gamma}{3}}$
