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]

Show Answer

Answer:

Correct Answer: 17. (c)

Solution:

  1. (c) Velocity of sound $(C_S)=\sqrt{\frac{\gamma P}{\rho}}$

R.M.S. velocity of gas molecules $(C)=\sqrt{\frac{3 P}{\rho}}$

$\frac{C_S}{C}=\sqrt{\frac{\gamma P}{\rho} \times \frac{\rho}{3 P}}=\sqrt{\frac{\gamma}{3}} \Rightarrow C_s=C \times \sqrt{\frac{\gamma}{3}}$



NCERT Chapter Video Solution

Dual Pane