Question

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

Answer 1

Answer: (C)

Velocity of sound $\left(C_{s}\right) = \sqrt{\frac{\gamma P}{\rho}} $
R.M.S. velocity of gas molecules $=\sqrt{\frac{3P}{\rho}} $
$\frac{C_{S}}{C} = \sqrt{\frac{\gamma P}{\rho }\times \frac{\rho}{3P}} = \sqrt{\frac{\gamma}{3}} \Rightarrow C_{s} =C \times\sqrt{\frac{\gamma}{3}} $