Question

Speed of sound in a gas is v and r.m.s. velocity of the gas molecules is c. The ratio of v to c is

• A. $\frac{3}{\gamma}$
• B. $\frac{\gamma}{3}$
• C. $\sqrt{\frac{3}{\gamma}}$
• D. $\sqrt{\frac{\gamma}{3}}$

Answer 1

Answer: (D)

$\sqrt{\frac{\gamma}{3}}$

Answer 2

We know

$v_{s} = \sqrt{\frac{\gamma P}{\rho}}$ and $v_{rms} = \sqrt{\frac{3P}{\rho}};$

\ $\frac{v_{rms}}{v_{s}} = \sqrt{\frac{\gamma}{3}}$