Question

The speed of sound in a gas is v. The r.m.s velocity of the gas molecule is c. The ratio of v to c is :

• A. $\frac{3}{\gamma }$
• B. $\frac{\gamma }{3}$
• C. $\sqrt{\left(3/\gamma \right)}$
• D. $\sqrt{\left(\gamma /3\right)}$

Answer 1

Answer: (D)

$\sqrt{\left(\gamma /3\right)}$

The speed of sound in gas is given by:

$v=\sqrt{\frac{\gamma RT}{M}}$

The RMS velocity is given by:

$c=\sqrt{\frac{3RT}{M}}$

The ratio of v to c is:

$\frac{v}{c}=\sqrt{\frac{\gamma }{3}}$

Hence option D is correct.