Question

In a mixture of gases, the average number of degrees of freedom per molecule is $6$ . The root mean square speed of the molecules of the gas is $c$ . The velocity of sound in the gas is

• A. $\frac{c}{\sqrt{2}}$
• B. $\frac{3 c}{4}$
• C. $\frac{2 c}{3}$
• D. $\frac{c}{\sqrt{3}}$

Answer 1

Answer: (C)

$\gamma =1+\frac{2}{f}=1+\frac{2}{6}=\frac{4}{3}$
Root mean square speed, $c=\sqrt{\frac{3 P}{\rho }}$
and speed of sound, $v=\sqrt{\frac{\gamma P}{\rho }}$
$\therefore \, \, \frac{v}{c}=\sqrt{\frac{\gamma }{3}}$
$\frac{v}{c}=\sqrt{\frac{\frac{4}{3}}{3}}$
$v=\frac{2 c}{3}$