Question

The relation between velocity of sound in a gas (v) and r.m.s. velocity of molecules of gas $\left(v_{r.m.s}\right)$ is

• A. $v=v_{\text{r.m.s. }}(\gamma /3{)}^{1/2}$
• B. $v_{\text{r.m.s. }}=v(2/3{)}^{1/2}$
• C. $v=v_{\text{r.m. s. }}$
• D. $v=v_{\text{r.m.s. }}(3/\gamma {)}^{1/2}$

Answer 1

Answer: (A)

Velocity of sound in a gas is
$v=\sqrt{\gamma P/\rho }\text{ and from }P=\frac{1}{3}\rho v_{\text{r.m.s. }}^2$
$v_{\text{r.m.s. }}=\sqrt{3P/\rho }$
$\therefore \frac{v}{v_{\text{r.m.s. }}}=\sqrt{\frac{\gamma }{3}}$