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{3 P / \rho} $
$\therefore \frac{ v }{ v _{\text {r.m.s. }}}=\sqrt{\frac{\gamma}{3}}$