MCQ
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 }} $
- ✓$\sqrt {\frac{\gamma }{3}} $
✓
Answer
Correct option: D.
$\sqrt {\frac{\gamma }{3}} $
d
As we know, ${v_s} = \sqrt {\frac{{\gamma \,P}}{\rho }} $ and ${v_{rms}} = \sqrt {\frac{{3P}}{\rho }} ;$
As we know, ${v_s} = \sqrt {\frac{{\gamma \,P}}{\rho }} $ and ${v_{rms}} = \sqrt {\frac{{3P}}{\rho }} ;$
$\therefore$ $\frac{{{v_{rms}}}}{{{v_s}}} = \sqrt {\frac{\gamma }{3}} $
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