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  4. The speed of sound in a gas is v. The r.m.s. velocity of the gas molecules is C. The ratio of v to C is

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Q. The speed of sound in a gas is v. The r.m.s. velocity of the gas molecules is C. The ratio of v to C is

Kinetic Theory

Solution:

The speed of sound in gas is given by:
$
v =\sqrt{\frac{\gamma RT }{ M }}
$
The RMS velocity is given by:
$
c=\sqrt{\frac{3 R T}{M}}
$
The ratio of $v$ to $c$ is:
$
\frac{ v }{ c }=\sqrt{\frac{\gamma}{3}}
$