At standard temperature and pressure the density of a gas is $1.3$ $kg/{m^3}$ and the speed of the sound in gas is $330\, m/sec.$ Then the degree of freedom of the gas will be
Medium
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As we know, $v = \sqrt {\frac{{\gamma P}}{\rho }} $
$\gamma = \frac{{{v^2}\rho }}{P} = \frac{{{{(330)}^2} \times 1.3}}{{1.015 \times {{10}^5}}} = 1.4 = 1 + \frac{2}{n}$
$\Rightarrow n = 5$
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