Speed of sound in gases

A certain ideal gas is made up of unknown identical molecules. It is known that under standard conditions, i.e., atmospheric pressure and zero degrees Celsius, the density of the gas is \(\rho=1.3~ \text{mg}/{\text{cm}^{3}}\) and the speed of sound in it is \( v=330~\text{m}/\text{s}\). Surprisingly, by measuring the density and the speed of sound we can determine the number of degrees of freedom \(i\) of the molecules. Find \(i\). The atmospheric pressure is \(p_{A}=101.05~\text{kPa}\)

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