At STP,the speed of a sound wave in a gas is | vedclass

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(C) Given: Speed of sound $v_s = 330 \ m/s$,density $ho = 1.3 \ kg/m^3$,and pressure at $STP$ $P = 1.01 	imes 10^5 \ N/m^2$.The formula for the spe

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$5$

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(C) Given: Speed of sound $v_s = 330 \ m/s$,density $ho = 1.3 \ kg/m^3$,and pressure at $STP$ $P = 1.01 	imes 10^5 \ N/m^2$.The formula for the speed of sound in a gas is $v_s = \sqrt{\frac{\gamma P}{ho}}$.Rearranging for $\gamma$: $\gamma = \frac{v_s^2 ho}{P}$.Substituting the values: $\gamma = \frac{(330)^2 	imes 1.3}{1.01 	imes 10^5} = \frac{108900 	imes 1.3}{101000} \approx \frac{141570}{101000} \approx 1.4$.The relation between the adiabatic index $\gamma$ and degrees of freedom $f$ is $\gamma = 1 + \frac{2}{f}$.Solving for $f$: $f = \frac{2}{\gamma - 1} = \frac{2}{1.4 - 1} = \frac{2}{0.4} = 5$.

At $STP$,the speed of a sound wave in a gas is $330 \ m/s$ and the density of the gas is $1.3 \ kg/m^3$. Calculate the degrees of freedom $(f)$ of the gas.

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