The densities of two diatomic gases at consta | vedclass

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(B) The speed of sound $v$ in a gas is given by the formula: $v = \sqrt{\frac{\gamma P}{\rho}}$,where $\gamma$ is the adiabatic index,$P$ is the press

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$\sqrt{d_2 / d_1}$

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(B) The speed of sound $v$ in a gas is given by the formula: $v = \sqrt{\frac{\gamma P}{\rho}}$,where $\gamma$ is the adiabatic index,$P$ is the pressure,and $\rho$ is the density.Since both gases are diatomic,the adiabatic index $\gamma$ is the same for both.Given that the temperature and pressure $P$ are constant,the ratio of the speeds $v_1$ and $v_2$ is:$\frac{v_1}{v_2} = \sqrt{\frac{\gamma P / d_1}{\gamma P / d_2}} = \sqrt{\frac{d_2}{d_1}}$.

The densities of two diatomic gases at constant temperature and pressure are $d_1$ and $d_2$. The ratio of the speed of sound in these gases is:

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