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(A) The speed of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{d}}$,where $\gamma$ is the adiabatic index,$P$ is the pressure,and

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$\sqrt{\frac{d_2}{d_1}}$

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

If at the same temperature and pressure,the densities of two diatomic gases are respectively $d_1$ and $d_2$,then the ratio of the velocities of sound in these gases will be

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