v_1 and v_2 are the velocities of sound at th | vedclass

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(C) The velocity of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$.Since the temperature is the same and the gases are mono

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$2:1$

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(C) The velocity of sound in a gas is given by the formula $v = \sqrt{\frac{\gamma P}{\rho}}$.Since the temperature is the same and the gases are monoatomic,the adiabatic index $\gamma$ is the same for both.Assuming the pressure $P$ is the same,we have $v \propto \frac{1}{\sqrt{\rho}}$.Therefore,the ratio of velocities is $\frac{v_1}{v_2} = \sqrt{\frac{\rho_2}{\rho_1}}$.Given $\frac{\rho_1}{\rho_2} = \frac{1}{4}$,it follows that $\frac{\rho_2}{\rho_1} = 4$.Substituting this value,we get $\frac{v_1}{v_2} = \sqrt{4} = 2$.Thus,the ratio $v_1 : v_2$ is $2:1$.

$v_1$ and $v_2$ are the velocities of sound at the same temperature in two monoatomic gases of densities $\rho_1$ and $\rho_2$ respectively. If $\frac{\rho_1}{\rho_2} = \frac{1}{4}$,then the ratio of velocities $v_1$ and $v_2$ will be

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