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

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$1:4$

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(A) The velocity of sound 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 of the gas.Assuming the temperature and pressure are the same for both gases,the ratio of the velocities is inversely proportional to the square root of their densities:$\frac{v_{O_2}}{v_{H_2}} = \sqrt{\frac{\rho_{H_2}}{\rho_{O_2}}}$Given that the density of oxygen is $16$ times that of hydrogen,i.e.,$\rho_{O_2} = 16 \rho_{H_2}$,we have:$\frac{v_{O_2}}{v_{H_2}} = \sqrt{\frac{\rho_{H_2}}{16 \rho_{H_2}}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$Thus,the ratio of the velocities of sound waves in oxygen and hydrogen is $1:4$.

If the density of oxygen is $16$ times that of hydrogen,what will be the ratio of their corresponding velocities of sound waves?

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