Oxygen is 16 times heavier than hydrogen. Equ | vedclass

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(A) The speed of sound in a gas is given by $v = \sqrt{\frac{\gamma P}{\rho}}$. Assuming the temperature and pressure remain constant,$v \propto \frac

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$\sqrt{\frac{2}{17}}$

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(A) The speed of sound in a gas is given by $v = \sqrt{\frac{\gamma P}{\rho}}$. Assuming the temperature and pressure remain constant,$v \propto \frac{1}{\sqrt{\rho}}$.Let the density of hydrogen be $\rho_{H_2} = \rho$. Since oxygen is $16$ times heavier,$\rho_{O_2} = 16\rho$.For equal volumes $V$ of hydrogen and oxygen,the density of the mixture is $\rho_{mix} = \frac{m_{total}}{V_{total}} = \frac{\rho_{O_2}V + \rho_{H_2}V}{2V} = \frac{16\rho + \rho}{2} = 8.5\rho$.The ratio of the speed of sound in the mixture $(v_{mix})$ to that in hydrogen $(v_{H_2})$ is:$\frac{v_{mix}}{v_{H_2}} = \sqrt{\frac{\rho_{H_2}}{\rho_{mix}}} = \sqrt{\frac{\rho}{8.5\rho}} = \sqrt{\frac{1}{8.5}} = \sqrt{\frac{2}{17}}$.

Oxygen is $16$ times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of the speed of sound in the mixture to that in hydrogen is

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