The velocity of sound measured at a given tem | vedclass

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(A) The velocity of sound in a gaseous medium is given by the formula:$v = \sqrt{\frac{\gamma RT}{M}}$Since the temperature $T$ and the adiabatic inde

Vedclass · Accepted Answer

$1:4$

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(A) The velocity of sound in a gaseous medium is given by the formula:$v = \sqrt{\frac{\gamma RT}{M}}$Since the temperature $T$ and the adiabatic index $\gamma$ are constant for the given conditions,the velocity is inversely proportional to the square root of the molar mass $M$:$v \propto \frac{1}{\sqrt{M}}$Therefore,the ratio of the velocity of sound in oxygen $(v_{O_2})$ to that in hydrogen $(v_{H_2})$ is:$\frac{v_{O_2}}{v_{H_2}} = \sqrt{\frac{M_{H_2}}{M_{O_2}}}$The molar mass of hydrogen $(H_2)$ is $2 	ext{ g/mol}$ and the molar mass of oxygen $(O_2)$ is $32 	ext{ g/mol}$.$\frac{v_{O_2}}{v_{H_2}} = \sqrt{\frac{2}{32}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$Thus,the ratio is $1:4$.

The velocity of sound measured at a given temperature in oxygen and hydrogen is in the ratio of:

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