Physics - Sound Wave Question with Solution | TestHub

The formula to calculate the speed of sound in hydrogen gas is given by

$v_{H_2}=\sqrt{\frac{\gamma RT}{M_{H_2}}} ...\left(1\right)$

The formula to calculate the speed of sound in oxygen is given by

$v_{O_2}=\sqrt{\frac{\gamma RT}{M_{O_2}}} ...\left(2\right)$

Divide equation (1) by (2) and simplify to obtain the required ratio.

$\frac{v_{H_2}}{v_{O_2}}=\sqrt{\frac{M_{O_2}}{M_{H_2}}} ...\left(3\right)$

Substitute the values of the known parameters into equation (3) to calculate the required ratio.

$\begin{array}{rcl}\frac{v_{H_2}}{v_{O_2}}& =& \sqrt{\frac{32}{2}}\\ & =& 4:1\end{array}$