The ratio of speed of sound in hydrogen gas to the speed of sound...

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

${v}_{{H}_{2}} = \sqrt{\dfrac{\gammaRT}{{M}_{{H}_{2}}}} . . . \left(1\right)$

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

${v}_{{O}_{2}} = \sqrt{\dfrac{\gammaRT}{{M}_{{O}_{2}}}} . . . \left(2\right)$

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

$\dfrac{{v}_{{H}_{2}}}{{v}_{{O}_{2}}} = \sqrt{\dfrac{{M}_{{O}_{2}}}{{M}_{{H}_{2}}}} . . . \left(3\right)$

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

$\begin{cases}\dfrac{{v}_{{H}_{2}}}{{v}_{{O}_{2}}} & = & \sqrt{\dfrac{32}{2}} \\ & = & 4: 1\end{cases}$