1. Use the formula for speed of sound in a gas

   The speed of sound in an ideal gas is $v = \sqrt{\frac{\gamma R T}{M}}$ where:

   • $\gamma$ = ratio of specific heats,
   • $R$ = universal gas constant,
   • $T$ = absolute temperature,
   • $M$ = molar mass of the gas.

2. Compare hydrogen and oxygen at the same temperature

   At the same temperature, and since both hydrogen ($\mathrm{H_2}$) and oxygen ($\mathrm{O_2}$) are diatomic gases, we take $\gamma$ to be the same for both.

   So, $v \propto \frac{1}{\sqrt{M}}$

3. Write the ratio

   $\frac{v_{\mathrm{H_2}}}{v_{\mathrm{O_2}}} = \sqrt{\frac{M_{\mathrm{O_2}}}{M_{\mathrm{H_2}}}}$

4. Substitute molar masses

   • For hydrogen gas, $M_{\mathrm{H_2}} = 2$
   • For oxygen gas, $M_{\mathrm{O_2}} = 32$

   Therefore, $\frac{v_{\mathrm{H_2}}}{v_{\mathrm{O_2}}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$

5. Final ratio

   $v_{\mathrm{H_2}} : v_{\mathrm{O_2}} = 4 : 1$

6. Check options

   • A: $1:1$ ❌
   • B: $1:2$ ❌
   • C: $1:4$ ❌
   • D: $4:1$ ✅

So the correct option is D.