The speed of sound in a gas is given by the formula:

$$v = \sqrt{\frac{\gamma RT}{M}}$$

where $$v$$ is the speed of sound, $$\gamma$$ is the adiabatic index, $$R$$ is the universal gas constant, $$T$$ is the temperature, and $$M$$ is the molar mass of the gas.

For diatomic gases, such as hydrogen (H₂) and oxygen (O₂), the adiabatic index $$\gamma$$ is the same, approximately equal to $$\frac{7}{5}$$, and the temperature is given as the same for both gases.

Let's denote the speed of sound in hydrogen as $$v_\text{H}$$ and in oxygen as $$v_\text{O}$$. The ratio of the speeds can be calculated as:

$$\frac{v_\text{H}}{v_\text{O}} = \sqrt{\frac{M_\text{O}}{M_\text{H}}}$$

The molar mass of hydrogen (H₂) is $$2\, \text{g/mol}$$, and the molar mass of oxygen (O₂) is $$32\, \text{g/mol}$$.

Now, we can calculate the ratio of the speeds:

$$\frac{v_\text{H}}{v_\text{O}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$$

This means the ratio of the speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is $$4:1$$.

Therefore, the correct answer is $$4:1$$.