The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

<p>The speed of sound in a gas is given by the formula:</p> <p>$v = \sqrt{\frac{\gamma RT}{M}}$</p> <p>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.</p> <p>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.</p> <p>Let&#39;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:</p> <p>$\frac{v_\text{H}}{v_\text{O}} = \sqrt{\frac{M_\text{O}}{M_\text{H}}}$</p> <p>The molar mass of hydrogen (H₂) is $2\, \text{g/mol}$, and the molar mass of oxygen (O₂) is $32\, \text{g/mol}$.</p> <p>Now, we can calculate the ratio of the speeds:</p> <p>$\frac{v_\text{H}}{v_\text{O}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$</p> <p>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 $4:1$.</p> <p>Therefore, the correct answer is $4:1$.</p>