1. Use the formula for speed of sound in an ideal gas

For an ideal gas, $v = \sqrt{\frac{\gamma R T}{M}}$ where:

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

At the same temperature, $R$ and $T$ are same for both gases, so $v \propto \sqrt{\frac{\gamma}{M}}$

2. Write the ratio for helium and oxygen

$\frac{v_{He}}{v_{O_2}} = \sqrt{\frac{\gamma_{He}/M_{He}}{\gamma_{O_2}/M_{O_2}}}$

3. Substitute known values

• For helium (monoatomic): $\gamma_{He} = \frac{5}{3}, \quad M_{He} = 4$

• For oxygen (diatomic): $\gamma_{O_2} = \frac{7}{5}, \quad M_{O_2} = 32$

Thus, $\frac{v_{He}}{v_{O_2}} = \sqrt{\frac{\left(\frac{5}{3}\right)/4}{\left(\frac{7}{5}\right)/32}}$

4. Simplify

$\frac{v_{He}}{v_{O_2}} = \sqrt{\frac{5}{3\cdot 4} \cdot \frac{32\cdot 5}{7}}$

$= \sqrt{\frac{5}{12} \cdot \frac{160}{7}}$

$= \sqrt{\frac{800}{84}} = \sqrt{\frac{200}{21}}$

Numerically, $\frac{200}{21} \approx 9.524$

$\sqrt{9.524} \approx 3.086$

5. Find the speed in helium

Given: $v_{O_2} = 460\,\text{m s}^{-1}$

So, $v_{He} = 460 \times 3.086 \approx 1419.6\,\text{m s}^{-1}$

$v_{He} \approx 1421\,\text{m s}^{-1}$

6. Match with options

The correct option is: $\boxed{A}\; 1421\,\text{m s}^{-1}$