The velocity of sound in air is doubled when the temperature is raised from $$O^{o}$$C to $$\alpha ^{o}$$ C. The value of $$\alpha$$ is _______.

Since the velocity of sound in an ideal gas is proportional to the square root of the absolute temperature, we have

$$v \propto \sqrt{T}$$

which implies $$\frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$$.

Substituting $v_2 = 2v_1$ and $T_1 = 0°C = 273 \, K$ into this relation gives

$$\frac{2v_1}{v_1} = \sqrt{\frac{T_2}{273}}$$

so

$$2 = \sqrt{\frac{T_2}{273}}$$.

Squaring both sides yields

$$4 = \frac{T_2}{273}$$

and hence

$$T_2 = 4 \times 273 = 1092 \, K$$.

Converting to Celsius gives

$$\alpha = T_2 - 273 = 1092 - 273 = 819°C$$.

Therefore the required temperature is 819°C, so the answer is Option X.