Question

The velocity of sound in air is doubled when the temperature is raised from $0 ^\circ$C to $a ^\circ$C. The value of a is ___.

Hint:

Always use Kelvin scale for temperature in gas laws and wave velocity formulas ($v = \sqrt{\gamma RT/M}$).

Answer 1

Correct Answer: 819

The speed of sound $v$ is proportional to the square root of absolute temperature $T$.
$v \propto \sqrt{T}$.
Given $v_2 = 2v_1$. This implies $\sqrt{T_2} = 2\sqrt{T_1}$, or $T_2 = 4T_1$.
Initial temperature $T_1 = 0^\circ C = 273 \text{ K}$.
Final temperature $T_2 = 4 \times 273 = 1092 \text{ K}$.
Convert $T_2$ back to Celsius: $a = 1092 - 273 = 819^\circ C$.