Temperature dependence of speed of sound could be expressed as $v = k\sqrt{T}$, where $k$ is some positive constant. In a medium sound is travelling along the $x$-axis. At $x = 0$, temperature is $T_1$ and at $x = L$, temperature is $T_2$ and the temperature varies linearly with $x$. Time taken by sound to travel from $x = 0$ to $x = L$ is