When the room temperature experiences a small variation from T to T...

The fundamental frequency of an organ pipe is given by $\nu = \dfrac{v}{\lambda}$, where $v$ is the speed of sound and $\lambda$ is the wavelength.

The speed of sound in a gas at absolute temperature $T$ is given by $v = \sqrt{\dfrac{\gamma R T}{M}}$.

Thus, the fundamental frequency is directly proportional to the square root of the absolute temperature:

$\nu \propto \sqrt{T}$

$\nu = k T^{1/2}$

Taking the natural logarithm on both sides:

$\ln \nu = \ln k + \dfrac{1}{2} \ln T$

Differentiating both sides for small variations:

$\dfrac{\Delta\nu}{\nu} = \dfrac{1}{2} \dfrac{\Delta T}{T}$