The fundamental frequency of a vibrating string is directly...

$\sqrt{\dfrac{T}{\mu}}$

where $L$ is the length of the string, $T$ is the tension, and $\mu$ is the linear mass density.

From the formula, it is clear that the fundamental frequency is directly proportional to the inverse of the length of the string, i.e., $f \propto \dfrac{1}{L}$.

The frequency is proportional to the square root of tension ($f \propto \sqrt{T}$), inversely proportional to the square root of density ($f \propto \dfrac{1}{\sqrt{\rho}}$), and inversely proportional to the diameter ($f \propto \dfrac{1}{d}$).

Thus, the fundamental frequency is directly proportional to the inverse of its length.