Notice how the sound of strings of different thickness changes when you pluck them. The strings with a bigger number are thicker.

What is the relationship between the thickness of the string and the pitch (f) of the sound produced by it?

A thicker string produces a deeper sound. The frequency of the oscillation is smaller, because the propagation speed of the oscillation is smaller in a string which has a bigger mass.

Naturally, it is also true if the density, and accordingly the mass of a string selected from strings of the same size is bigger, because the oscillation propagation speed in that string will be lower as well, so we can hear a deeper sound again.