What differentiates their fundamental frequency? In a guitar all the strings are of the same length, they have the same mass per length and the...

The formula for the fundamental frequency of a stretched
string is given by:

sqrt [ T/ (m/L)]/ 2*L , where T is the
tension in the string, m is the mass per length and L is the length of the
string.

We have been told that all the strings are of the
same length, they have the same mass per length and the same tension is applied to all
of them. So if we substitute the values in the formula for fundamental frequency we see
that it is the same for all of them. Nothing differentiates it except the factors that
have already been mentioned.

To get different fundamental
frequencies either the length, the tension or the mass/ length of the strings has to be
altered.