v = sqrt(T/m)

Here, v is the speed of waves traveling on the string, T is the tension in the string, and m is the linear mass density (mass per unit length) of the string.

What we call the "natural frequency" in here is actually the lowest natural frequency of the string. Given f is the lowest natural frequency of the string, 2f, 3f, 4f, etc. are also natural resonant frequencies of the string, and these are called the "harmonics". This happens because a string has an infinite number of degrees of freedom.

The natural frequency of a string can be found by looking for a sinusoidal solution where the nodes coincide with the fixed ends of the string. This yields the equation:

f = sqrt(T/m) / 2L

Here, T and m are as before, and L is the length of the string. and f is the frequency of the vibration in Hertz (that is what you hear!).