Standing waves on strings

The animation shows three harmonics on a vibrating string. The top string is vibrating with the lowest frequency - this is the fundamental or first harmonic. The next is vibrating with a frequency double that of the first - this is the second harmonic and would give a note one octave above the fundamental. The lower string is vibrating four times faster than the top one - this is the fourth harmonic and would give a note two octaves above the first. (The third harmonic is not shown here).

First harmonic frequency (f) = 1/2L(T/m)^1/2
Second harmonic frequency (f) = 1/L(T/m)^1/2
Fourth harmonic frequency (f) = 4/2L(T/m)^1/2

A string can be made to vibrate in a selected harmonic by plucking it at one point (the antinode) to give a large initial amplitude and touching it at another (the node) to prevent vibration at that point.