harmonics A string fixed at both ends vibrates when plucked. In the fundamental tone the antinode (where maximum displacement occurs) is at the centre and the whole string vibrates with one segment. The frequency of the fundamental tone is,

n=(2 l)^-1 (T/m)^1/2

where l is the length of the string, T the tension on the string and m the mass of the string per unit length. The string can also vibrate with two or more segments. The frequencies of these overtones are 2n, 3n and so on. These are known as harmonics. Every vibrating system has fundamental and harmonics which are called the natural frequencies of the system.