Energy Distribution Amongst Harmonics

f = 0.1
N = 16 8 16 32

Animation shows the vibration of a string fixed at both ends. Vibration amplitudes are highly exagerated for convenience of observation.

You can also observe the behaviour if greater number of terms are used in the fourier expansion.The increase in the number of terms approximates the shape of the string better.

Individual components of the oscillations of the string are represented by the stationry wave patterns and so on.The values of amplitudes A1,A2,A3 of individual components depend on the position where the string is plucked. For any point of plucking all harmonics are present but the amplitudes of higher harmonics will be smaller.

Observe the difference between the behaviors of the string when it is plucked in the middle and when it is plucked close to a fixed end.When plucked close to an end more energy is distributed amongst higher harmonics making the sound richer.