Energy Distribution Amongst Harmonics

f = 0.1

N = 16 8 16 32

f = ℓ/L, where ℓ is the distance from left end where string is plucked and L is the length of the string. N is the number of terms in the Fourier series used to represent the oscillations.

Voice Over Quiz

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

Energy distribution amongst the first 8/16/32 harmonics is shown.
Energy of individual harmonics is shown relative to the fundamental.
The energy distribution depends on the position where the string is plucked.
Position of the plucked point can be varied and the dependence of relative enegy distribution amongst various harmonics observed.

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.