The Plucked String

• When a string is plucked, the finger chooses a point on the string and then displaces it a certain distance.

• Plucking a string therefore, introduces an initial energy displacement (potential energy).

• The shape of the string before its release defines which harmonics will be present in the resulting motion.

• A string plucked at 1/n$^{th}$ the distance from one end will not have energy at multiples of the n$^{th}$ harmonic.

• The strength of excitation of the $m^{th}$ vibrational mode is inversely proportional to the square of the mode number.

• A simple example is demonstrated by plucking the string exactly midway between its endpoints. In so doing, we have created a sort of triangle wave, with its corresponding harmonics.

  Figure 2: The motion of a string plucked one-half of the distance from one end.