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The Physics of Vibrating Strings

A short version of my article on vibrating strings which appeared in Computers in Physics

A program (in C) which calculates the time evolution of a guitar string.

A program (in C) which calculates the time evolution of a piano string which is excited by a blow from a piano hammer. The string is assumed to be perfectly flexible, and the hammer is modeled with a nonlinear force law, as appropriate for real hammers.

Motion of a more realistic piano string. This program (in C) calculates both the transverse and longitudinal vibrational motion of a piano string. The string is excited by a blow from a piano hammer, and nonlinear effects for the string are included to lowest order. This results in the excitation of a longitudinal vibration (i.e., a compressional wave). This longitudinal vibration is thought to play an important role in the "attack" portion of a piano tone. This program also connects one end of the string to a "bridge," and this causes the vibration to decay slowly with time.