Transverse-longitudinal waves excited by a plectrum in a plucked instrument string

A solution of the problem of the propagation of longitudinal-transverse waves in the string of a plucked instrument excited by a wedge-shaped plectrum when the plectrum has an arbitrary law of motion is obtained within the framework of the formulation proposed previously in [1]. The presence of an additional spectrum of transverse-longitudinal vibrations while the plectrum is acting is established. For the case of a wedge-shaped plectrum, moving with constant velocity, an exact non-linear solution of the problem is obtained, which confirms the possibility of using linearized equations [1,2] to describe the free play on plucked instruments. The presence of a velocity field in the string when the action of the performer is completed, leads to a new formulation of the problem of the longitudinal-transverse vibrations of the string of a plucked instrument after the performer has completed his action, which differs from the existing formulation of the problem [3, 4]. (C) 2003 Elsevier Ltd. All rights reserved.