Longitudinal, Transverse, and Torsion Waves and Oscillations in Musical Strings

摘要

The equations of propagation of transverse, longitudinal,and torsion waves and oscillations are obtained taking into account their interference in musical strings with winding. It is shown that the contributions of the transverse, torsion, and longitudinal components to the dynamic string load prove to be of the same order of magnitude. The equations of the torsion and longitudinal oscillations are inhomogeneous. The initiation of transverse and torsion motions leads to the occurrence of longitudinal motion; at the same time, the transverse and longitudinal components play the role of the driving force for the torsion oscillations. During the deformation, the string particles achieve the complicated joint transverse, torsion, and longitudinal motions.