Waves and vibrations in strings with windings: Commemorating the 100th anniversary of the birth of Kh.A. Rakhmatulin

The equations of the propagation of transverse, twisting and longitudinal waves and vibrations are obtained, taking into account their interactions in musical strings with windings. Their solutions are obtained. The occurrence of transverse and twisting motions leads to the appearance of longitudinal motions, while the transverse and longitudinal components play the role of inducing forces for the twisting components. The contributions of the transverse, twisting and longitudinal components to the dynamic loading of the string are of the same order. The longitudinal-twisting vibrations occur both at natural frequencies and at frequencies of the transverse vibrations. Resonance phenomena between the individual modes of these vibrations are possible.