Interference between the transverse and longitudinal vibrations in musical strings

The effect of stiffness on the transverse and longitudinal motions of a musical string

“…Solution (4) can be represented in the form (6) (everywhere henceforth, unless otherwise stated, summation is carried out from n = 1 to n =∞). Then…”

“…4 When the frequency of the individual modes of the natural longitudinal vibrations is identical with the frequency of the forced vibrations, that is, when resonance occurs between these forms of vibrations.…”

“…For small deviations from the initial stress state, the increment of the deformation will have the form [2][3][4] where the contributions of the longitudinal and transverse displacements to the dynamic component of the deformation will be of the same order. 2…”

Waves and vibrations in strings with windings

“…2 and also from an analysis of the equations and relations on the discontinuities that the transverse, longitudinal and twisting components of the dynamic loading of the string with a winding are of the same order. where x p (s, t) and p (s, t) are particular solutions, related to the the effect of the transverse components.…”