Understanding nonlinear effects on wave shapes: Comment on “An experimental analysis of a vibrating guitar string using high-speed photography” [Am. J. Phys. 82 (2), 102–109 (2014)]

Abstract

In a recent paper, Whitfield and Flesh found unusual bowing behavior in the waveform of a guitar string for large amplitude plucks. This Comment discusses the theory needed to understand this nonlinear effect, and it is shown that this theory provides reasonably good qualitative agreement with the observed wave form. This theory is interesting because: (i) it allows one to quantify the boundary between linear and nonlinear behavior in terms of key physical parameters; (ii) it reveals the importance of taking into account longitudinal displacements even when they are much smaller than the associated transverse displacements; and (iii) it reveals that dispersion due to tension changes and dispersion due to flexural rigidity have very similar functional forms, which leads to the question of when one effect can be neglected in comparison to the other.