The surprising influence of longitudinal motion in vibrating strings: Comment on “Video-based spatial portraits of a nonlinear vibrating string” [Am. J. Phys. 80 (10), 862–869 (2012)]

Abstract

An error in the quoted nonlinear coefficient that is commonly found in the literature is identified. The subtle origin of this error is identified as the neglect of longitudinal displacements of points in the string, which leads to a nonlinear coefficient that is a factor of 3/2 too large. A correct derivation is outlined and numerical simulations verify the correction.