Experimental Verification of Dispersive Wave Propagation on Guitar Strings

Abstract

Experimental research into the fundamental acoustic aspects of musical instruments and other sound generating devices is an important part of the history of musical acoustics and of physics in general. This paper presented experimental proof of dispersive wave propagation on metal guitar strings. The high resolution experimental data of string displacement are gathered using video-kymographic high-speed imaging of the vibrating string. The experimental data are indirectly compared against a dispersive Euler-Bernoulli type model described by a PDE. In order to detect the minor wave features associated with the dispersion and distinguish them from other effects present, such as frequency-dependent dissipation, a second model lacking the dispersive (stiffness) term is used. Unsurprisingly, the dispersive effects are shown to be minor but definitively present. The results and methods presented here in general should find application in string instrument acoustics.