Impact excitation of piano string vibration

Abstract

Piano strings are well described by linear partial differential equations, even when stiffness is included. But compressed-felt piano hammers have a distinctly nonlinear force–compression relation, so it is challenging to model the hammer–string interaction correctly. In recent years it has been practical with personal computers to carry out numerical integration of the nonlinear equations for specific examples, though hammer/string mass ratio, hammer compliance, hammer resistive loss, string stiffness, striking point, and striking velocity present a large parameter space to explore. Examples of such integrations, showing calculated string motions and spectra, will be presented on videotape. Related investigations have been carried out by several authors, and are of interest both for offering an understanding of energy transfer to the strings in acoustic pianos and for suggesting digital algorithms for synthesizing sounds that represent a generalization of the piano family.