Nonlinear generation of sum frequencies in Sitka spruce

Abstract

It has been known for several decades that there are anomalous frequency components in the sound of a piano. These occur at the sum and difference frequencies of the overtones attributable to string motion, and are commonly referred to as phantom partials. Recent work has shown that, contrary to the generally accepted theory, the majority of power in these frequency components originates in the wooden parts of the piano and not the string. However, the etiology of the nonlinearity is not clear. To determine if the source of the nonlinearity is the stress caused by the pressure of the strings on the soundboard, experiments were performed on isolated pieces of Sitka spruce. The results indicate that stress can significantly increase the nonlinear response of the wood. [Work supported by NSF Grant #PHY-160749.]