What are the limits of the discrete stringed instrument model?

Abstract

Many different analytical models for stringed instruments have appeared in the technical literature, but one of the most widely used is a simple discrete model presented by Christensen and Vistisen in 1980. This model accounts, in a simple and approximate way, for the first two or three modes of a typical stringed instrument such as a guitar and includes coupling between the structure and the enclosed air. For the model to be used in predicting the effect of design changes, it is important to understand its limits. In order to explore the applicablity of the model, we have constructed a fixture that models the volume of an acoustic guitar with rigid side walls and flexible top and back plates, which can be changed quickly. A group of different tops was tested to show the effect of changes in mass and stiffness. Additionally, different soundhole geometries were used. In order to change the interior volume of the body, rigid plates were inserted into the body cavity. We report on the ability of tuned discrete models to account for changes to the geometry and the structure. Further, we show the experimentally determined trends in dynamic response of the guitar fixture.