Iterative Calculation of the Acoustic Impedance of a Trumpet-Like Musical Instrument

Abstract

The acoustic impedance is an important quantity in characterizing the behavior of an acoustic system. The acoustic impedance of musical instruments determines the instrument’s response to excitation, reveals resonance frequencies, and shows which notes can be played. While the acoustic impedance is easy to calculate for simple shapes, it is very complicated to do so for the shapes of real musical instruments. This talk outlines an interactive method of calculation of the acoustic impedance of an arbitrary shape of an axially symmetric air column by approximating the air column by a series of cylindrical elements. We demonstrate the feasibility of the method by comparing the iterative result with the closed form solution for air columns of simple shape. Moreover, we discuss the calculation of the acoustic impedance of a trumpet-like instrument and show how different parts of the instrument affect its acoustic behavior.