Exponential horn revisited: wave equation, normal modes and experimental measurements

Abstract

In this work, a theoretical analysis is first presented to find the wave equation corresponding to the propagation of disturbances in the air contained inside a tube of variable cross section. In particular, the case of a tube with a circular cross section whose area varies exponentially as a function of the axial coordinate is studied. The hypotheses of the model used are discussed and the solutions of the wave equation obtained are presented. Secondly, and with the aim of validating the model used, measurements are made on a tube such as the one described, built using a 3D printer.