Weak nonlinear propagation of sound in a finite exponential horn

This article presents an approximate solution for weak nonlinear standing w aves in the interior of an exponential acoustic horn. An analytical approac h is chosen assuming one-dimensional plane-wave propagation in a lossless f luid within an exponential horn. The model developed for the propagation of finite-amplitude waves includes linear reflections at the throat and at th e mouth of the horn, and neglects boundary layer effects. Starting from the one-dimensional continuity and momentum equations and an isentropic pressu re-density relation in Eulerian coordinates, a perturbation analysis is use d to obtain a hierarchy of wave equations with nonlinear source terms. Gree n's theorem is used to obtain a formal solution of the inhomogeneous' equat ion which takes into account Linear reflections at the ends of the horn, an d the solution is applied to the nonlinear horn problem to yield the acoust ic pressure for each order, first in the frequency and then in the time dom ain. In order to validate the model, an experimental setup for measuring fu ndamental and second harmonic pressures inside the horn has been developed. For an imposed throat fundamental level, good agreement is obtained betwee n predicted and measured levels (fundamental and second harmonic) at the mo uth of the horn. (C) 2001 Acoustical Society of America.