A note on a WKB application to a duct of varying cross-section (Q1600346)

The authors study the two-dimensional problem of plane wave propagation of sound along a tube of gradually varying cross-sectional area. The classical equations of this problem are written. In the case of stationary medium, these equations yield the classical wave equation governing the sound pressure. The steady-state solution of this equation is converted to Liouville standard form: a differential equation of second order, with variable coefficients. Using the WKB method, the authors obtain an approximate harmonic solution for this differential equation, and give the impedance of a particular cosine-shaped horn terminated in an infinite baffle. The presented computation of normalized acoustic impedance shows less floating point operations when compared with the Runge-Kutta algorithm.