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

In this paper, the two-dimensional problem of an incident plane sound wave traveling along a rigid duct or a rigid horn is studied. It has been shown that a simple one-dimensional analysis gives accurate predictions of the sound propagation. The impedance of a particular horn is obtained using the Wentzel-Kramers-Brillouin (WKB) approximation to solve the Webster equation. The mouth of the horn is assumed to be terminated in an infinite baffle. Computation of the normalized acoustic impedance using the WKB approach shows less floating point operations when compared with a Runge-Kutta algorithm.