Abstract
One-dimensional sound propagation in a waveguide of continuously varying area is governed by Webster's equation. For certain axial variations in area and in locally reacting wall impedance, closed form solutions can be obtained. However, for arbitrary variations in these parameters as well as for more complicated forms of the equation, numerical solution techniques are required. In this paper, modified versions of Webster's equation are derived which allow consideration of horns with axial temperature gradients and with inserts of porous material. Numerical solutions to the equations are effected by means of a transfer matrix technique. The horn is segmented axially and the segment length is used as an expansion parameter with which to perform an asymptotic expansion of the governing differential equation. As a result the segment boundary value problem is replaced by a sequence of initial value problems. These are solved to yield a transfer matrix relating the acoustic pressure and particle velocity on the right end of the segment to those on the left. Transfer matrices are developed for each of the horn configurations for which governing equations are derived. Some sample numerical results are included.
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