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A modelling of low-frequency sound propagation in slowly varying ducts withsmoothly varying lining is proposed leading to an acoustic mild-slope equationanalogue to the with mild-slope equation for water waves. This simple 1D MildSlope Equation is derived by direct application of the Galerkin method. It isshown that the acoustic mild-slope equation can serve as a good alternative tocomputationally expensive Helmholtz equations to solve such kind of problem.The results from this equation agrees well with FEM based solutions ofHelmholtz equation.

Acoustic Propagation in lined ducts with varying cross-section using a Mild-Slope approximation