Finite-amplitude plane waves in ducts with varying properties

The method of multiple scales is used to determine a first-order uniform expansion for finite-amplitude plane waves of continuous waveforms propagating in a duct having a slowly varying cross section and filled with an inhomogeneous fluid. Losses due to the acoustic boundary layer or a slight wall admittance can be accounted for by decomposing the continuous waveform into its Fourier components and correcting the amplitude and phase of each component independently. Losses at shocks can be accounted for by using weak-shock theory. The results show that the shock formation distance tends to be shortened in a converging section and tends to be lengthened in a diverging section of the duct.