Analytical Time Domain Normal Mode Solution of an Acoustic Lossy Waveguide

Normal mode method has widely been used for various applications in underwater acoustics. For broadband signals, this conventional frequency domain approach needs to solve the problem repeating for every frequency component. In this paper, a direct, analytical and causal time domain solution for an acoustic lossy waveguide problem is derived by using Time Domain Normal Mode (TDNM) method. The proposed approach splits an acoustic lossy wave equation into a Sturm-Liouville problem and an inhomogeneous lossy Klein-Gordon equation. A Green’s function technique is used to solve the second equation resulting a cut-off frequency formula to define number of propagating modes. The analytical TDNM solutions are compared with a Time Domain Image (TDI) method for both a causal cosine and a causal shock wave source. Good agreements are observed between the results.