Theoretical investigations are undertaken with the propagation of sound inside the tube filled with liquid. Previous theoretical works by Del Grosso's, Lafleur and Shields, and Elvira-Segura are here reviewed and extended to the complex domain inorder to predict the attenuation, as well as the sound speed, of the modes as a function of frequency. Phase velocity, group velocity, the attenuation, and cut-off frequencies of modes are obtained for the water-filled PMMA (Perspex) tube of internal radius, b=4.445 cm, and thickness, h=0.5 cm in the range of the wavenumber-radius product, k b 1 , up to 18. The theory was then applied to the case of a stainless-steel pipe filled with mercury having the dimensions as used in the Spallation Neutron Source at Oak Ridge National Laboratory, Tennessee
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