Acoustic scattering by a two-layer cylindrical tube immersed in a fluid medium: Existence of a pseudo wave

The present paper studies the acoustic signal backscattered by an air-filled copper–solid polymer two-layer cylindrical tube immersed in water. The work is done from the calculation of the backscattered pressure, an inverse Fourier Transform, which allows us to obtain an impulse signal. Smoothed pseudo Wigner–Ville and Concentrated spectrogram representations have been chosen to analyze the scattering phenomenon. For reduced frequencies ranging from 0.1 to 200, the resonance trajectories and time–frequency images have shown the presence of the guided waves. The bifurcation of the A0 wave into the A0(-) and the A0(+) waves has also been observed. The authors provide the phase and the group velocities of guided waves and investigate the differences between curves. The findings are then compared with those obtained for the copper and the solid polymer one-layer cylindrical tubes. Group velocity values have also been extracted from smoothed pseudo Wigner–Ville and Concentrated spectrogram time–frequency images. A good agreement with the theory has, therefore, been observed. The study of acoustic backscattering by a copper–solid polymer two-layer tube has revealed the interaction and the coupling of guided waves, specially the presence of a pseudo A1 wave; which is a very interesting, remarkable phenomenon.