Evolution study of the phase and group velocities by Choi-Williams and Born-Jordan time-frequency representations

The propagation characteristics of circumferential waves around a thin aluminum tube filled by air and immersed in water, are investigated theoretically and experimentally. In particular, the experimental study focuses on the determination of the dispersion velocity. Choi-Williams and Born-Jordan representations are used to produce a good resolution in time and frequency domains and extract group velocities from arrival times of circumferential waves. On some time-frequency images, the symmetric (S
₀
) and antisymmetric (A
₁
) circumferential waves propagating around tube are observed. In comparison with the results from the theory and experiment, it is confirmed that the measured group velocities agree well with that computed by the theoretical method of proper modes.