In viscoelastic pipes, where the material properties depend on a complex bulk modulus as well as on a complex shear modulus, the sound field within the fluid is affected. Therefore, the dispersion of flexural waves occurs in the pipe, while the speed of flexural waves decreases due to the coupled fluid mass. Coupling between the pipe wall and the fluid also decreases the sound speed in the fluid. Likewise, the speed of sound in fluid is frequency dependent, just as the group velocity of bending waves depends on the frequency. Wavelet transform of nonstationary sound signal was used to identify the frequency-dependent fluid sound speed. Measurement and analysis of nonstationary signals with the use of time-frequency method provides a view to frequency-dependent transfer characteristics of fluid-pipe coupled system. The so-called fluid mode and pipe mode resonant frequencies are evident and the impact of different pipe wall material properties is shown. The results also showed that, in the case of propagating small disturbances (such as acoustic waves), the pipe wall inertance has a minor influence on the wave propagation characteristics. The elastic reaction of the wall to expansion of the cross section greatly exceeds the inertial reactions.