Explanation for the frequency shift pattern of nonuniform blocked pipeline systems from an energy perspective

It was found in a previous study that the transient frequency shifts induced by nonuniform blockages in water pipelines become less evident as the frequency increases, but its physical mechanism is unclear. This paper explains this non-uniform blockage induced frequency shift pattern from an energy perspective. The results indicate that the non-uniform blockages have a less blocking effect on the propagation of high frequency waves; thus, the induced frequency shifts become less evident. In practical applications of non-uniform blockage detection, the frequency of the incident wave should be selected carefully to ensure that the reflected wave contains enough energy.