High-frequency acoustic wave properties in a water-filled pipe. Part 2: range of propagation

Abstract

ABSTRACTThis paper is Part 2 following on from the authors’ paper “High-frequency acoustic wave properties in a water-filled pipe. Part 1: dispersion and multi-path behaviour”. The present paper focuses on the spatial distribution of energy and the important factors influencing the range of propagation of high-frequency waves (HFW). Practical implications of energy distribution and wave propagation range for selecting an appropriate number and arrangement of sites to monitor and sample HFW (mainly pressure) are highlighted. The results show that the energy of radial modes becomes trapped near the pipe centreline and decreases with distance from the centreline. The role of multi-path, frequency bandwidth of the transient source, fluid viscosity and source size on the range of propagation of HFW are investigated and an approximate expression for estimating this range is developed. Overall, the range of propagation of HFW is reduced as mode number increases because higher modes take longer (less direct) paths to travel a given stretch of a pipe.