Acoustic analysis of a finite cylindrical duct based on Greenʹs functions

An approximate acoustic model of a finite cylindrical duct for studying the sound radiation of MRI scanners is presented in this paper. The finite duct was regarded as a “virtually closed cavity” with a specific boundary definition at the two open ends. The eigenfunctions ψ chosen as consisting of the acoustic modes at the cut-off frequencies were used for the Greenʹs functions to solve the Kirchhoff–Helmholtz (K–H) integral. The sound fields calculated by the analytical model were similar to the results obtained by the boundary element method (BEM) model except for some relatively minor differences in the region close to the open ends. When compared to the previous work, this model is relatively simple and much more computationally efficient.