Mode Matching Analysis of Sound Waves in an Infinite Pipe with Perforated Screen

The propagation of sound waves in an infinite circular cylindrical pipe with an inserted perforated screen is investigated rigorously through the mode matching technique. The pipe walls are assumed to be rigid for \( - \infty < z < - l\) and coated for \( - l < z < 0,{\text{ }}0 < z < \infty \) with different linings. An analytical solution for the field terms are determined in form of eigenmodes which are matched across the boundary of each junction discontinuity. Numerical results are performed to show the effect of the different parameters such as waveguide radius, length of the partial lined part and acoustic absorbing lining properties on the propagation phenomenon. The use of such components is effective in reducing noise effects from various sources. The results of the mode matching technique are also compared graphically with the results of the Wiener–Hopf technique which is more difficult to implement and perfect agreement are observed.