A coherent model for predicting noise reduction in long enclosures with impedance discontinuities

A theoretical model has been developed for the prediction of sound propagation in a rectangular long enclosure with impedance discontinuities. Based on the image-source method, the boundaries are assumed to be geometrically reflective. An infinite number of image sources are generated by multiple reflections. The sound pressure of each image is obtained by an approximate analytical solution, known as the Weyl-van der Pol formula. The total sound field is then calculated by summation of the contribution from all images. The phase information of each image and the phase change upon reflection are included in the model. A single change of impedance in a two-dimensional duct is focused on as the fundamental problem of the current study. The diffraction effect at the impedance discontinuity is proved to be insignificant, and it is ignored in the formulation. On the assumption that the diffraction effect is not important, the investigation is moved on to a rectangular long enclosure. Measurements are conducted in two model tunnels to validate the proposed prediction model. The predictions are found to give good approximations of the experimental results. The theoretical model serves as the first attempt to optimize the position and pattern of sound absorption materials in a long enclosure, such as an underground railway station or a building corridor, for the reduction of noise and improvement of sound quality.