Predicting the sound reduction index of finite size specimen by a simplified spatial windowing technique

The transfer matrix technique is an efficient tool for calculating sound transmission through multilayered structures. However, due to the assumption of infinite size layers important discrepancies may be found between predicted and experimental data. The spatial windowing technique introduced by Villot et al. Predicting the acoustical radiation of finite size multi-layered structures by applying windowing on infinite structures, Journal of Sound and Vibration 245 (2001) 433-455] has shown to give data much closer to measurement results than other measures, such as limiting the maximum angle of incidence when integrating to obtain the sound reduction index for diffuse incidence. Using a two-dimensional spatial window, also including the azimuth angle implies, however, that two double numerical integrations must be performed. As predicted results are compared with laboratory data, where the aspect ratio of the test object is required to be less than 1:2, a simplified procedure may be applied involving two single integrals only. It is shown that the accuracy in the end result may in practice be maintained by this simplified procedure.