Spatial Windowing for Finite-Size Incident Sound Transmission Coefficient of Multi-Component Surfaces

Spatial windowing was introduced for alleviating problems related to the infinite behaviour of rectangular surfaces. For finite rectangular surfaces, the radiation efficiency can be computed very efficiently. Considering multi-component surfaces such as a building façade, which include both rectangular and non-rectangular surfaces (e.g., wall and window), an adjusted version of the spatial windowing is here applied, using a divide-and-conquer approach of rectangular surfaces and applying the correlation between two adjacent surfaces. Hence, the transmission coefficient and sound reduction index (SRI) of multi-component finite surfaces can be calculated. For a glass surface, the adjusted radiation efficiency presents good agreement with the non-adjusted one. Applying a convergence study to the adjusted radiation efficiency with respect to the glass surface, it was found that a coarsely divided surface approximates the relative undivided surface very well, under far-field conditions. Similar results were obtained with respect to the SRI of a single-component (glass) and a multi-component (glass and wall) surface. Applying both far-field and near-field conditions in a multi-component surface, the glass typically dominates the total SRI, especially with increasing its area. However, in the coincidence region of the wall, the SRI of the wall can be decisive for the total SRI.