The Influence of an Impedance Obstacle on the Acoustic Field Inside a Rectangular Room

Abstract

Abstract The problem of sound propagation inside a rigid-walled room containing a rectangular obstacle was solved by dividing an acoustic field into subregions and using the continuity conditions. Acoustic waves were generated by a point source. The formulas valid for an impedance obstacle extending from a room floor to its ceiling were obtained. The considered obstacle can model such elements as a ventilation shaft, furniture, or construction pillar. The solution was expressed in the form of convergent series. To obtain accurate results, the error resulting from the use of truncated series was controlled. Additionally, to check the correctness of the proposed solution and its computer implementation, the results obtained for a negligibly small obstacle were compared with those given by the empty room model. An excellent agreement was achieved which proves a high accuracy of the used methodology. The numerical analysis shows that the calculation time of acoustic pressure in a part of an empty room can be significantly reduced using the obtained solution. An appropriate source location for noise reduction was found. The distribution of acoustic field was illustrated and some conclusions were formulated. The changes in acoustic field due to the presence of an obstacle were predicted and discussed.