A formulation based on the uniform theory of diffraction (UTD) for the analysis of the multiple-diffraction of a spherical sound wave caused by a series of wedges or knife-edges is hereby presented. The receiver location has to be considered at the same height as the preceding obstacles and at the same inter-obstacle distance from the last wedge. The solution, which is based on a UTD-physical optics formulation for radio-wave multiple-diffraction and has been validated through comparison with a geometrical theory of diffraction acoustic model, is computationally more efficient than other existing methods thanks to the fact that only single diffractions are involved in the calculations (high-order diffraction terms are not considered in the diffraction coefficients), thus allowing for the consideration of a great number of obstacles. In such a way, the proposed solution overcomes the limitations of previous works when multiple acoustic diffraction caused by an array of elements of equal height is to be analyzed. Therefore, the results can be applied in the study of sound propagation in scenarios where multiple-diffraction over a series of edges of equal height and periodical spacing has to be considered, such as the typical audience seating of a concert hall.