This invention provides a radiation boundary integrator ("RBI") for integrating sound radiation from mid-range and high-frequency sources in multi-way loudspeakers. The RBI is a substantially solid boundary that is placed over the mid-range speakers to provide smooth, wave-guiding side walls to control the angular radiation of the high-frequency sound waves emanating from the high-frequency sound sources. To allow the mid-range frequency sound waves generated from mid-range sound sources to pass through the RBI, the RBI is designed with openings. To further prevent the possibility of having high-frequency sound radiate through the openings in the RBI, the RBI may be designed with porous material in the openings of the RBI. The porous material would be transparent to the mid-range sound radiation, but would prevent the high-frequency sound radiation from being disturbed by the openings in the RBI. As such, the RBI provides an outer or front surface area that forms an acoustical barrier to high frequencies radiating across the front surface, yet is acoustically transparent to mid-range frequencies radiating through openings in the RBI. The RBI may also serve as a volume displacement device to compression-load the mid-range sound sources by contouring the back side of the RBI to the shape of the mid-range sound sources thus reducing the space between the RBI and the mid-range sound sources and loading the mid-range sound sources to generate greater mid-range sound energy.