Controlling 3D sound field generated by a 2D surface from its 1D boundary

As described by the Kirchhoff-Helmholtz integral equation, for a 3D space without internal sources, the inside sound field is completely determined by the sound pressure and its normal gradient on the boundary, so if only a portion of the boundary surface vibrates as the primary sound source while all the remaining portion of the surface is acoustically rigid, a sufficiently large number of secondary sound sources can be located evenly on the primary sound surface to control the 3D sound field completely. The question to be investigated in this research is whether it is possible to control the 3D sound field by only applying secondary sound sources along the 1D boundary of the 2D primary sound surface, for example, controlling the sound transmission from a door with secondary sound sources only on its frame. Simulation and experimental results will be presented to demonstrate the feasibility of the idea.