For acoustic arrays (microphones or loudspeakers) the main beam width of the radiation pattern is determined by the spacing between the elements in terms of the wavelength. Thus the beam pattern depends on the frequency. It is demonstrated that by controlling the spacing and the frequency response of a pair of superposed arrays, constant directivity of the main beam lobe over a wide frequency range can be achieved. Large powers can be achieved with relatively low energy densities at each element. A procedure is described by which line arrays of loudspeakers can be superposed with appropriate signal conditioning to control the main beam coverage with frequency. This methodology is extended to an X-shaped planar array for three-dimensional beam control with frequency. Computer models and experiments verify the process for one octave, and models are used to extend the method to wider frequency ranges and more optimal beam synthesis.
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