A set of mathematical expressions to analyze the performance of loudspeaker line arrays is provided. At first a set of expressions for straight-line arrays is developed, including the directivity function, polar response, quarter-power angle, on-axis and off-axis pressure responses, and two-dimensional pressure field. Since in practice many loudspeaker line arrays are not actually straight, expressions are provided for curved (arc), J, and progressive line arrays. In addition, since loudspeaker systems are often not perfect sources, the effects of spherical radiating sources and gaps between sources are analyzed. Several examples of how to apply the models are given, and modeled performance is compared to measured polar data.
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