Little work has been done in the study of loudspeaker directivity dynamics, particularly with arrays of drivers suitable for sound reinforcement applications. We have developed a mathematical model which allows the three-dimensional directivity characteristics of an arbitrarily configured arrangement of "real" drivers (that is, loudspeakers with defined amplitude, phase, and horizontal/vertical polar directivity characteristics as a function of frequency) to be simulated using a set of interactive computer programs. The mathematical basis of the author's model is derived and the set of computer programs in the simulation package is described. Results of several case studies illustrate its utility.
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