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Apparent Apex Part IV: Direct Radiators

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The apparent apex issues regarding the measurement of far field polar response at close distances are examined for direct radiators. Earlier apparent apex studies on horn loudspeakers suggest that the location of the apparent apex changes with frequency and that significant measurement errors are obtained when a test microphone is placed too close to a source. The present paper develops and validates a model of a piston in half-space and presents directivity map error as a function of frequency, piston diameter, and microphone distance. Guidelines are offered for directivity measurements made in common-sized anechoic chambers.

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