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I was wondering if there's an underlying physical reason why detection in microphones and antennas is a cardioid, or if it's just that a cardioid happens to be the mathematical object that best approximates the shape of the detection pattern.

In other words, is there an "ab initio" reason, or it's an empirical fact?

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The "that's how it is" answer may be given for mics with bidirectional acoustic pattern (that's just what a voice coil constrained to one axis of motion will provide), but not for cardioid type mics. enter image description here

The cardioid shape is apparently formed via the superposition of the omni & bidirectional shapes, implying more than one type of audio elements being used in the microphone. Signals from the rear end of the bi element is subtracted while signals from the front end are added to the signals coming from the omni element--resulting in the cardioid pattern above.

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