Directivity & coverage
Q, DI & sensitivity
Directivity factor from coverage angles by Molloy’s formula, and the sensitivity that efficiency plus DI delivers.
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Directivity & coverage
Directivity factor from coverage angles by Molloy’s formula, and the sensitivity that efficiency plus DI delivers.
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A horn does two separate things for sensitivity. It raises the efficiency of the driver, turning more electrical power into sound, and it concentrates that sound into a limited angle. The second effect is described by the directivity factor : the ratio of the on-axis intensity to that of a source radiating the same power equally in all directions.
For a horn whose beam is roughly rectangular, with −6 dB coverage angles and , Molloy's formula gives a good estimate:
The inverse, , is the fraction of the full sphere the horn illuminates; Fig. 1 draws it on a sphere unwrapped like a world map. A 90° by 40° horn covers about 8 % of the sphere, which is a of 13 and a directivity index of 11 dB.
One acoustic watt radiated uniformly into a full sphere produces 109.2 dB SPL at one metre (20 °C). Efficiency and directivity then add in decibels:
This explains why horn sensitivities of 105 to 115 dB are ordinary: 25 % efficiency costs only 6 dB against the 109 dB reference, and a 10 dB directivity index more than pays it back. It also shows the limit. No passive device exceeds 100 % efficiency, so beyond about 109 dB plus DI there is nothing left to gain.
Molloy's expression assumes all the energy stays inside the nominal coverage angles. Real horns spill some outside, so measured Q is usually a little lower, most of all at low frequencies.