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RE: Why do line arrays using directional speakers require shorter lines for similar near field performance?

That is a hard question to answer simply.
Line sources use the size of the radiating area (height) to produce a forward beam which is summed form the forward radiation of each source. The problem is 20 hz to 20Khz is a 1000 to 1 span so far as the size of wavelength so a given size line is a different acoustic size at every frequency and so it's vertical behavior is different at every frequency.
Because that effect is so strong and frequency dependent, lines are usually curved to make them more like a point source in the vertical as well as horizontal but the longer you make the line and or the more curved it is, the more radiation is sprayed sideways in addition to rear.
Anyway, the idea of making them short is it will have a wider vertical angle and act less like a line source.
Keeping it short will also minimize the spreading of energy in time as well as there is only a small range of distances from the source to your ears Conversely, line arrays only have a reduced spl fall off with distance when they are acoustically large and are exhibiting destructive cancellation in the near field and then any energy impulse you feed in, will arrive spread out at separate times from each box or source according to the distance. DSP can correct for that in one location but not elsewhere.

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