https://www.soundonsound.com/techniques ... -explained
Earlier, I said that to achieve directionality a sound source needs to be larger than the wavelength it is producing. To achieve focus, or near–zero dispersion, which is a more stringent requirement, it needs to be somewhere approaching four times the wavelength. The wavelengths of audible sound extend all the way to 17 metres (20Hz) and beyond. But taking a reasonable lowish frequency of 170Hz with a wavelength of two metres (taking 340 metres per second as a nice round figure for the speed of sound), a line source eight metres high will be necessary. Quite tall! But at least we have a notion with some science behind it.
The next question is: how exactly do you make a loudspeaker that is several metres high? Currently, the way to do it is to stack multiple loudspeakers on top of each other. But instead of stacking 10–inch or 12–inch loudspeakers featuring identical drive units with poor HF response, as they did in the 1960s, each loudspeaker consists of LF and HF drive units and covers the full audio range (down to a reasonably low frequency). Also, rather than making one very tall cabinet, the modern line array consists of multiple small cabinets. The benefit of multiple cabinets is that you can assemble a line array that is as big or small as you like, or can fit in, or can budget for. You can also manipulate the shape of the array, which, as we shall see shortly, has significant benefits. Time for more science...
Since the line array is not actually one single tall–but–narrow drive unit, but is made up from discrete loudspeaker cabinets, one has to ask whether the individual units will couple together as though they were a genuine line source? The answer is yes, they will, but only where the drive units are separated by less than half a wavelength. This is easy for the lower frequencies, but more difficult to achieve as the wavelength shortens. As a benchmark, the wavelength at 400Hz is around 85 centimetres. So to couple at 400Hz the cabinets have to be less than 42.5 centimetres high. OK, that's doable, but we are not even halfway up the audio band here.
Still, at least we know the criteria to aim for. The longer the array is, the more tightly directional it will be in the vertical dimension, and for individual cabinets to couple well into the array, they have to be small vertically. The better both of these criteria can be achieved, the more controllable the beam of sound from the array will be. A good point is made by Ralph Heinz of PA manufacturers Renkus–Heinz: "The answer to the question of whether a line array is a line source is 'almost never'." Heinz's comment demonstrates that a theoretically perfect line source is virtually impossible to achieve. Only the best line arrays will come close.