Belief System #2: In this second look at arrayable loudspeakers we see a smaller following among loudspeaker designers because the rules aren’t as easy to comprehend. If you put two 90 degree loudspeakers next to each other, and splay them apart at a 20 degree included angle, should you not get 90 + 90 + 20 = 200 degrees of dispersion? It would seem so. But that’s not at all what happens.
Instead, the pressure from the two or more radiating devices, that’s the horns and cones, will combine in some particular manner. Exactly how they combine is the grand issue behind whether or not they will form a useful array or conversely, are just a bunch of speakers placed near each other that combine like oil and water.
For the record, this is the belief system that Apogee Sound based its designs upon. And it really can be called a “practice” rather an a “belief system” because the patterns and response curves of the resultant arrays were exhaustively measured outdoors, 30 feet above ground level, and carefully documented using Hewlett Packard and TEF measurement equipment. It was a process that took several months of full time work.
The net value, simplified as much as possible from the exhaustive process, was that low pressure audio sources combine much more readily than high pressure sources. Stated another way, sonic energy emanating from the mouths of horns is far more amenable to summing with like units than at the throat of horns.
The New Math
So it turns out that a certain 90-degree horn sitting adjacent to another 90-degree horn – both with very gradual fall-off characteristics – actually combine together quite well. The behavior is something like an old fashioned multi-cellular horn, producing a summed output that is on the order of 70 degrees.
Add a third horn to the array and the -6 dB points become even narrower, about 60 degrees. Build it larger, let’s say seven 90-degree horns, and the – 6 dB points become narrower still, about 40 degrees.
But here it’s important to note that we’re focusing on -6 dB points which, as noted earlier, are the industry standard for defining dispersion angle. The forward radiated power is much greater than that of a single horn, and that’s exactly what proper arrays should accomplish.
The useful angle of coverage of this array is much wider than its forward radiated power (again, based on -6 dB points). What do we mean by useful angle? That would be any point in the overall dispersion pattern that remains reasonably flat. If only 50 Hz to 100 Hz exhibits 180 degrees of coverage, but higher frequencies are far narrower, than 180 degrees would not be considered a useful angle of coverage.
Loudspeaker cones are altogether different from horns. Horns are designed to cover a certain dispersion angle. Cones are designed for everything but. The diameter and the geometry of a given cone’s flare-rate dictate the angle of coverage of an individual cone driver which, as one might suspect, will always be conical in nature.
The angles and configurations in which multiple cones are arrayed in respect to one another effect how a grouping of cone drivers will array together (and by the way, “array” is both a noun and a verb). That said, and as previously noted, in practical terms all acoustical behavior is a function of frequency.
So here we have some diameter of cone driver that will exhibit a wide pattern at lower frequencies and a narrower pattern at higher frequencies. And we wish to combine it with others of like kind. And that leads us to line arrays…