This is a quote from Roger’s email to me with explanation:
The curves in the diagram ‘Controlled Horizontal Dispersion Using Adjacent Flat-Cells’ is based on ideal circumstances. There are things in the acoustic environment such as equipment characteristics, room acoustics, etc., that affect the sound field. In order to keep the discussion simple the diagram does not recognize these. Concerning the controlled horizontal dispersion, a cell radiates sonic energy much like a flashlight radiates light. The beam is most intense at the center and energy tapers off as one deviates from the center. Using a meter one can measure a loss of 6dB along with the angular departure from the beam center line. A flashlight uses a very narrow spectrum of frequencies so it appears that the dispersion angle is always the same. However, with a speaker there are about 10 octaves of frequencies, and we have to confine our thinking as to what frequency we are looking at since In any radiator, light, sound, ocean waves, etc., the energy dispersion angle is a function of the width of the radiator compared to the wavelength being radiated. It works like this, if the wavelength is small compared to the radiator the beam will be narrow. This is why tweeters are made small so that they have usable dispersion. In contrast, the reason why woofers spread bass energy everywhere is because the wavelength of bass frequencies is huge compared to the diameter of a woofer.
To make the story short, when I talk about dispersion in our speakers I am using the worst-case scenario, which is that I use a high frequency (20khz) to determine speaker dispersion. A cell has approximately 12 degree dispersion (at the -6dB points) at 20,000 Hz. I set the angle between cells at 12 degrees (-6dB points), which means that below 20,000Hz there will be no gap in the total dispersion of the panel. With the narrow speaker models I increase the angle a bit so that the total speaker radiation covers 45 degrees, but this is small and doesn’t cause a discernible sound gap. The beams of sound that you see on the drawing are the sonic beams at 20,000Hz. At lower frequencies the adjacent beams expand and crossover each other such that there is not a sonic gap, or vertical picket-fence effect when walking in front of the speaker.