As is well known, the nominal coverage angle of a loudspeaker is defined by its off axis, 6dB down points. Where the value of 6dB came from no one seems to know, having been lost in the murky depths of audio history! (If you do know, please get in touch and enlighten me.)
Be that as it may, on the face of it, 6dB down would seem to be a very reasonable value. For some sounds, it is subjectively almost half as loud. (Yes, I know we normally take 10dB as subjectively being half as loud but, as in all things audio, “it depends.”) Either way, a 6dB reduction in level can be very noticeable.
In benign acoustic environments (e.g., rooms and spaces where the reverberation time is one second or less), a 6dB variation can be quite acceptable, but in challenging acoustic environments, a 6dB variation in the direct sound level can be problematic or even disastrous. For example, a 6dB variation in level in a noisy environment could reduce the STI (Speech Transmission Index) by 0.1 to 0.2, which could cause a sound system used for emergency purposes to fail its mandated certification requirements.
Therefore, using the nominal coverage angle of a loudspeaker to determine the required speaker spacing may not always be a valid design approach. I usually use an angle closer to the 3dB down value, though it depends. Equally, it should not be forgotten that the coverage angle of most loudspeakers is highly frequency dependent (see Figure 1).
Therefore, for speech intelligibility purposes, I look at the 2kHz and 4kHz polar diagrams/coverage angle data and use these as a guide. For example, in Figure 1, the manufacturer’s stated coverage angle is 115°, but at 4kHz, this drops to 90°. I would therefore tend to go with the 90° angle as a starting point, particularly bearing in mind my earlier comment about the 3dB coverage angle.
An important factor that is often forgotten is that, if you project the on-axis point and the 6dB (or 3dB) coverage angles from the loudspeaker to the area it is to cover, the outer angle projections will have to travel significantly further than the axial one. For example, let’s take the simple case of a ceiling loudspeaker. Here, the floor-to-ceiling height is say, 4m (13 feet), and we are to cover a seated listener with a typical ear height of 1.2m (4 feet) above the floor. I will also assume that the loudspeaker’s coverage angle is 120° (i.e., 60° off axis to the sides, as shown in Figure 2).
Directly under the loudspeaker, the distance that the sound has to travel is 4-1.2 = 2.8m. However, the off-axis sound at 60° has to travel 5.6m to the off-axis listener (i.e., twice as far). The extra distance traveled, therefore, means that it will be 6dB lower in level due to inverse square law loss. However, this is also at the coverage angle that, by definition, is already 6dB down, so the net result is that the SPL will be 12dB lower with reference to the on-axis position.
In many cases, of course, there will be some overlap from adjacent loudspeakers that reduces the discrepancy. However, the result can be that there is a greater than 6dB variation in sound level, particularly at the ends of a row of loudspeakers.
Carrying out this simple analysis is a task often forgotten by many sound system designers. When the listening plane is also raked or at a non-constant distance from the loudspeaker, the situation becomes a little more complex, further increasing the discrepancy in coverage. It is surprising just how effective a simple sketch or geometric drawing can be in identifying potential coverage problems.
Figure 3 shows how I quickly checked the coverage being provided in a stadium sound system bid offer I was asked to review. The illustration clearly shows that there will be poor coverage (and hence potentially poor intelligibility) at the front and rear of the stand (area not covered by green or blue beams). Sure enough, when I modeled the system, it did, indeed, show poor predicted intelligibility in these areas. Whereas, with my first simple analysis, I was able to warn the owner of the potential problem, it wasn’t until I had the full modeling results (Figure 4) that I could quantify the size of the problem, and get the integrators in question to believe me!
The coverage completely fails to comply with the associated life-safety requirements at the front and rear sections of the stand, even allowing for the overlap, as shown in the intelligibility plan view plot in Figure 4. I viewed the whole exercise as a waste of my time and the owner’s money, all for the lack of understanding of what coverage angle really means and its inherent frequency dependence. Still, I suppose it keeps my bank manager happy, but more importantly, a potential life-safety issue was avoided prior to installation.