We have a big job with a small budget. One loudspeaker. How hard could it be? The goal is straightforward: uniform coverage over the seating area, i.e., minimum variance over the space.
There are four answers required for our specification: horizontal and vertical aim, horizontal and vertical coverage. We seek to match the loudspeaker coverage shape to the audience shape. The audience shape is visible. Loudspeaker coverage, not so much. Let’s work on defining the loudspeaker shape in terms of uniformity over the space.
Standard Lines Of Variance
The propagation of a single loudspeaker can be described by four standard lines of variance (Figure 1) in each plane:
• Forward variance line—between 0 dB and -6 dB in a forward direction
• Radial variance line—between 0 dB and -6 dB on an equidistant radius
• Lateral variance line—between 0 dB and -6 dB on a straight line perpendicular to the loudspeaker
• Minimum variance line—between 0 dB and 0 dB in a forward, radial or lateral direction
The forward radial and lateral variance lines are all maximum acceptable variance lines (0 dB to -6 dB). The minimum variance line for a single loudspeaker is derived by linking the location milestones: ONAXfar (the -6 dB end of the forward line) and OFFAXnear (the -6 dB end of the radial/lateral line). The key is that both ends of the line are the same, hence minimum variance.
It’s tempting to think of the horizontal and vertical planes as simply two versions of the same story. Our approach to coverage belies the fact that these are vastly different from our perspective. The key difference is how we reach the people.
In the horizontal plane we plow the coverage through the front rows to the back. The path of propagation flows over the shape and it matters whether or not our coverage shape matches the room shape. We need wide enough coverage to fill the width at the front row and yet we don’t want to overflow when we reach the rear.
By contrast, the vertical plane is only one person deep (lap child excepted). It doesn’t matter if our coverage is too narrow a few meters above the audience, just as it doesn’t matter if we have excess overlap when the lines of coverage hit the basement. We evaluate the shapes in fundamentally different ways, and will use the different versions of the loudspeaker shapes as required to fill them.
Horizontal Room Shape
The horizontal room shape is evaluated as a solid, a container to fill. We design to the audience seating plan (not the walls). The macro shape is depth by width: the distance from the loudspeaker to the last seat versus audience width at the midpoint depth. The loudspeaker’s coverage shape seeks to approach this dimensional ratio.
A rectangle shape is the easiest to evaluate since the beginning, middle and ending width are the same. A splayed room (trapezoid) uses the mid-point width, as would other variations around the basic rectangle. A narrow fan-shaped room can be approached this way, but a wide fan can’t easily be characterized as having a mid-point width. If a fan shape resists rectangular approximation then it is probably a bad candidate for a single loudspeaker (a helpful correlation).