Modelling (getting the finger …)
We will now use electro-acoustic modeling to reveal the phenomenon. These predicted coverage maps are very close to what happens in real life in open air applications. Closed rooms add a reverberant field, which tends to smooth coverage out, and room modes, which create additional zones of their own.
We have placed 3 x 2 stacks of double 18-inch bins both sides of an 8-meter (27 feet) wide stage. An audience area of 60 meters (200 feet) wide and 52 meters (175 feet) long is used.
The first coverage map (Figure 3) corresponds to 100 Hz. We have switched on just one side of subwoofers just to see what happen when all our bass emanates from a single stack. Sound pressure level expands smoothly in a way that is close to the distance-squared law. So far so good.
Problems knock on our door when both sides are on (Figure 4). Also at 100 Hz, we can now see some kind of alien hand with five fingers. These are maximum pressure lobes, where the phase difference between the left and the right sides is small.
The areas between the lobes represent cancellation. Level readings show levels down 20 dB from the lobes. That means our 100 Hz pretty much walks out on us.
OK, so at least some folks are enjoying good bass, right? Wrong. Areas where the 100 Hz are in phase will have other frequencies out of phase, so there aren’t any “good” areas (except for the centre line).
Naturally, some frequencies are more important than others when dealing with bass guitar or bass drum, so our problems will be more evident in some areas than others.
Figure 5 shows what is taking place in the location seen on Fig. 4, which is 4 meters (13 ft) off to the side. On the top part we see that the closest group of subwoofers arrives about 2.5 ms before the other.
On the bottom, we see the resulting frequency response, where the first trough occurs at about 100 Hz. Figure 6 shows the same for a position 13 m (43 ft) off to the side – note how it differs from the previous one; and the 40 Hz comb.
The following illustrations show modeling for 80, 63 and 50 Hz, respectively, on Figures 7-9. Note how the number and location of the lobes varies with frequency.
So, where is that alley?
For each frequency we have a map with fingers. If we sum several frequencies and plot them on a single map, the alley emerges, since it represents the only locations where bass sums coherently at all frequencies.
The width of the alley depends on the spacing of the subwoofers: as the two sides of subwoofers increase in spacing between each other, the alleyway will narrow.