Why do I need more subwoofers than tops?
Many customers are surprised to learn we recommend far more subwoofers than tops. This article explains why, and will hopefully shed some light on how our AT212, for instance, can keep up with 8 (or more) of our double 18" subwoofers. It comes down to a combination of the demands of modern music plus the efficiency of high frequency drivers.
The first thing to realize is modern music has most of its signal power in lower frequencies. How much? We can easily calculate this. Several studies have been performed by passing music through a spectrum analyzer, and the results show that most modern music has a downtilt of -4.5dB/Octave. If you were to view your music through a flat spectrum analyzer, you would see something similar to the following track I produced:
For this image, we used Voxengo's VST3 plugin called SPAN, a free spectrum analyzer you can load in a DAW like Ableton Live or FL Studio: https://www.voxengo.com/product/span/
The slope of this line is almost exactly -4.5dB/Octave. As a result, most spectrum analyzers used in music production actually build in a +4.5dB/Octave correction by default. This makes it easier for producers to mix their music relative to the usual -4.5dB/Octave curve; a song that is "flat" on an analyzer with a +4.5dB/Octave actually has a -4.5dB/Octave downtilt that has become very popular, as it sounds good to most people.
Many people are not aware of what this implies, so let's follow the logic. A +3dB increase refers to doubling power. So we can calculate how much more power is present at a lower frequency such as 40Hz versus a higher frequency like 15kHz. The first thing to calculate is how many octaves are between 40Hz and 15kHz (15,000) Hz. Since an octave represents a doubling of frequency, we need to calculate how many times we need to double 40Hz to get 15kHz. This is found by solving 
. Taking a logarithm of two of both sides, we have 
. This means there are more than 8 octaves between 40Hz and 15Khz, meaning you have to double 40 more than 8 times to get to 15000 Hz. Now if each octave represents a -4.5dB decrease in volume, this means is >36dB (8.55*4.5dB) more gain at 40Hz than at 15kHz. How much more power is this? Dividing by 3dB, which represents a doubling of power in a logarithmic scale, we have that the power at 40Hz is double the power at 15kHz, 
or more than twelve times a doubling of power. In other words, the power at 40Hz is 
times the power at 15Khz. Hence, you'll want more loudspeakers dedicated to frequencies around 40Hz than 15kHz to account for this huge difference, and why we recommend far more subwoofers than tops! Note that these are conservative numbers; if you were to calculate the difference in power between 20Hz and 20kHz (a span of about 10 octaves), you'd find the power at 20Hz is 32768 times the power at 20kHz! Some of our subwoofers, such as the ZV28, are excellent at reproducing frequencies down to the low 20's.
The other thing to keep in mind is high frequency drivers, which are often horn loaded, are usually far more efficient than low frequency drivers. A good compression driver, such as the one we use in the AT212, has a sensitivity of 108dB/W. This number increases when it is horn loaded, which is what we do on the AT212 to provide even more efficiency. For a low frequency transducer, you are lucky to get a sensitivity of 98dB/W. The driver we use in the VS21 has a sensitivity of 99dB/Octave. Horns are not an option for these kinds of loudspeakers because to provide loading to 20Hz or 30Hz, you need a horn whose mouth is half the wavelength. Half the wavelength of a sound wave of 30Hz is 19 feet, which is hard to fit on a truck. Hence you need additional low frequency elements to make up for the difference in efficiency/sensitivity between your low and high elements independent of the source material.