Frequency responses are lower for pairs of subwoofers

Why are the frequency responses lower for pairs of subwoofers than single subs?

If you have a loudspeaker that’s operating at its bottom limit, and then you supply another box to assist that first box, collectively their bottom limit extends lower.

That effect is true for any subwoofer and subwoofer pair. When you put multiple boxes together, the low-frequency corner does shift down slightly. It’s the same principle that allows multiple horns to extend lower than individual horns. It’s a ratio of frontal area to wavelength. There is also a slight increase in directivity that affords a slight increase in the measured output at the lowest frequencies.

The effect is much more noticeable with horns because most of the time their frontal area is way too small to make them efficient at those lowest frequencies, so multiple horns are required to achieve the intended frequency response if that response extends below the wavelength represented by the perimeter of the frontal radiating area of a single horn.

There is another principle involved. It can best be understood as being similar to boundary loading. When you have a box operating in free space versus half space versus quarter space versus eighth space the box in question will measure higher SPL at the same distance from the source in each environment. This is because you constrain the radiation of that energy. There is, however, an additional effect. There is a very slight change in their resonance due to the constraint of the boundary.

Similarly, an adjacent loudspeaker acts as a boundary constraint but it also contributes energy into the same space, and that energy is pressure. Both loudspeakers are now contributing pressure into the space and, if their wavelengths and time relationship overlap, they are effectively pushing into a higher pressure environment collectively, and individually, than if they were each operating alone. This shifts the resonance of the system down ever so slightly, which contributes to the low-frequency extension of the vented enclosure via a second mechanism.

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