Loudspeaker and enclosure design

Subwoofers use speaker drivers (woofers) typically between 8" and 21" in diameter. Some uncommon subwoofers use larger drivers, and single prototype subwoofers as large as 60" have been fabricated.[12] On the smaller end of the spectrum, subwoofer drivers as small as 4" may be used, depending on the design of the loudspeaker enclosure, the desired sound pressure level, the lowest frequency targeted and the level of permitted distortion. The most common subwoofer driver sizes used for sound reinforcement are 10", 12", 15" and 18" models. The largest available sound reinforcement subwoofers, 21" drivers, are less commonly seen.
The efficiency of a speaker driver is given by:

Where the variables are Thiele/Small parameters. Deep low frequency extension is a common goal for a subwoofer and small box volumes are also considered desirable. Hoffman's Iron Laws therefore mandate low efficiency under those constraints, and indeed most subwoofers require considerable power, much more than other individual drivers.
So for the example of a sealed speaker box, the box volume to achieve a given Qts is proportional to Vas:
 Where:
Therefore a decrease in box volume and the same F3 will decrease the efficiency of the sub woofer. Similarly the F3 of a speaker is proportional to Fs:

As the efficiency is proportional to Fs3, small improvements in low frequency extension with the same driver and box volume will result in very significant reductions in efficiency. For these reasons, subwoofers are typically very inefficient at converting electrical energy into sound energy. This combination of factors accounts for the higher power output of subwoofer amplifiers, and the requirement for greater power handling for subwoofer drivers. Enclosure variations (e.g., bass reflex designs) are sometimes used for subwoofers to increase the efficiency of the driver/enclosure system, helping to reduce the amplifier power requirement.


Subwoofer mounted in a sealed enclosure
Subwoofers have been designed using a number of enclosure approaches: bass reflex, acoustic suspension, infinite baffle, horn loaded, tapped horn, transmission line and bandpass. Each enclosure type has advantages and disadvantages in efficiency increase, bass extension, cabinet size, distortion, and cost. Subwoofers are typically constructed by mounting one or more woofers in a cabinet of medium-density fibreboard (MDF), oriented strand board (OSB), plywood, fiberglass, aluminum or other stiff materials. Because of the high air pressure they produce in the cabinet, subwoofer enclosures often require internal bracing to distribute the resulting forces.
The smallest subwoofers are typically those designed for desktop multimedia systems. The largest common subwoofer enclosures are those used for concert sound reinforcement systems or dance club sound systems. An example of a large concert subwoofer enclosure is the 1980s-era ElectroVoice MT-4 "Bass Cube" system, which used four 18" drivers. An example of a subwoofer that uses a bass horn is the Bassmaxx B-Two, which loads an 18" driver onto an 11-foot (3.4 m) long folded horn. Folded horn-type subwoofers can typically produce a deeper range with greater efficiency than the same driver in an enclosure that lacks a horn. Some experimental fixed-installation subwoofer horns have been constructed using brick and concrete to produce a very long horn that allows a very deep sub-bass extension.[13]
Subwoofer output level can be increased by increasing cone surface area or by increasing cone excursion. Since large drivers require undesirably large cabinets, most subwoofer drivers have large excursions. Unfortunately, high excursion, at high power levels, tends to produce more distortion from inherent mechanical and magnetic effects in electro-dynamic drivers (the most common sort). The conflict between assorted goals can never be fully resolved; subwoofer designs are necessarily compromises. Hoffman's Iron Law (the efficiency of a woofer system is directly proportional to its cabinet volume and to the cube of its cutoff frequency) applies to subwoofers just as to all