There are many different types of subwoofer enclosure options. It comes down to available space, the sound you are looking for, and personal preference. We are going to discuss the two that are most common and a few others.
A sealed enclosure is precisely what you would think it is. It is a box that is air tight. When the speaker moves, the air inside the box does not escape, it alters the pressure inside. They provide a clean sound and are the most compact, however, sealed enclosures have a lower efficiency. They need more power to reach high volume.
A ported, or vented, enclosure has a cylinder or rectangular port. This allows for a higher output. The speaker can reach lower frequencies, outside its frequency response. The port has a predefined length and diameter. These types of subwoofer enclosures are louder than sealed and generate more bass. The woofer and port work together with the port resonating like a pipe organ.
A few other types of subwoofer enclosures.
Bandpass enclosures have a port as well, but the speaker is out of sight. It consists of two chambers, one ported and the other obscuring the speaker. These bang out an aggressive sound with great efficiency within their range. These enclosures are quite impractical in size and have a narrow frequency response. You can make the woofer play a broader spectrum, but that is at the expense of efficiency.
Also known as Infinite Baffle, this set up consists of the woofer mounted to a surface attached to the rear deck or in the trunk against the rear seat. This placement acts as an enclosure which houses the sub and isolates the front wave from the back of the speaker. This type of subwoofer enclosure saves space and has flat frequency response but has lower power handling levels than other options.
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For a detailed description on how to build your own subwoofer enclosure, click HERE.