An acoustic suspension enclosure is a sealed box that provides accurate, tight bass response, though it may sacrifice some efficiency and /or overall volume to achieve this.
A bass reflex enclosure includes a "tuned" port that releases some of the energy produced by the woofer's backward movement. This design increases bass response, though it may sacrifice some accuracy in exchange for the added output.
A passive radiator is a type of woofer cone found on some enclosures which isn't driven by the speaker's magnetic motor, but rather moves in response to the main woofer, increasing bass output.
An in-wall or in-ceiling speaker uses the space behind your wall or ceiling as a large cabinet, so it has the ability to produce slightly more bass than some standalone speakers of the same size.
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