Originally Posted by RUR
Drew, can you point me to the science behind desired driver size vs. lowest cleanly reproduced frequency? Less technical is better.
To create a pressure wave a driver must accelerate with longer acceleration at lower frequencies and therefore more total displacement required. For example,
a 20Hz tone takes .050 seconds for each cycle versus .0125 seconds at 80Hz.
SPL into free space at one meter is
102.4 dB + 20 log(Vp) + 40 log(f)
with Vp one-way displacement in cubic meters and f frequency in Hz.
A typical 22cm (8.5") driver has about 220 cm^2 of effective moving area (cone size plus 1/3 of the surround, with the mathematically observant noting that 220cm^2 is about the surface area of a 16.75 cm disc because most drivers are marketed based on basket dimensions) and 5mm of linear travel where the same length of voice coil is in the magnetic field producing the same acceleration for a given current with a total one-way displacement of .00011 m^3.
At 80Hz you'll get 99dB SPL peak from that driver into free space.
Using an even order cross-over to another driver like a sub-woofer the two sound sources are in phase at the cross-over point so you have 6dB over the SPL from one source totaling 105dB SPL.
Outside and in many web calculators that would have dropped to 99dB at 2 meters and 94dB at 3 but inside we have reverberant spaces that tend towards a 3dB per doubling draw-down rate (Floyd Toole summarizes this nicely in Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms) leaving you with a 100-102 dB SPL capability at a pleasant 2-3 meter seating distance.
Dolby Digital reference level actually places dialog at 74dB SPL. With default encoder settings allowing for 27dB of dynamic range that nets 101dB screen channel peaks which just squeak by.
Good jazz recordings push 20dB of dynamic range. Listening at a pleasant 85dBC SPL which may take 82dB from each speaker to add incoherently you get back to 105-107dB at the speaker which squeaks by since you're not listening to test tones.
You get a little breathing room because some of the bass energy which would be lost outside is bouncing off room boundaries and adding incoherently.
You loose a lot of clean headroom at lower frequencies because at a given displacement distortion product amplitude can be fairly constant while the fundamental tone SPL is inversely proportional to the fourth power of frequency. A driver which produces an acceptable 4% distortion at 30Hz using half its linear excursion can reach an unacceptable 10% at 20Hz (Linkwitz has some good measurements of a 12" Peerless XLS). With pure tones you might loose 6dB of those limits. OTOH, we don't listen to pure tones.
A typical 18cm (7") driver has about half the displacement of a 22cm driver so it takes a pair to net that displacement. A Seas W18 measures 126 cm^2 yielding 252 cm^2 for a pair, although that's only good for an extra 1.2dB over the W22 which isn't significant.
The best argument may be that empirically good 22cm mid-bass drivers crossed over at 80Hz or above work well for music at subjectively real (but less than live) levels (primarily for the above reasons) and smaller ones limit you to a sort of scale model experience. Pairs of 18cm drivers in MTM arrays can be as clean but don't sound as natural due to power response issues.
Some people want larger drivers still. That would allow more efficiency (which is at best proportional to driver surface area, with twice the driver size netting a 3dB gain) which reduces thermal compression. Some time I'll build a speaker with a 12" mid-bass and see how that works.