Let me back up a little for some more conceptual issues creeping in here.
First, remember that an octave is a non-linear and relative idea. An octave is a doubling - not a fixed number of hertz, so it's a distance measured relative to a specific "place" not to be laid down at any position like a ruler. (I know that's a rough analogy) From 80Hz, one octave up is 160Hz (a "distance" of 80Hz), but one octave down is 40Hz (a "distance" of only 40Hz this time).
This goes back to what I started with about perfect speakers (see above). When you look at a frequency response plot for a speaker or sub, you're seeing the SPL generated at any frequency for the same power input. Classically, the speaker designer applies a 1W (or 2.83V, those are different, but the difference is not significant to the concept) signal - generally a sweep, like from REW. The power of the signal at 5Hz is 1W - the woofer makes a sound, the mic records the amplitude, and the sweep moves on - the power of the input signal at 100Hz is still 1W - the woofer makes the sound, the mic records it, the sweep moves on. If everything were perfect, the loudness at every frequency would be the same - the graph output would be a flat line from 0Hz ("DC") all the way to 20KHz and beyond. Of course, it's not flat, but that's the goal. That's the goal because that's the reference standard that everyone in the content production chain assumes - the guy recording the music, the guy mastering the disc, the DAC manufacturer, the speaker designer and so on. If everyone in the chain is working from this same basic assumption, we can hear at home what the musician or director or whoever intended (as nearly as possible) - that's the whole premise of hi-fi, in a nutshell.
Drivers don't behave linearly like this, unfortunately. There will be ranges of their functional bandwidths that approach this ideal, and there will be things that designers do for a variety of reasons that will force the performance away from this ideal. One of those things that is done is to place drivers in boxes. By mounting a woofer in a box (an acoustic suspension), you place an artificial limit on its performance. When the woofer cone is driven away from the back of the box, out into the room, it is attempting to draw a vacuum on the volume behind it; just like a piston in an engine, or a syringe - when the volume of the sealed box changes due to the displacement of the driver, the pressure changes inside the cabinet. Meanwhile, outside the cabinet, atmospheric pressure hasn't changed; the result is that there is a net force of pressure pushing the cone back to its neutral position - where the air pressure inside the cabinet equals the atmospheric pressure outside the cabinet. That force puts a very real limit on the effectiveness of the driver - as though the driver were connected to the back of the box by a spring (an "air-spring" in this case). The designer knows this, and accounts for it in the design. In a smaller cabinet, the movement of the driver represents a very large change in volume of the trapped air, so the force returning the driver to its neutral position is very strong, and the limit to the driver's output is high. In a large cabinet (or mounted in an infinite baffle) the change in volume of trapped air is insignificant (or actually non-existent), so there is no pneumatic return force exerted, and the driver can produce more acoustic output at low frequencies. (How's that for a blast back to your high school chemistry class - do you remember Boyle's Law?)
When the volume of the cabinet is optimized to THX standards, the roll-off below f3 is second order, or 12dB per octave. So, if 1W of power at 120Hz produces an acoustic output of 90dB in this THX satellite speaker, at 80Hz, the same 1W power produces 87dB acoustic output. At 40Hz, 1W produces 75dB. At 20Hz, 1W yields 63dB; at 10Hz 51dB; and at 5Hz 39dB. This is natural "acoustic roll-off" of an optimised sealed cabinet. If the volume is excessively large or small, the roll-off will vary (I'm not familiar enough with the details of what to expect to describe that in any detail).
When bass management is not employed, the full range signal is delivered to the loudspeaker, and output below tuning (80Hz here) is limited by the air-spring of the sealed cabinet. When bass management is engaged (speakers are set to "small," and subwoofer is connected) in a THX processor (or probably most home theater receivers these days), an additional 2nd order filter is overlayed with the natural acoustic roll-off, resulting in the 4th order slope I described last night.
This is one of the same set of concepts used to design passive crossovers in multi-driver loudspeakers (the whole process is much more complicated, obviously - whole books written about it are mere primers). Let's look at a different example - something I've seen discussed with SEOS designs. Compression driver tweeters are small plastic or metal diaphragms (just little coin-sized bits of nothing, really) mounted in a way that the signal causes them to vibrate - really much the same way that a woofer does. But in a CD, the diaphragm is brittle and easily damaged by large waves of energy, especially at low frequency - a high power signal at 500Hz or so would cause most 1" CDs to ripple and crack (like the ground opening to swallow cars in movie earthquakes - or at least that works as an image). Each CD has a different natural response based on its material, diameter, thickness, etc. but within its intended bandwidth, the response is very linear. If a full-range signal were applied to a CD alone, the results would be ugly - the output at low frequencies would be basically non-existent, and if you turned up the gain to get enough output to hear it, you'd fry the thing. In this case you need to remove the low frequency signal content (so that's a high-pass filter) before the signal makes it to the driver. A passive crossover is the common way to do this - the details are not important to this conversation and are outside my understanding at this point, but involves a capacitor and a resistor. The order of the crossover and the cut-off frequency are manipulated to protect the CD from accidental overexcursion when powered at high voltage and keep the acoustic output in the intended bandwidth. (Marty, I'll come back in a few minutes if I can and tell you what I know about passive crossover design (shouldn't take too long
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If a loudspeaker is designed with three different drive types (A 3-way design) the low frequency driver will need a low-pass filter for its signal (it will also probably get an acoustic high-pass filter based on cabinet design). The midrange driver will need a lowpass filter as well as a high pass filter, and the high frequency driver will need a high pass filter only, because there is generally no signal present to cause trouble in the playback in the ultra-high ranges.
