You have essentially answered your own questions. The problem with a single subwoofer is that it can not be crossed low enough to integrate with the two bookshelf speaker mains most of the time. One point is to cross high enough to substantially reduce the excursion(thus substantially increasing dynamic range and lowering distortion) of the mid-bass drivers on the bookshelf speaker, which typically requires a crossover point of 90-100Hz. In a very small room, one could theoretically place the subwoofer directly in the middle of the two bookshelf speakers.... but this position is typically the worst for the subwoofer, resulting in substantially reduced acoustic output and a worse room response curve.
-Chris
Thanks, Chris. When you state the benefits of increasing dynamic range and lowering distortion, what kind of thresholds are you talking about? If, say, I listen to classical music at roughly 75db slow weighted, the peaks that may occur at over 100db will have more headroom? What if any peaks I listened to were considerably less than 100db? I assume the distortion is audible indeed, since you would not have mentioned this benefit otherwise.
If the subwoofer is playing at sub 40hz frequencies, one might say that the larger excursions would reduce the dynamic range of the freq range, say, of 60hz-100hz. Now, of course, if you knew that to be true, you would not make this sort of recommendation. Thinking along these lines, could a pair of bookshelves (if they existed), with 7" mid drivers work successfully with a mono sub? (Of course, you would fear the larger cabinet and the resonances that come along with that. Oh yeah, and of course you might mention again the less than ideal placement of the SW).
Sorry that I'm beating this topic; I just think that aesthetically speaking, a single sub could be nice, as well as with reduced costs with some luck. I understand that your recommendation is based on performance for the dollar, and not prettiness. With that in mind, any suggestions to make the dual bookshelves + dual subs look a bit more welcome in a living room? A hefty short bookshelf stand with rubber feet on top of the sub would be fine?
I'm just blabbering along. Could you tell me what the excursion normally is for a typical sized mid woofer playing, say, 80hz at a typical volume?
I can find the 1/4 wavelength distance by using: velocity = wavelength * frequency... ? Therefore, 1/4 wavelength of 90hz is roughly 3.14 feet(?). Which would mean that if using only one subwoofer, I'd need the mains to be within 6.28 feet of each other?
Thanks for answering any of the questions.