What is the effective difference between an integrated three way and two way with sub? Both require 2 crossovers, but it seems (in my admittedly ignorant head) that since all of the details of the three drivers are known in a three way speaker, that would be less expensive to successfully engineer than a subwoofer crossover which needs to be adaptable to a wide array of match-ups.
Thanks!
You have a point but in practice it is difficult to pull off. Your reasoning is not incorrect.
The issue is that home speakers usually have passive crossovers and engineering passive crossovers to work well below 350 Hz is very difficult and or expensive, and when all cast up very inferior to an active powered crossover with bi-amping.
The next issue is that small drivers have improved a lot, and many can reach into the 40 Hz range. The small drivers make for a narrow cabinet which improves imaging. However the narrow cabinet comes at a price. This is diffraction loss where there is first order roll off starting between 400 and 600 Hz depending on the size of the drivers, and cabinet width. This can be easily compensated for by shelving in another driver to "fill" the diffraction loss. This does mean that whatever the speaker manufacturer says the impedance is, it will be four ohms or lower, and two thirds of the amp power will go to the band where the diffraction loss correction starts.
So if you are going to make a three way you need a woofer at least 8" diameter to consider making it worthwhile, and preferably 10" or larger or multiple 10" drivers.
Now to really benefit from a three way, the mid range driver needs to be wide band and cover a bandwidth of at least 400 Hz to 4 kHz. Drivers that can do this really well are few and costly. Ones I would recommend would exceed you speaker budget by themselves.
The next issue is space. Drivers designed to operate above sub range won't be able to be inefficient and handle large power. So to benefit from the large driver, the cabinet has to be large to make an integrated full range speaker.
Now subs can have heavy coned rigid drivers that are inefficient but handle lots of power. This is how you get deep bass in a small package. It is fairly typical that at a crossover point of 80 Hz where the contribution of mains and sub to the spl is equal, for the sub to take three or four times as much amplifier power as the mains, because the sensitivity gap is usually in the 9 to 12 db range.
The next issue is that subs are cut in with active and not passive crossovers, which are far more ideal at these frequency ranges. They also have class D amps a s a rule which can be made to produce a lot of power fairly inexpensively and with high efficiency.
For all these reasons, this is the way the industry has become geared.
There are however significant integration issues with subs, that are seldom ideally solved. It so happens that at the usual crossover point the ear is not as sensitive to the aberrations caused.
So in essence if you want a good three way speaker, it needs to have large bass drivers in a big enclosure, and preferably have at least the low pass/band pass crossover active, and require two amplifiers or more. This is the route I have taken, but the enclosures are large and complicated, not only because they are transmission lines, but to handle the imaging problems. They require three power amps to drive each speaker. However they are genuine full range speakers not requiring a sub.
You can build a set if you wish!