Language has a funny way of confusing and misleading us sometimes. Take for example the word subwoofer - it is a thing, an object - something that performs a task specific to bass. Compare that to the more descriptive term Sub Woofer and you quickly understand this is something that works below a woofer - and that is a very important distinction - one many people get wrong.
Most poorly setup subwoofers I have seen go too high and start to enter into the territory of the main loudspeaker's woofer - which in most cases is more than adequate to handle the bass. It's rare that a full range loudspeaker doesn't go below 40Hz and even a decent bookshelf speaker should be flat to 50Hz - yet routinely I see subs with their low pass filters set to 80Hz, perhaps 100Hz.
The job of a subwoofer is NOT to give you more bass. That's something I want to make crystal clear as we move forward.
The job of a subwoofer is to extend the bottom octaves of bass where your main speakers don't reach to properly - and it does that by taking advantage of two main attributes: it is physically separate from the main speaker and if properly designed, it can reach down into the very low visceral area of bass we need.
Being physically separate from the main speaker has a number of advantages, chief among them is optimal placement for best bass support at your listening position, self powered to remove the requirements your main amp has to handle, and a woofer larger enough to couple the air in the room without making your main speakers a 4-way system that is physical huge and stupid looking.
Subwoofers should be like salt or herbs in cooking - the missing finishing touch to an already fine meal that completes the chain - it should not be one of the main ingredients. In other words, if your main speakers don't work well in producing a full range sound down to, say, 40Hz flat - then adding a sub should not be your first priority - getting a better pair of loudspeakers would be the best bet.
So for the rest of this series, let's imagine you do have a decent pair of full range loudspeakers and they do adequately go down to at least 40Hz without any help at all - just relying on proper placement and their good design.
We'll pick up from there tomorrow.