Here I'll introduce the basics of bass traps and give you enough information to start building your own. The topic is not complex, but for some reason a lot of the information online about bass traps is not very helpful.
Two modes of operation
Bass traps can work in two ways:
1. Pressure mode
2. Velocity mode
You don't need to fully understand what this means, but the implications are critical. Pressure mode traps need to be located very close to the boundary surface of the floor, ceiling or wall in question. The further they are from the surface, the less effective they will be.
Velocity mode traps need to be located as far as possible from the surface. They work best at 1/4 of one wavelength of the frequency in question. So to work at 100 Hz, ideally such an absorber would be 860mm in depth. In reality this ideal is not practical, but it should be understood for now that distance from the wall matters more than the thickness of the absorbing material.
3 types of bass trap
There are three types of bass trap:
1. Broadband traps
Broadband traps are recommended as the first to place in a room. They are porous velocity mode absorbers, so they should be placed as far away from boundaries as possible. They should be placed in corners since this is where they will be most efficient and typically they will straddle a corner and run from floor to ceiling. A typical design will be 600 - 900 mm across on the diagonal. The angle helps as the depth varies and tends to assist in working over a wide range.
As a minimum, aim for the two corners behind the speakers, but four corners is ideal. Next you may consider the corner between the wall and ceiling junction as well as the floor/wall junction.
Foam or fibreglass insluation can be used, but they are less dense than the ideal so should be compressed. The ideal material is rigid fibreglass insulation which has already been compressed so that it is more dense. You may choose to apply a face over the insulation to reflect midrange if you don't want the absorption, but ensure that it isn't too solid, which would may undermine the effectiveness.
Porous broadband traps are recommended because they can potentially work over the entire audible range. Other types have a much narrower range.
2. Membrane traps
Membrane traps are desirable because they can be very low profile, typically 75 - 100mm. They are pressure source absorbers so they must sit on the surface. This means they are the easiest to integrate into a room and you can paint them the same colour as the wall/ceiling.
The downside is they are resonant traps with a limited bandwidth. This means you will need to use a number of them with different depths to work over a broader range. Like all traps, they work best in corners, but instead of running them across the diagonal, they are best forming an L shape. So when putting them into a room, start with the corners. A rectangular room has 12 corners.
Essentially a membrane trap is a sealed box where the outside membrane would be 3 or 6 mm plywood or similar. Rigid fibreglass should be placed inside but should not touch the membrane. You can make it with 5 sides if you attach it permanently to the room and seal up the joins. If mobile, they require 6 sides.
They work as the bass exerts pressure to bend the membrane. Energy is absorbed in this way.
Membrane traps should be added after broadband traps have first been used.
3. Helmholz resonator traps
While these have an appeal as rare devices, they present a design challenge and are a more difficult way to achieve a result. The British Broadcasting Commission did some research on such traps and found them to be impractical due to their expense and various difficulties. They are senstive to misalignment and tend to need custom design for a particular room. They could be an interesting solution for someone with great patience who is willing to build many versions before getting it right. There are few who would persist and be willing to build many large traps before getting one them all to work well.
How should I trap my room?
1. Start with as many broadband corner traps as you can fit and make them as big as you can live with. Run them floor to ceiling if possible and aim for 4 in a rectangular room, or more if you have a different shape.
2. Next apply similar traps to other corners formed between walls/ceiling and floor/ceiling.
3. Add membrane traps next with different depths. Start close to the corners. If cost is no object and you have the space, then cover all surfaces you can with membrane traps. You probably can't have too much.
Naturally there is a balance to be found where you weigh up space, cost, performance and aesthetics, but I would consider two decent bass traps to be a minimum. If you simply stick a 400mm wide piece of foam in a corner, don't expect to discover what I've beent talking about.