Can someome give me a quick layman's explanation of what corner bass traps do - or help with - with the sound of the room?
Superposition of waves: net amplitude caused by two or more waves traversing the same space is the sum of the amplitudes which would have been produced by the individual waves separately.
In a room, sound waves are created by speakers. The sound bounces off hard surfaces like walls, ceilings, and floors; resulting in superpositions with subsequent waves coming from the same speaker(s) tiny fractions of a second later.
Of the various reflective interference situations, one is 'room modal resonance'.
When the sound frequency's wavelength is an integer multiple of the room length, the reflected wave superpositions are in resonance (in phase), and build up to extremes.
Extremes that can eliminate a frequency at some spots in the room (nulls) and quadruple the volume of that frequency at other spots in the room (peaks).
Thus, two people sitting side by side, one might not hear a frequency at all (sitting in a null) and the next might find it booming (sitting in a peak).
Although most reflections (other than room modal resonance) tend to be multiple angles like lasers off mirrored walls; the sound waves that make up axial modes (the primary room modal resonance) quickly settle down into back-front, or left-right, or up-down, directions. The room mode reflection is across the entire surface of the reflecting/opposing pair of walls (or floor/ceiling).
Corner traps have a couple of bits of physics and dollars in their favour
a) the diagonal shape of a corner trap uses little human usable space, yet is deeper than most wall absorbers are likely to be, that depth increasing the low frequency absorption
b) because its on a corner, it's involved in at least two axial modes directions (e.g. a vertical corner would affect the left-right and the front-back axial modes). Thus you're affecting multiple directional problems with a single purchase.
c) if you build the corner trap to completely fill the corner, then at least some of it is in a tri-corner (wall and ceiling and floor) thus hitting all three axial mode directions (up-down, left-right, front-back).
So, what you're trying to do with corner traps is knock down the strength of the reflecting wave at each reflection, thus reducing the resonant/superpositioned peaks and nulls, evening out the sound at more seating locations in the room.
Here's what a room looked like before corner traps
and here's what it looks like after corner traps
Notice the reduction in peaks in the 30hz to 200hz range.
Here's a waterfall version, before corner traps
and after corner traps
Notice the reduction in the bottom axis. This represents a reduction in the time the sound is active in the room,
aka a reduction of the 'ringing' time/duration at that frequency,
caused by the corner traps absorbing a bit of each reflection.
Because mineral wool (including fiberglass) porous absorber corner traps tend to be broadband absorbers (multi frequency) they automatically hit whatever modal frequencies happen to hit them.
A tuned membrane absorber, on the other hand may waste a corner -- because its absorption is aimed at a specific single room mode (e.g. a front-back resonance), but multiple modes are active in corners (e.g. front-back and left-right), the space used by the tuned membrane absorber means that you can't simultaneously use the same space for treating other room modes (e.g. left right).
The frequencies of room modes can be somewhat predicted using a room mode calculator, that translates the integer multiple wavelengths based upon the room dimensions. e.g.
I say 'somewhat' because walls are not perfect reflectors, so the frequencies tend to be near these, but not exactly. You can't tell until the room is built and full of stuff what needs to be treated.