I thought this would be good place to explain absorbers, reflectors and the combination of the two, "diffusers".
If we look of the coefficient of absorption of a material we make get a factor from 0 to 1.
What does this tell us?
1 is = completely absorbed and 0 is completely reflected (blocker). This is likened to an open window having a factor of 1 (fully absorbed) and a lead wall fully reflected.(0)
If we use rock-wool at 100 mm thick it would suggest a rating of 1 at 100 Hz, versus rock-wool of 25 mm thick giving us a factor of 0.5.
If we therefore use 100 mm thick rock-wool we will therefore fully absorb a 100 Hz wave, and none will reflect.
If we use this in a vehicle doors will we get standing wave at 100 Hz across our vehicle?
Quite probably
The coefficient of absorption only tells us if it will reflect or absorb, what it does not tell us how much acoustic energy is converted to heat (attenuation)
Example if we had 100 thick rock-wool with a speaker on the other side with 100 Hz sine wave how loud would it be?
If it was 100 dB, we would hear none of it? what if it was 200 dB?
Clearly we need to know the coefficient of attenuation.
So why do you always talk about how those diffuser pads are ineffectual for lower range frequencies, and what is this "magical" 1/4 wave point?
Velocity
(Direction of travel in a certain time)
Imagine a wall, if we throw a tennis ball against it, what is the velocity when it is deforming at the wall?
Zero
It has no direction, IE at that instant it is stationary.
When a sound wave hits a wall, the velocity is zero (same as radiating driver cone exciting an air molecule) at the quarter wave the velocity is the highest, (in fact every 1/4 there after)
For an absorber to turn acoustic energy into heat, it is required to induce the wave to diffract (bend around corners). You can try this yourself, by bending a wire in the same place several times and observing how hot it at the bend. If the diffraction is too sharp (too tight a corner) it will reflect, and therefore this determines the maximum density the substance can have before it shifts from an absorber, (least dense) to a diffuser (middle dense) to a reflector (most dense). This is your coefficient of absorption.
Therefore the most efficient place to turn acoustic energy into heat is on the quarter wave, it is also the point at which a wave of the same frequency will sum or cancel, because the velocity (interchange) is at its peak.
To get a measurable change we need to be therefore a minimum of 1/10 of the wave length away from the point of reflection, to get an audible change, consider 1/4 wave length mandatory.
Sorry but diffusers need to be 1/4 deep to have any real use.
So we are suggesting an absorber 215 mm thick for a 400 Hz wave?