What's inside your speaker cabinet, apart from air?
Here we are looking at the types of loudspeakers known as the closed box (a.k.a. acoustic suspension) and the bass reflex. This does not apply to open-back cabinets, such as guitar cabinets.
The reason loudspeakers are made in the form of a box is to contain the sound radiated from the rear of the diaphragm. If there were no box, this would bend around to the front and cancel out the sound that is projected forward. This is particularly noticeable in the bass. One solution to this is to mount the drive unit on a large flat board, known as a 'baffle'. The trouble with this is that the baffle has to be extremely large to be effective. So by 'folding' the baffle around the drive unit, we reach a more acceptable solution.
The problem now is that the enclosed volume of air inside the cabinet acts as a spring, opposing the motion of the cone of the drive unit. So when the cone is pushing outwards, the air inside is trying to pull it back in. When the cone is pulling inwards, the air inside is trying to push it back out.
The best way to minimize this effect is to make the cabinet as large as possible. But in reality, this makes the cabinet too large for most practical purposes. But is there a way of making the inside of the cabinet larger than its dimensions would suggest? (No, not Doctor Who's TARDIS).
As it happens there is. That is to partially fill the cabinet with a material known as BAF (bonded acetate fiber) wadding. If you want to see what this looks like, poke your finger through a hole in a worn out winter coat and pull out some of the lining. It is a very similar material.
The effect of filling the cabinet loosely with BAF wadding is that the air inside now reacts differently to changes in pressure. Here comes the science...
Rapid changes in air pressure inside the cabinet are 'adiabatic', meaning that the temperature rises during compressions and drops during rarefactions. Slow changes in air pressure are 'isothermal', meaning that there is no change in air temperature. In adiabatic conditions, the air molecules acquire more momentum and therefore press against each other and the walls of the cabinet harder. In isothermal conditions, there is less momentum and therefore the walls of the cabinet 'seem' to the air molecules to be further away. Including the BAF wadding makes the pressure changes isothermal, and hence the cabinet is magically bigger.
It's amazing what a bit of BAF will do. However, don't stuff it in too tightly or the cabinet will start to shrink again. Doctor Who never had that problem.