woofer in sealed box
 

Suppose we have a woofer in a sealed cabinet. Is it true that as you try to play lower and louder, the cone excursion will be limited by air pressure behind it but not in front of it where there is clearly no increase in air pressure?

I have read that there's more protection from over driving a drive unit in a sealed cabinet due to the air pressure behind the cone but the cone moves in both directions and the increase in air pressure is not in both directions so I am not so sure what this really means?

When it move in wards the pressure will increase in the box when it moves outwards it will make a vacuum. That will create a opposite force to the direction the cone moves.

When you use winisd-pro freeware, it calculates the extrusion from TS-parameters box and given power.

A back-enclosed cabinet will increase the stiffness of the suspension system of the speaker cone by s (nt/m) where p=the density of air (kg/m3), c=the speed of sound (m/sec), A=the area of the piston (m2), and V=volume of the cabinet (m3).
s = p.c2.A2/V

There's also the isobaric drivers/loudspeakers systems and the 6th order bandpass systems where the front of the driver is under pressure of the enclosure/cabinet/driver-system (and that giving more protection at Xmax).

What 'e said.