I think like Holmz said - a bandpass box would get you close, although it's more the speaker between two boxes.
What you are asking is "what would the effect be, if you built a big sealed box with a little vented box just sitting inside it - no speaker attached to the vented box, just a box with a port in it" right?
Let's think through it to see if we can get close-
I'd believe sure enough the sub in the sealed box would cause pressure fluctuations in the sealed box... which would in turn act on the air in the vent, which would move in resonance with whatever frequency it was tuned to given that box... and that would follow the same rules as vented boxes, as far as the vent resonating in phase or out of phase with the cone...
That WOULD have the excursion limiting effects on cone motion (I believe) above the tuning frequency, since the port air motion in this case would purely be adding to or decreasing the effective pressure in the enclosure - same as a vented box, but not [significantly, anyway] contributing to the sound outside the box, since the vented box is trapped inside the sealed box.
Also similar to a vented box, I would think that below the vent tuning frequency, the vent-effect collapses, and now you'd re-capture the air inside the vented box, for use by the sealed box.
Same goes if you used a passive radiator, if my thinking above is all correct.
So let's assume we stuck a 1 cu.ft. empty box with a vent (or passive radiator) in it tuned to 40hz (but no sub or sub hole) inside of a sealed box that was large enough to give us a 2 cu.ft. sealed volume even with that vented box inside it...
if the air inside box one is Vb1 and the air inside box two is Vb2, I'd predict (but I don't know for a fact):
- Below 35-40hz, the sub would behave as if it were in a 3 cu.ft. box. So if you modeled up a 3 cu.ft. box, and looked at 40hz and down - that's what you'd get.
- Right near 40hz, the sub and vent are as close to in-resonance as it gets - which would in this case cause the vent to add pressure inside the sealed box causing a sharp reduction in excursion, causing a dip in frequency response.
- Above 40hz, the sub and vent go progressively out-of-phase, so that destructive interference would fade away, until you get to whatever frequency the vent wouldn't have any impact any more... above that frequency, we're behaving like we're in a 2 cu.ft. sealed box... which at those upper frequencies is going to be pretty close to the 3 cu.ft. response anyway.
So - overall, I think if you modeled your sub in a 3 cu.ft. box and imagined a decent dip in the frequency response around 40hz (I'm guessing about 6dB), and then rising back up to the -0dB level again progressively by about an octave higher (1 octave is also a guess) as you move further up the frequency spectrum.
But that's just me trying to think through it - I can't say I know that is what would happen. I don't believe there's any software that models this, to know for sure.
Do you have a need for a sealed box with a dip in the response? I could only see this as being really beneficial for subs stuffed in sealed boxes that are too small and have peaky responses to iron out - but in those cases of course you don't have room to stuff a vented box inside, or you'd have enough air space to begin with. [emoji38]