What I would say is getting a woofer, press it up against the wall, then seal the woofer to the wall with hot glue or something and then line it with rubber or something that absorbs vibration (sound)
I think that would lead to vibrations in the wall and would be hearable everywhere in the house too.
How about installing rubber filament where the wall meets another wall? That way the wall can vibrate freely without affecting any other wall. But this still leaves the problem of you having one whole wall shaking.
Yeah, and if you are lucky you find a resonance tone of something in the buildings construction that backs the whole building.