An assembly with acoustic dampening properties for use in building or structure construction, a first panel, a second panel, and one or more connection elements therebetween. The first panel is a manufactured-wood acoustic panel with multiple lignocellulosic material-based layers, wherein one or more of the layers having a noise-reducing polymer integrally coating or permeating the lignocellulosic material. The noise-reducing polymer does not form a homogenous layer. The assembly can include insulation, gypsum board, or similar materials to form wall assemblies, roof assemblies, floor assemblies, and ceiling assemblies.