Acoustic transmission through walls

When one hears sound from a wall, that means that the wall moves. There are two mechanisms: contact sound (when some neighbour in the building is drilling etc) or sound transmitted from the air on the other side of the wall. The questions was about transmitted sound.

An interior wall acts like a massive membrane with stiffness. The stiffness couples the oscillations of different parts of this surface. Averaging of the forces over an area makes that only long wavelengths in the air on the other side will sett a panel in motion. The forces from shorter wavelengths will cancel out. That is also a reason why such a wall is a low-pass filter.

Heavy walls are more difficult to set in motion, so that would reduce transmission.

I have not considered thickness, internal structure or damping. This is just theory. In reality, most of the sound may be transmitted by leaks. I do not know.

I'm not really sure if this can help you because I don't know about your background, but for a first approach to the topic I recommend Kinsler's "Fundamentals of Acoustics". It even has a chapter dedicated to reflection and transmision of waves, and although it mainly focuses on fluid media, it also have a section about solid walls.