It's physically impossible for practically any kind of 4 inches of soundproof to prevent a 50hz frequency from vibrating through the walls.
Maybe if it was 4 inches of solid lead and even then particularly sensitive people might still feel a normal sized subwoofer placed against the wall on the opposite side.
Maybe if it was 4 inches of solid lead and even then particularly sensitive people might still feel a normal sized subwoofer placed against the wall on the opposite side.