It's said that putting heavy furniture (especially soft furniture) against a wall reduces the noise coming through the wall. I wondered, does this work just by blocking the sound in the area covered, say, by the sofa, or does it reduce vibrations and therefore sound transmission in the whole wall?
You will get a very minor improvement from the soft furnishings basically "absorbing" a bit of the sound energy which comes through the wall. This is unlikely to be more than 1-2dB and would make no difference if you were actually sitting on the sofa. If you covered the whole wall with large objects you would see a minor reduction. If your problem is that the wall is 'loose' (e.g. a single layer of plasterboard on a frame) then bracing it by pressing a sofa up against it can stop it resonating, but again the improvements would be minor.