The sound reduction is a very complicated subject with several aspects to it. First we need to consider if the customer is talking about in room sound reduction, or transmitted sound reduction (to the room below).
In both cases the secret to reducing noise is in increasing mass. In this context ‘mass’ means weight – we need to increase the weight of the floor (or bond it to something heavy) so that it is more difficult to move the floor. When a person walks across a floor their foot steps cause the floor to vibrate or move. The heavier we make the floor the less it will move.
If the floor must be ‘floating’ then a good quality foam or rubber underlay will make a small difference to both the in room sound and the transmitted sound in comparison to having no underlay at all.
If the floor can be fixed down, then we have two options for in room sound reduction. If the subfloor is concrete then fixing the wood floor to the concrete will reduce in room sound because we have fixed the (light weight) wood floor to a large mass in the form of the concrete subfloor thereby increasing the mass of the floor and reducing vibrations. If the subfloor is timber then fixing the new wood floor down will help a little but the subfloor is not really heavy enough to significantly add mass to the overall floor covering. In this case we need to add mass to the floor covering. This can be done as is described in the next paragraph.
If we need to reduce sound transmission to comply with building regulations then we only have one option. This is the first layer: a very soft thick layer of foam or rubber (to act as the isolation layer) followed by a new subfloor of as much mass as possible. This is normally a thick (10mm+) dense rubber, then a thick plywood layer, and finally the new flooring. All of these 3 layers must be fixed together. The idea is that the plywood and dense rubber add significant mass to the flooring layer and help it to resist movement or vibration. If it does move at all the vibrations are absorbed by the soft layer at the bottom. However this method is both very expensive (likely to be more than the floor covering) and will increase the height of the floor by 40-50mm.