How to soundproof a floor
Once again, mass rules. But also there is a technique known as the 'floating floor', which is widely used in studio construction.
The fully engineered floating floor would consist of a concrete slab formed on metal shuttering, supported on rubber pads or even heavy-duty springs.
The mass of the slab is important as the mass-spring system will have a resonant frequency, at which the sound insulation properties will be worse than if the floor were not floating!
A massive slab can push this resonant frequency below the audio band.
Where restriction on cost or loading prevents a heavy floating floor, a lighter-weight version can be constructed to BBC recommendations by putting down a resilient layer of high-density mineral wool (approximately 30 mm) covered with a plastic sheet, and then laying a 70 mm reinforced concrete slab on top of that, with a further 40 mm concrete screed on top.
A wooden domestic floor may be improved by adding two layers of 18 mm particle board on top, with the joints staggered to avoid gaps.
The gaps around the edges can be filled with a mastic material, or by compressing mineral wool tightly into the gaps.
There would be no harm in 'floating' this on top of an old carpet, but the additional benefit, other than for impact noise, would be slight.