We have a disused doorway, on one side of which is a bed and the other side
of which is the food preparation surface in the kitchen. The door remains
in place, but is hemmed in by the kitchen units. It's a single
skin plywood panel door, so the panels are only a few millimetres thick.

All kinds of kitchen noises can be heard perfectly clearly through the door,
which is annoying. Blocking up the doorway permanently sadly isn't an
option. Without changing the door or modifying the fabric (so in a way that
can be installed and removed without marks) how might the soundproofing of
this doorway be increased?

There's plenty of space thickness available on the kitchen side, so I
thought about placing a second skin in front, perhaps another old door, and
then filling the gap with something. Thermal insulation (mineral) wool is a
possibility, but how good is this for sound rather than heat insulation? As
the noise is primarily low frequencies I imagine I want something that's
layered but denser than fluffy foam (like books rather than candyfloss).
(And, as I can't seal it, loose fibreglass floating round the kitchen isn't
so great)

Any ideas?

Thanks
Theo