Sound insulation between brick walls/concrete belt and wooden beam ceiling

Hello,

Our wooden beam ceiling was (presumably due to low walls in the upper floor, placed by the carpenter not directly on the concrete ring beam of the brick walls but on wooden pads.
This results in an approximately 5 cm high gap between the walls and the ceiling. The ceiling will still be suspended with plasterboard, but I fear this gap will cause a significant sound bridge between the rooms.

Now the question:
With what can I insulate this space against sound?
The following ideas came to me:
- Rock wool (ISOVER acoustic)
- Foaming the cavity (are there special sound insulation foams? They should be open-pored, I think?)

What would you recommend in this case? Filling the gaps in the walls or similar is practically no longer possible due to the already installed battens, etc.

I look forward to helpful advice.

Regards
mertmk3

Sketch the situation first. I see no point in filling the gap, since the ceiling isn’t solid anyway.

Nevertheless, the ceiling is well soundproofed, right?

Here is a picture, at the top a wooden beam ceiling with a vapor barrier, on the left the battens, and at the bottom the wall between the rooms. You can practically see through. On the 30mm battens, there will be 12.5mm plasterboard, the gap to the wall can just be closed. But then there are only 2x12.5mm plasterboards between the rooms.

I wouldn't use foam, I think special soundproof wool would be an option.

Oh, so there is still insulation and covering inside/on it? Well, just stuff in some mineral wool.

Yes, there is 240mm insulation in the ceiling.

Which mineral wool would you recommend?