I am having trouble with noise from the underlying room (house with a basement) and am considering adding an additional layer of gypsum in the ceiling of the basement room and have a few questions.

  • Should I have an air gap between the gypsum layers? e.g. 10 mm
  • Is it worth putting up two more layers, i.e. a total of 3 layers of gypsum boards (3x12mm)?
Grateful for any advice
 
What kind of noise do you want to dampen? Stereo? Washing machine?
Start by thinking about whether the noise can take another path than through the floor structure. Even small gaps leak a lot of sound.

Regarding the renovation proposal.
Short answer: no, soundproofing is tricky.
Putting on a layer of gypsum directly dampens a bit, but it’s probably not enough if it’s a problem today.

Long answer:
gyproc.se said:
Construction on the underside of old
wooden floor structures:
Old floor structures with an underside of perforated panels and
approximately 30 mm plaster have poor low-frequency sound insulation
therefore a larger air gap or more layers of Gyproc Gypsum
boards are necessary. At least 95 mm wood framework (c 600
mm), at least 45 mm mineral wool, and Gyproc AP profile
(c 400 mm) are recommended for 2 layers of Gyproc Gypsum
boards. The improvement with this measure is approximately
10–15 dB, which is usually sufficient to meet
apartment-separating floor structures, for example, when decorating
an attic.
If the underside of the above floor structure is renovated
with Gyproc Gypsum boards on battens, these should be dismantled
before implementing the aforementioned measures, as otherwise
it will have significantly reduced low-frequency sound
insulation.

For old floor structures with an underside of wood panel
no general advice can be given. Contact an acoustician for
measurement of existing sound properties and dimensioning of measures.
So: Remove existing gypsum and spacing.
Install insulation, sound-dampening steel studs, and one or two layers of gypsum.

Or look here if you want to read yourself:
http://gyproc.se/bibliotek/gyproc+handbok/gyproc+handbok+pdf
Chapters 2.4
Chapters 3.4
Chapters 4.1

Edit: There are of course other solutions. But it was convenient to copy from this gypsum board manufacturer instead of writing it myself ;)
 
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Yes, if you can specify a bit more what type of noise you want to dampen, it will help in giving advice. Low frequencies can be difficult to dampen.
 
Clarifications:

The floor structure is 220 mm insulated with mineral wool, a layer of gypsum, and on top, 22 mm chipboard flooring (built in 1980).

The sounds I want to eliminate primarily are talking and stereo.
 
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