gOd5_g1ft, I have a question. You want to lessen the noise coming from the outside, or you want to lessen the noise going to the outside? First, use split type aircon. Seal off your window airc con hole. Second, seal off any window, etc. by making sure that any possible opening is caulked or sealed with silicon caulking material. Put heavy drapes on two portions of the wall. Put the drapes about 2 to 4 inches from the wall. That will help your sound in your room.
BAMF, you put glass fiber in betweem the leaf of the walls to remove resonances, not for sound proofing purposes. There is no such thing as the first school of thought in acoustics. Always put insulation in between the leaf of walls. Use 50 mm or 2 inches. 1 inch will not really matter much. Use fills, about 16 kgm - those that come in rolls, no foil backing. Glass fiber is your best isolation. Instead of using one gypsum per side, use two. The heavier or denser the wall, the better it is to stop sound from seeping through. Also, caulk all joints with non hardening caulking material, but silicon caulk will do. For your room acoustics, follow the one I outlined above.
Good luck.