garage sound insulation

Hi, I'm new to the forum, so apologies if this goes over old ground. I have a 4.8m x 3.6m garage space, ceiling only 2.1m. It's fibro-lined, very battered weatherboard externally. The floor is concrete, with a thin carpet. I'm wondering if the fibro will act like a second skin if I add a layer of Firestop 13mm with a small air gap? I can access the ceiling by lifting a sheet or two of the colourbond roofing. Does any-one know if there is a cost-effective way of insulating this space to keep sound in and out? I'm only interested in a control room, with possibly a small vocal booth. Thanks