Like most people, you don't understand how sound works. The majority ( about 85%) of sound will travel through the drywall and wood. Empty voids actually reduce most sound. The more dense the material the faster sound can travel through it. However, the heavier the material, the more energy it takes to travel.
Sound proofing is more about 1) designing longer routes for sound to travel or 2) weighing down the path of so that it takes more energy for sound to travel a distance.
For the ceiling the best solution is resilient channels or 1x3 wood straps up before drywall. They need to run perpendicular to the ceiling joists and under no circumstances can you allow a screw from the drywall to touch a ceiling joist. Getting a minimum of two inches away when possible is best. In this setup gravity is going to pull down the drywall and wood strap will become taunt. In order for sound to go through the ceiling it has to push the ceiling up but cannot pull down, which heavily resists half of the sound wave.
On the wall you can't use gravity, but you can design the wall to limit any solid path from side to side. This is the purpose of staggered stud walls and double walls. In a basement I don't know how useful either would be, but they might be worth a study in some situations.
The other two key issues is absorption, and mass.
Mass is easy, the heavier the wall is, the less sound can travel through it. Every time you double mass of the wall, you double the sound resistance overall. 2 sheets of drywall is double of 1. 4 sheets is double of two. 8 sheets is double of 4. You get the idea.
Absorption: this is the conversion of sound to other energy. If you put tar paper between sheets of drywall, the resulting friction that happens when sound travels through converts some sound to heat. More effective is sound reducing treatments. For about a dollar a square foot you can put a glue/gel between the sheets of drywall. The gel has high resistance to movement and will warm up about a 1/10 of a degree when you crank up the volume on a high power stereo.
Insulation provides modest amounts of resistance to the mid range of most people's voices. A wet cellulose install will give you the most bang for the buck on soundproofing. Mainly that is because it seals the cavity and has some amount of mass. Don't expect it to do away with low range sounds. The booms from a stereo will go through the wood studs and joists easily, unless otherwise prepared. Don't expect foam sheets to accomplish anything.
And make certain you seal any edges with caulking before covering with plaster or drywall mud. Due to the nature of drywall mud to have tiny cracks, it is almost worthless as soundproofing or sealant in a sound proofing application.