The problem is that noise is generated across a wide range of frequencies but sound insulation products can only generally deal with a narrow range of frequencies. It is a rule of thumb that you need low density components to attenuate high frequency sound but, paradoxically, you need high density components to attenuate low frequency sound. That's why the sounds tapped out by prisoners on the heating system is always the high pitched tink, tink sound. Pipes are high density, which attenuates the low frequencies and allows the high frequencies through. So mineral wool, or dense concrete blocks, heavy plasterboard etc. will only do part of the job. You need both somewhere in the construction.
Is is also a rule of thumb that 90% of sound will travel through 10% of gaps. If you were awake during the bell jar experiment at school, you might remember that, before sucking the air out the jar, the physics teacher pushed the jar down on the mat and the sound reduced dramatically. That's because most of the sound was coming through the gap between the mat and the jar rather than through the glass.
Finally, sound will travel through components that penetrate or touch the wall. i.e. wall ties, rafters, joists, abutting walls, etc. To avoid this a cavity is usually introduced. The optimum cavity depends on the surrounding materials. For glass it is about 200mm. The key thing here is frequency again. If the width of the cavity is equal to the sound wave then the wave will cross uninterrupted. Because sound is generally comrised of all the frequencies then obviously one or other of those frequencies is going to get through.
So, you need a heavy, light wall with no gaps and no penetrations and all the components seperated by several cavities of different widths.