What is a good sound insulater?

Answer 1

There are a number of good ways to insulate from sound. Headphones use a number of different polymers in solid or foam forms.

Some modern recording studios are soundproofed by expensive materials which are good at dissipating sound energy in the audible spectrum, but the traditional approach is instead to disperse the sound.

Using the egg-box shape (I've heard egg boxes can themselves be quite good, but don't rely on that) crates an uneven surface on the wall. Wavefronts therefore do not "push" the wall in a single force as they would if it was flat and face on to a source of sound, but instead hit different points of the surface at different times and scatter in a pseudo-random manner. This significantly reduces the sound heard on the other side of the wall.

Also, make sure no sources of sound are touching the wall and that nobody who might be bothered by the sound is on the floor below