Why can radio and microwaves travel through space but sound can't?
Because sound waves are vibrational waves, while radio and microwaves are electromagnetic in nature.
Sound waves require a certain density of matter in order to travel and vibrate through. That’s why sound works on earth, but that doesn’t in space. There is an abundance of free molecules to vibrate through (molecules in the air). That’s how sound works by vibrating atoms and molecules.
But in space there are so little molecules available that sound waves cannot propagate.
Why electromagnetic waves can travel through space or a vacuum is more complicated and is a bit beyond my knowledge. But the gist of it is that, its because of wave particle duality and the fact that the particle involved is a photon. And photons do not require a medium to travel through.
If any physics people can elaborate or correct me, feel free.