The amount of time for one particle of the medium to make one comlpete vibration cycle is a good description of

That's the definition of the PERIOD of the vibration.
It's exactly the reciprocal of the vibration's frequency.

Aform of energy that is reflected or emitted from objects in the form of electrical and magnetic waves that can travel through space. there are many forms of  electromagnetic  energy including gamma rays, x rays, ultraviolet radiation, visible light, infrared radiation, microwaves and radio waves.