1) "What is a medium?"
The historical way waves have entered in the world of physics is through cases of small (linear) perturbations of physical systems/ The "medium" is the physical system. One ore more physical quantities of an extended system (medium) may be described by a wave-equation. Examples may include:
- local pressure or density of a fluid;
- the local height of the liquid-air boundary in the presence of a gravitational field;
- departure from equilibrium configuration of a stretched string;
In these examples the medium is respectively: the fluid, the free surface of the liquid, the string.
2)What is the physical notion behind it?
In all those cases, the quantity exhibiting wave-like motion is a physical property of a physical system made of matter. This explains the reason nineteenth century physicists tried hard to find a material system underlying electromagnetic waves.
It required some effort to get convinced that in the case of electromagnetic waves is the electromagnetic system which has to be considered the physical system and that there is no experimental basis justifying the existence of a physical system carrying a property called electromagnetic field.
3)What are the kinds of it?( I know of one' the material medium ' ,this provokes me to ask this.)