Can a wave propagate in any substance? Aren't there any prerequisites? We see waves propagate in air, water, through the cristal of a metal and along a rope.
Isn't a wave a wonder of Nature, or is it just a simple phenomenon?
Are  homogeneity and isotropy necessary properties  for the correct propagation of waves?
Update
are a rope, water and space/EM field elastic in the same way?
 A: A wave is generated by a disturbance in a medium. For a wave to propagate, do not necessarily need a medium.
For example, an electromagnetic wave can propagate in vacuum, while a sound wave requires an elastic medium to travel.
The requirements for the propagation of a wave, are dependent on the nature of the wave.
A: A wave can propagate in any medium that is:
a) elastic
b) less than critically damped
Neither homogeneity nor isotropy are necessary.
Any elastic system will return to it's original state when deformed, the question is just whether the deformation can propagate, and this is down to how quickly the energy of the deformation is dissipated. If the damping is high enough, this is critical damping, the material will return to its original state with a $e^{-\alpha t}$ dependance on time and no wave will propagate.
For example, in water common experience tells a gravity wave (i.e. a wave) propagates just fine, and a longitudinal wave (i.e. sound) propagates just fine. However shear waves will not propagate because they are too rapidly damped.
