Question

What happens when waves encounter a medium that they cannot travel through

Answer 1

Then the waves (and the energy they carry) are completely reflected from the surface of the impenetrable medium.

Example:
An ordinary mirror is a sheet of glass with a thin layer of aluminum
or silver stuck to the back of the glass.  Light waves have no trouble
traveling through the glass, but they can't get through the silver layer
on the back of it.  So the waves completely bounce off of the silver, and
go back through the glass in the direction they came from.