What type of wave requires a medium to transfer energy

Mechanical waves.

Explanation:

A mechanical wave is a perturbation on the mechanical properties of the material medium (position, velocity, pressure, etc. ) in which it propagates.

Mechanical waves need a source that creates the perturbation and, a physical medium in which perturbation propagates, the medium can be a gas, a liquid or, a solid.

Some examples are sound, earthquakes and, waves on a guitar string.