A mechanical wave takes place in a medium. In other words: a solid, liquid or gas.

A longitudinal wave, on the other hand, is a wave in which the displacement of the particles occurs in the same direction as that in which the wave is travelling. One example is sound waves.

Alternatively, a transverse wave is where the displacement of the particles within the medium is perpendicular to the direction in which the wave is travelling. One example is water waves.

An electromagnetic wave is an oscillating electric and magnetic field. It is a form of transverse wave and, in a vacuum, all types of electromagnetic wave travel at the speed of light. Examples include:

radio waves
microwaves
infra-red
visible light
ultra-violet
x-rays
gamma rays

Polarised light

Another difference between transverse waves and longitudinal waves is that the former can be polarised while the latter cannot.

Unpolarised light is composed of a mixture of waves which are at different planes. If this light passes through a polaroid material, for example polaroid sunglasses, only light waves travelling on one plane are transmitted and the light is now said to be polarised.