# Classification of non-mechanical waves

Transverse and longitudinal waves are classified according to the direction of propagation of wave motion and direction of oscillations of particles of the medium. But in the case of non-mechanical waves there is no medium, so there are no particles of a medium to oscillate. In this case how does one classify longitudinal and transverse waves?

## 2 Answers

Usually you consider a test particle and describe the wave based on how that test particle would move within the wave. For instance EM waves you imagine a charged particle within the field and the direction that charged particle moves in would determine the classification, Transverse or longitudinal for instance.

Even for non-mechanical waves, there is still something that varies in time and space and fulfills a wave equation. If that something has a direction, we can classify transverse and orthogonal waves.

The obvious example is the electromagnetic field: In an electromagnetic wave, the $\vec{E}$ and $\vec{B}$ fields are vector fields, i.e.\ they have a direction, and they are orthogonal to the direction of propagation.

A direct consequence of the transversality is that these waves can be polarised: Since there are two directions transversal (in three spatial dimensions) to a give direction, there can be two independent transverse waves. A longitudinal wave, on the other hand cannot be polarised, since there is only one direction.