# Is the electromagnetic wave produced by a linearly accelerating charge sinusoidal?

I have just learnt that accelerating charges produce electromagnetic radiation. When a charge initially at rest suddenly accelerates, the transition between the new and old elctric field lines propagates out as a wave at the speed of light. Moreover, the electric field is transverse to the direction of propagation. This phenomenon is explained here: http://www.springer.com/cda/content/document/cda_downloaddocument/9783642309694-c1.pdf?SGWID=0-0-45-1349311-p174514828

However, it doesn't seem to look like a harmonic(sine) wave to me. So if it doesn't have oscillating electric and magnetic fields, how is it classified as an electromagnetic wave? Also, does it satisfy the wave equation? For something to be called an electromagnetic wave, do we need to have sinusoidal oscillations of electric and magnetic fields?

One more question:Are all the electromagnetic waves that we observe in the universe sinusoidal? Or are there other types as well?

• So, according to you, only sinusoidal waves can satisfy wave equation? According to you, there are no periodic functions other than sinusoidal functions? I doubt that.
– user36790
Jul 14, 2016 at 4:02
• One can decompose almost all periodic functions into sinusoidal components and since electromagnetism in free space is completely linear, that decomposition is an extremely good description of the many non-sinusoidal phenomena that surround us. Jul 14, 2016 at 4:34