Waves are a very generic phenomenon: water waves, sound waves, radio waves and fashion cycles are all periodic motions of some sort. Waves are oscillations that propagate through a medium such as water or air, or even through empty space, as is the case with the electromagnetic waves described by the equations given here. These wave equations follow directly from the Maxwell equations in the absence of charges and currents. We exhibit them separately because of their tremendous importance.

Propagating waves are characterized by a wavelength λ, a velocity v and a frequency f. Between these three quantities there exists a simple relation, namely λ f = v. The magnitude of the oscillation is called the amplitude. The electromagnetic waves involve propagating electric and magnetic fields, with the property that the magnetic and electric oscillations are perpendicular to the direction of propagation and perpendicular to each other – so-called transversal waves (see figure). Maxwell showed that the propagation speed of these waves exactly equals the known speed of light c. Visible light was apparently just an electromagnetic wave phenomenon and turned out to be part of a continuous spectrum of electromagnetic waves, which vary in wavelength and frequency. Moving from very long to very short wavelengths, we identify this radiation subsequently with radio waves, microwaves, heat radiation, infrared light, visible light, ultraviolet light, and X-rays.

Maxwell's equations thus managed to unify the description of electric, magnetic, optical and radiation phenomena. The combined equations of Maxwell and Newton therefore form the beating heart of all of classical physics.