Electromagnetic radiation
Electromagnetism 

Electricity · Magnetism 
Electric charge • Coulomb's law •
Electric field • Electric flux • Gauss's law • Electric potential energy • Electric potential • Electrostatic induction • Electric dipole moment • Polarization density 
Magnetostatics
Ampère's law • Electric current • Magnetic field •
Magnetization • Magnetic flux • Biot–Savart law • Magnetic dipole moment • Gauss's law for magnetism 
Electrodynamics
Lorentz force law • emf • Electromagnetic induction • Faraday’s law • Lenz's law • Displacement current • Maxwell's equations • EM field • Electromagnetic radiation • Liénard–Wiechert potential • Maxwell tensor • Eddy current

Electrical Network
Electrical conduction • Electrical resistance • Capacitance •
Inductance • Impedance • Resonant cavities • Waveguides 
Covariant formulation
Electromagnetic tensor • EM Stressenergy tensor • Fourcurrent • Electromagnetic fourpotential

Electromagnetic waves are waves that contain an electric field and a magnetic field and carry energy. They travel at the speed of light.
Quantum mechanics developed from the study of electromagnetic waves, which include visible light seen in the colors of the rainbow, but also other waves including the more energetic and higher frequency waves like ultraviolet light, xrays, and gamma rays plus the waves with longer wavelengths including infrared waves, microwaves and radio waves.
Some types of electromagnetic radiation, such as Xrays, are ionizing radiation and can be harmful to your body. Ultraviolet rays are near the violet end of the light spectrum and infrared are near the red end. Infrared rays are heat rays and ultraviolet rays cause sunburn.
The various parts of the electromagnetic spectrum differ in wavelength, frequency and quantum energy.
Sound waves are not electromagnetic waves but waves of pressure in air, water or any other substance.
Mathematical formulation
In physics, it is well known that the wave equation for a typical wave is
The problem now is to prove that Maxwell's equations explicitly prove that the electric and magnetic fields create electromagnetic radiation. Recall that two of Maxwell's equations are given by
By evaluating the curl of the above equations and vector calculus one can prove the following equations
Note: the proof involves making the substitution
The equations above are analogous to the wave equation, by replacing f with E and B. The above equations mean that propagations through the magnetic (B) and electric (E) fields will produce waves.
Related pages
Images

Electromagnetic waves can be imagined as a selfpropagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. Note that the electric and magnetic fields in such a wave are inphase with each other, reaching minima and maxima together

Electromagnetic spectrum with visible light highlighted