What is a wave?

Say that a wave is the propagation of a disturbance of the environment is not enough to understand what a wave.
Say that speed, wavelength and frequency are the three properties characterizing a wave and that the relation between the three variables is v = λ * ν that does not sufficient to understand what a wave.
Say that a wave travels with a specific speed which depends on the characteristics of the propagation environment, it does not show the wave.
Say that a wave carries energy without transporting of matter, it tells us, always nothing in the nature of a wave.
Now imagine a rope that is shaken, of a vertical gesture. This simple movement will draw a wave of a certain height, which appears to be spreading to the front but in reality no point in the rope moves each point, comes and goes, moving vertically. This amplitude gives us an idea of the force with which you shake the rope but not the wave itself.
To understand what is a wave must remove the rope and imagine the air molecules undergoing the mechanical pressure of the rope. At this point it only remains in the medium (air) than the energy, a force generated by the movement of the rope. This energy makes the pressure of the air oscillate around an equilibrium value, the pressure increases and decreases alternately around this value. The wave (energy) moves the air molecules without transport them. As the rope is shaken, one can measure the distance between two bosses or, two hollow, this distance is the wavelength, measured in meters. The rate at which the rope is shaken, corresponds to the wave frequency measured in Hertz. The wave velocity measured in meters / second is equal to the wavelength multiplied by frequency.

One wave propagates in a stable environment, able to return to an equilibrium state, for a sound wave that is the air pressure which moves relative to an average value, for an electromagnetic wave is the intensity of the electromagnetic field which moves relative to an average value of the field.
Electricity can be static, such as amber after being rubbed, attracts small objects. Magnetism can also be static like a magnet. But when these fields move together, they become electromagnetic waves (see image). Electromagnetic waves are formed when an electric field (shown by red arrows) couples with a magnetic field (represented by blue arrows). The electric and magnetic fields of an electromagnetic wave are always perpendicular one with respect to another but also perpendicular to the direction of the wave.
These two types of waves, mechanical and electromagnetic, are two ways of transporting energy in a medium. The waves in the water and the sound waves in the air are two examples of mechanical waves. This energy transport disrupts or makes vibrate matter (solid, liquid, gas or plasma) without transport, water or air molecules collide but remain in the same place.
A variable magnetic field induces a variable electric field and vice versa, the two are connected. When these two fields are coupled (Maxwell equations) form electromagnetic waves (see image). Electromagnetic waves unlike mechanical waves, do not need medium to propagate, they travel everywhere, even in the vacuum of space.
Light, electromagnetic waves and all radiation are from the same physical phenomenon: the electromagnetic energy.