Draft1

=The Waves and Math=

1. Introduction.
=== When we hit a bell or turn on the radio, the sound is heard in distant parts of the bell or radio. If we throw a stone into a pond we note that the water forms a roll and that this spreads. When lit the lamp illuminates this quarter. The images produced on a television travel through space to receivers that are in our homes. All the above processes have something in common: they are physical situations produced at a point in space that travel through it and received at another point. All these processes are examples of wave motion or put another way are waves. ===

===**According to Wikipedia: "A wave is a disturbance that propagates (travels) through space and time, usually by transference of energy. A mechanical wave is a wave that propagates through a medium due to restoring forces produced upon its deformation. For example, sound waves propagate via air molecules slamming into their neighbors, which push their neighbors into their neighbors (and so on); when air molecules collide with their neighbors, they also bounce away from them (restoring force). This keeps the molecules from actually traveling with the wave." **===

===**In simplest words, a wave is a disturbance that propagates in a fluid or an elastic eviroment, often transferring energy. For example, the waves in the water when we drops a rock on it. **===

** Depending on the environment in which they are propagated **
Mechanical Waves : Mechanical waves need an elastic medium ( solid, liquid or gas ) to propagate. The particles of the medium oscillate around a fixed point, so there is no net transport of matter through the media. As in the case of a carpet or a whip whose end is shaken, the carpet does not move, however, a wave propagates through it. The speed can be affected by environmental characteristics such as uniformity, elasticity, density and temperature.

Electromagnetic Waves **: **Electromagnetic waves propagated in space without a medium, and may therefore spread into the vacuum. This is because electromagnetic waves are produced by the oscillations of an electric field in conjunction with an associated magnetic field. Electromagnetic waves travel at a speed of approximately 300,000 km per second, depending on the speed can be grouped into frequency range. This arrangement is known as electromagnetic spectrum, an object that measures the frequency of the waves.

Gravitational Waves: Gravity waves are disturbances that alter the same geometry of space-time and although it is common to represent traveling in a vacuum, technically we can not be moving for any space, but in themselves are disturbances in spacetime.

Dimensional Waves: One-dimensional waves are those that propagate along a single direction of space, like the waves on the docks or in the ropes. If the wave propagates in one direction only, their wave fronts are flat and parallel.

Two-dimensional or surface waves: They are waves that propagate in both directions. Can propagate in any direction from a surface, therefore, are also called surface waves. One example is the waves that are produced in a liquid surface at rest when, for example, drops a stone in it.

Three-dimensional waves: They are waves propagating in three directions. The waves are also known as three-dimensional spherical waves, because their wave fronts are concentric spheres emerging from the source of interference to expand in all directions. Sound is a three-dimensional wave. Three-dimensional waves are sound waves (mechanical) and electromagnetic waves.

** Depending on the direction of the disturbance **
===**Longitudinal Waves**: Those are that characterized by particles of the medium move (or vibrate) parallel to the direction of wave propagation. For example, a spring that is compressed resulting in a longitudinal wave. ===