Final+paper

=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 room. The images produced on television and that travel through space to reach receptors 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 travelling with the wave." **===

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

3. Elements of a Wave.
The elements of a wave are:

4. Wave types.
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 them traveling in a vacuum, technically we can not be moving for any space, but in themselves they 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. They can propagate in any direction from a surface, therefore, are also called surface waves. One example __is the waves that are p__roduced 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. ===

**5. Relationship between the waves, the circle and trigonometric functions**
===** To fully understand the waves, we need to understand the measures associated with them, for example, how often are repeated (frequency), how long are (their wavelength) and vertical size (amplitude). **===

===** While these measures will enhance t__he waves describe__, do not help us predict the behavior of the same. To achieve this, we need to see the waves more abstractly, what can be done using a mathematical formula. You can see the waves mathematically, since the form of a wave is repeated at constant intervals over time and distance. This behavior reflects the repetition of the circle. Imagine drawing a circle on paper. Now, pretend to draw the same shape as, slowly, her friend removed the paper from under the stylus. Had drawn the line takes the form of a wave. To appreciate this idea, go to the link "From the circle on the wave" in the Experiment! In the menu on the right. A rotation around the circle, completing a cycle of ascent and descent of the wave, as shown in the picture below. **===



** Mathematicians use the sine function (not) to express the form of a wave. The mathematical equation that represents the simplest wave is: **

 * y = sin (x)**

** This equation describes how a wave could be plotted on a graph, in which y (the vertical coordinate value in the graph) is a function of sine of the number x (the horizontal coordinate). **
===** Getting the measure of an angle of a triangle, one can calculate the ratio of the sides of the triangle. The exact size of the triangle varies, but the proportion of the length of the sides is defined by the size of the angles. The specific relation between the measure of angle and the sides of the triangle are what are known functions. The three main functions are: **===


 * ===** Sine A = opposite / hypotenuse **===


 * ===** Cosine A = adjacent / hypotenuse **===


 * ===** Tangent A = opposite / adjacent **===

_ The word trigonometry means "measurement of triangles." The sine, cosine and tangent are the trigonometric ratios, which have their origin in the former studio of the triangles.

= = ===** The waves have a wide variety of applications, and we find them everywhere. Here is where science makes use of them to conduct research in various fields, including research relating to light, sound, electromagnetism, and gravitation. **=== ** For example, we use electromagnetic waves to create a magnetic force field and able to handle dangerous structures, such as particles of plasma. Or, to understand how they affect the gravitational waves to be able to place satellites in orbit with extreme precision. **

**7. Importance of waves**
===** Although not widely discussed in waves during the day, they play an important role in it. We can find waves on the radio, turning on the light in the room, turning on the TV, even to see the rain fall. **===

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===** Here is where we realize that the waves belong to the dynamic world we live in. If we did not know their behavior, communication, scientific studies would not be possible and life in the modern world would be very different. **===

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 * Source: [|http://www.visionlearning.com/library/module_viewer.php?mid=131&l=s][|http://es.wikipedia.org/wiki/Onda_(física)]**======