Learning Objects

THE WAVES

1. What is a wave?

Have you ever tried to throw a stone into a lake? Probably yes. What happens when you do it? Exactly, there appears a circle which moves in all direction making itself bigger and bigger. In Physics, when we make a system that was quiet suddenly change, we say that we perturb the system. So, when you throw that stone you are creating a perturbation.

So, that what a wave is: a perturbation that propagates in the space. Or, in a more accurate way:

A wave is a propagation of Energy which carries no matter.

A wave carries no matter because if it would, the amount of water in the lake would change, but, if you think about that, it never does.

Examples of waves are the light we see by our eyes, or the sound we hear by our ears.

2. Types of waves

Basically, we have two different kind of waves according on the direction of the perturbation that the wave carries.

Longitudinal waves: The perturbation takes place in the direction of the propagation. For example: the sound.
Crossed waves: The perturbation takes places in the direction perpendicular to the direction of propagation. For example: the light.

3. Wave equation

If we want to work with waves in a proper way, we will need to know how a wave can be mathematically expressed. The equation of a wave has the following form:

It is very useful because you can know the value of the perturbation in any time and position. It depends on three different parameters:

Amplitud A: gives an idea of how big the wave is.
Angular frequency ω: Is the velocity of the vibration of the perturbation, it is closely related with de period of the wave.
Number of waves k: gives an idea of the length of the wave.

We can plot the equation to obtain:

And we can observe that it has the shape of an oscillation.

4. Properties of the waves

The waves, as we have said before, present some different properties than the properties of the common particles. Basically, there are four properties: reflection, refraction, diffraction.

Reflection: is the change of the direction of a wave when it comes across a separation between two medium and it returns back. An example of this is when you look at yourself on a mirror: the light rebounds on the mirror and it gets back so you can see yourself.

Refraction: is the change of the direction of the wave that happens when the wave passes from one media to another (this is the difference with the reflection). When refraction takes place, the objects seem to distort. An example of this is the pencil in the glass of water:

Image belonging to the Florida Center for Instructional Technology. University of South Florida.

is the capacity that the waves have overcome obstacles, and keep on propagating. The reason why this happens is because every point of the wave behaves as an emitter focus. One proof of this effect is that you can hear a person who talks to you although you can’t see them, as the next picture shows.

Sources and References

In progress.