# wave function

Configuration of a periodic wave propagating in a medium with speed v

When we studied waves, we saw that they originate in elastic media, such as strings, on the surface of water, air, etc. Thus, waves are oscillatory movements that propagate in a medium. Therefore, only energy is transferred in these elastic media.

We have also seen that waves can be both mechanical and electromagnetic. Mechanical **waves** are the result of deformations in material media, so they do not propagate in a vacuum. **Electromagnetic waves** are the result of vibrations of electrical charges. Only electromagnetic waves can propagate in a vacuum.

The function of a wave, that is, the function of a disturbance propagating in a medium, has two variables (position and time). In this case we will represent such variables by (xet).

Let’s see the figure above: in it we have the representation of a periodic wave with speed ve that propagates in a medium along the **x** -abscissa axis . In the figure, F is the generating source of the MHS, whose amplitude is *a*** , on the y** -ordinate axis .

Suppose the source F obeys the following time function:

*y=a.cos(ωt+φ _{0} )*

and that the **point P** performs the same simple harmonic movement of the source, however, with a delay of a time interval

in relation to her. Thus, one can write its time function as follows:

*y=a.cos[ω(t-∆t)+φ0 ]*

As the angular velocity is given as a function of period, we have:

So:

Since linear velocity is defined by the ratio of wavelength to period, we have:

So:

which is the wave function. Particularly, in the case of

*φ _{0} =0*

We have:

A wave function gives the configuration of the wave at a given time **t** or the MHS of a point at a given position x.