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.

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