periodic waves

One-dimensional periodic waves

Periodic waves are waves generated by sources that perform periodic oscillations, that is, that are repeated at equal intervals of time. The figure above represents a periodic wave propagating in a tensioned string. In the sequence, some important elements associated with it will be listed.

In the figure above, points A and B are called crests , that is, crests are the highest points of a wave. It is important to point out that these points oscillate in phase agreement, that is, they present, at each instant, identical sizes.

Points C and D are called valleys , that is, the valleys are the lowest points of the wave. Valleys, analogous to crests, oscillate in phase agreement. The amplitude of a wave is the distance between the crest and the valley of the wave, that is, it is the maximum distance that each point in the middle of the wave presents in relation to its equilibrium position, either up or down.

The period ( T ) of a wave is nothing more than the time interval for each point in the medium through which the wave propagates to execute a complete oscillation. The frequency ( f ) of a wave is the number of complete oscillations that each point of the medium in which the wave propagates executes, per unit of time. The frequency of a periodic wave is the inverse of its period, that is:

In the SI (System of International Units), the unit of frequency is the hertz ( Hz ). We can say that 1 Hz = 1 s -1 .

The length of a wave is represented by the distance traveled by it in the time interval of a period. The value of λ corresponds exactly to the distance between two consecutive valleys or crests. In the figure above we can say that the wavelength is the distance between points A and B and also the distance between points C and D.

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