Periodic waves

It is called periodic waves those described repetitive cycles that show frequency according to time. All periodic waves are deterministic waves. This is because these waves can be described mathematically or using a mathematical model.


  • 1 Formula and description of a periodic wave
  • 2 Values ​​and characteristics of periodic waves
    • 2.1 Average value
    • 2.2 RMS value
    • 2.3 Peak or crest factor
  • 3 Examples of periodic waves
  • 4 More types of waves

Formula and description of a periodic wave

xa (t) = xa (t + Tp) = xa (t + nTp)

In this formula the fundamental proper period is Tp = 1 / F

– F is defined as the frequency of the fundamental component of the periodic wave.

– N is an integer.

Values ​​and characteristics of periodic waves

Middle value

The mean value of a wave xa (t) is calculated over an interval that has the function that corresponds to a unique, proper and fundamentally complete period that is expressed in the form of Tp using any instant expressed in t0. The complete formula is as follows:

Amedio = 1 / Tp | t0 + Tp xa (t) dt

It happens frequently that the mean value of a periodic wave is equal to zero. In electronics and electrical engineering a non-zero mean value is the size of the magnitude of a continuous current component in a signal.

Effective value

The effective value of a periodic wave, also called root mean square or RMS for its acronym is represented by xa (t) and is calculated over an interval that corresponds to the function of a complete and fundamental proper period expressed as Tp at time t0.

The representative formula for the effective value is:

VRMS = square root of 1 / Tp | t0 + Tp | xa (t) | 2 dt

In physics, the effective value of a periodic wave is of particular interest when applying mechanical pressure, voltage or intensity for the purpose of calculating energy or power. There are three types of null value waveform that are related to the peak or peak value, also called the maximum Amax value, and they are the following:

  •  Simple harmonic or sine wave

ARMS = Amax / square root of 2

  • Square wave

ARMS = Amax

  • Triangular wave

ARMS = Amax / square root of 3

The relationship between the maximum amplitude and the effective value of a periodic wave will always depend on the shape of the wave.

Peak or crest factor

It is described as the factor that defines the relationship between the peak value and the effective value. Some examples of peak or crest factor are:

  • Simple harmonic or sine wave

fa = square root of 2

  • Square wave

fa = 1

  • Triangular wave

fa = square root of 3

Examples of periodic waves

  • Movement of the hands of a clock.
  • Phases and movements of the moon.
  • Trigonometric functions specifically the sine and cosine.
  • Sound waves.
  • Visible light.
  • Electromagnetic waves.
  • Gravitational waves.

If you compare the initial definition with the examples, you will notice that periodic waves are present around us. For them, we must know and understand how these are generated. It should be taken into account that sometimes we know about something, but we do not have the right words to define it.

More types of waves

  • Electromagnetic wave
  • Two-dimensional waves
  • Longitudinal waves
  • Mechanical waves
  • Periodic waves
  • Transverse waves
  • Three-dimensional waves
  • One-dimensional waves
  • Sound waves

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