What Is Sine Wave;5 Properties of a sine wave

A sine wave represents graphically the voltage of the electric current, where we can represent both the voltage of the electric current in direct current, and in alternating current.

The waveform

The alternating current is generated by different methods. The most used are the rotary mechanics, or alternators of the electric coils.

The most common waveforms are:

  • the senoidal,
  • the square,
  • the triangular,
  • the sawtooth

All are presented in different types very varied.

Properties of a sine wave

1 Statement

A disturbance along a string is described by the equation

with x and y measured in centimeters and t in seconds.

For this wave, find its amplitude, angular frequency, period, wave number, wavelength and velocity of propagation.

2 Solution

This function is a traveling wave corresponding to the general form

that, by itself of the form f ( x – v t ) is clearly a solution of the wave equation.

2.1 Amplitude

The amplitude of this wave, A, is the coefficient that multiplies the cosine. In our case

2.2 Angular frequency

The angular frequency, ω , is the coefficient that precedes the time in the cosine argument

2.3 Period

From the angular frequency we have the natural frequency and the period

 

2.4 Wave number

The wave number is the amount that multiplies x in the cosine argument

2.5 Wavelength

We calculate the wavelength from the wave number

2.6 Speed ​​of propagation

The speed of advance of the wave is equal to

Summing up we can say that a sine wave of alternating electric current is bidirectional with respect to time (with positive and negative values) and the mathematical sinusoid that normally draws can be expressed as:

A ( t ) = Am a x⋅ s i n ( 2 π⋅ f⋅ t )

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