# Sinusoidal Wave Signal

**To understand what a Sinusoidal Wave Signal or sine wave, let’s first try to understand what a signal is.**

**What is the Signal?**

**There are different measurable quantities in the world around us. Some quantities are constant, such as the acceleration of gravity, the speed of light, and the speed of sound in the air. Some are variable over time, e.g. B. AC voltage, pressure, temperature. This means that their value will change over time. The signal simply means the value of any amount that has been ingested over a period of time. Signals are generally variable over time. Usually, a graph is drawn between the values at different times. **

**This is known as a graphical representation **

**of the signal.**

### What is Sine Wave or Sinusoidal Wave Signal?

**A sinusoidal or sinusoidal signal is a special type of signal. It is given by **

**the function**

**When the sine wave starts at zero and covers positive values, it reaches zero; and again covers negative values, reaches zero, it should have completed a cycle or a single cycle.**

**The top part of the sine wave is called the positive cycle and the bottom part is called **

**the negative cycle in a cycle.**

**The signal indicates the quantity values at this point in time for various time values. The signal is therefore a function of time. It is therefore written f (t). The maximum value of the sinusoidal signal is also known as the amplitude (A). **

**Here ω is called the angular frequency of the signal and f is the frequency of the signal.**

** ∅ Is called the phase **

**difference.**

**The frequency**

** is measured **

**in Hertz (Hz). **

**It shows the number of signal cycles that occurred in one second. A large ω value or a large f value indicates that the signal executes more oscillations in a shorter time (ie changes from positive to negative values). Therefore, the signal is inherently more vibratory.**

**The sinusoidal signal does not have to start at zero. It can start after a certain period of time.**

** This is the time after which the sinusoidal signal begins, **

**is displayed with**

** the phase difference (∅).**

** It is measured**

** in **

**radians.**

**Periodic signals are those that repeat their pattern after a certain time. This time after which **

**the pattern is repeated is called **

**the time period (T) of the periodic **

**signal. It is the inverse of the signal frequency.**

**The sinusoidal signal is a periodic signal because the pattern repeats itself after a wavelength, as shown in the figure above.**

**All current signals in our home, office, and in our industry are sinusoidal AC signals. The frequency (f) in India and Great Britain is 50 Hz and in US countries 60 Hz**

**Why is Sinusoidal Wave Signal so Important?**

**Sinus signals are important in the fields of electrical engineering and electronics.**

**According to the theory of Fourier series, each signal (periodic signal) can only be written as a sine and cosine**

** signal with different frequencies. **

**Therefore, a complex signal can be decomposed into simple sine and cosine signals, **

**and the mathematical analysis becomes easy.**

** Hence, it is widely used in **

**electrical **

**and electronic analysis.**

**In addition, **

**the output voltage in transformers is a time derivative of the magnetic flux. The magnetic flux is itself a time derivative of the input voltage. But we want the same voltage signal at the input and at the output. The only functions that meet this condition are the sine and cosine functions. Since the sinusoidal signal starts at zero, it is preferable.**

** As a result, most of the world’s power systems use sinusoidal AC voltage today. All household appliances**

** are also**

** operated **

**with sinusoidal alternating voltage.**