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# Amplitude|Definition & Meaning

## Definition

**Amplitude** is defined as the **height** from the **middle value** of a periodic function to the **maximum** or the **minimum** value of the function. It is the height from the **center** of the periodic signal to the **trough** or the **crest** of a wave. It defines how much something is **enhanced** or amplified.

## Illustration of Amplitude

Consider a periodic function **y = sin 2x**. The amplitude of this periodic signal is shown in **figure 1**.

The height **AB** or **CD** is the **amplitude** of the sine wave. Note that point **A** is the **maxima** or the peak value and point **C** is the **minima** or the crest of the sine wave.

## Amplitude and Its Importance in Communication Systems

Amplitude is essential in **communication systems** where signals need to be projected over long distances.

The amplitude provides strength to the **periodic signal**. It is the height from the peak value or the crest to the center or the mean of a signal. The signal’s amplitude or strength changes by increasing or decreasing this height.

## Calculation of Amplitude

Amplitude can be** calculated** by adding the positive values of the **crest** and the **trough** and then dividing by **2**.

## Attenuation

Attenuation means that the amplitude of the signal decreases whereas a **booster** increases the amplitude so that it can be carried out to its destination.

## Amplitude in Angular Motion

A **periodic signal** can also be considered as a **circle** when discussing **angular** motion. The **radius** of the circle is the **amplitude** of the periodic signal. The circle’s radius decreases or increases by amplitude.

## Amplitude and Other Terminologies

In **communication systems**, the amplitude of the signal is accompanied by some other terminologies which cannot be left out while dealing with the **amplitude** of a signal.

These are such important as the amplitude of the function. These terms are** time period**, **frequency**, and **wavelength**.

All these terms define a complete set of properties for the periodic function. It is also necessary to understand a **periodic function** before discussing its amplitude.

The periodic function and the **terms** such as time period, frequency, and wavelength are defined as follows:

### Periodic Function

A **periodic function** is defined as a signal with **repeating values** of the function after **regular intervals**. The value of the function recurring after equal time intervals defines the **periodicity** of the function.

Periodic functions play an** important** role when dealing with terms such as amplitude, time period, frequency, and wavelength.

A **non-periodic** function has varying values of these terms as the signal’s values are continuously** changing**. They do not repeat after the same time intervals thus they can’t have constant amplitude, frequency, or wavelength.

### Time Period

The **time period** is the time the signal takes to complete one cycle. A **wave cycle** involves a maximum value and the minimum value of the signal, after which it drops to its recurring value.

The time period is measured in **seconds** and has an **inverse** relation with the **frequency** of the periodic function. The mathematical** formula** for the time period relating to the frequency is as follows:

**T = 1/f**

Where **T** is the time period and **f** is the frequency.

Consider **figure 2** for the **time period** for the particular sine wave. The time period is the time interval denoted by **T**.

Note that the function’s value is the **same** at both ends of the time interval and inhibits a **complete cycle**.

### Wavelength

The** wavelength** is the **distance** between two** successive** troughs or two crests in the two adjacent **cycles** of the signal. It is the distance between two **same** points from one cycle to the next.

The wavelength is measured in **meters** and is represented by the greek letter lambda **λ**. It is** inversely** proportional to the **frequency** of the wave.

Consider **figure 3** for the **wavelength** illustration. The distance **PQ** from **crest to crest** is the wavelength of the particular sine wave.

### Frequency

The **number of waves** passing through a fixed **point** in a specific time interval is called the **frequency**. The frequency defines the **oscillations** that occur **per second** in a periodic signal.

The mathematical **formula** relating frequency and wavelength is as follows:

**c = f λ**

Where **c**, **f**, and **λ** are, respectively, the speed of light, the frequency, and the wavelength. The frequency is measured in **Hertz** (**Hz**) or per second.

Consider **figure 4** for the **frequency** of the sine wave. The number of **wave cycles** passing through a **point** **M** highlighted in the figure in one second is the frequency.

It could be any point as it is just a **reference** point.

## Example of Altitude in Waves

Consider the **periodic** function **y = 5 sin x** as shown in **figure 5**. Calculate the periodic function’s amplitude, wavelength, frequency, and time period.

### Solution

The figure shows the **trough** of the sine wave at **5** and the **crest** is at **-5**. The amplitude can be calculated by **adding** the crest and trough values and **dividing** the result by **2**.

As the amplitude is a **height**, the crest value is taken** as positive**. So, the amplitude will be:

**Amplitude = (5 + 5) / 2 = 10 / 2 = 5**

The figure also shows the distance of **8 m** between **two** wave cycles. The **wavelength** can be calculated by **dividing** it by **2** as it is the distance between two successive troughs or crests.

So the** wavelength** will be** 4 meters**.

The **frequency** can be calculated by using the formula **c = f λ**. The frequency will be:

\[ \text{f} = \frac{c}{λ} = \frac{ 3 × 10^{8} }{ 4 } = 7.5 × 10^{7} \ \text{Hz} \]

The **time period** can be calculated as follows:

\[ \text{T} = \frac{1}{f} = \frac{1}{ 7.5 × 10^{7} } = 1.33 × 10^{-8} \ \text{sec} \]

*All the geometrical figures are created using GeoGebra.*