# What is Amplitude of a Wave? Definition, Formula, Example

In simple words, the amplitude of a wave is the measurement of maximum displacement or changes of the variable from a particular reference point. If you want to easily understand the concept of the amplitude of a wave then you must have a clear idea of the wave. Actually, the waveform is a graphical representation of changing variables with respect to time. For example, a sinusoidal wave represents how the AC voltage decreases and increases over time. So here the definition of amplitude will be the maximum changes of voltage with respect to a reference point it may be zero potential. In our 230V sinusoidal waveform the voltage decreases or increases from zero potential sometimes it goes to +230V and sometimes it goes to -230V. This change from 0V to 230V is expressed as the amplitude of that sinusoidal waveform.

Here you can see the below diagram to understand the concept of amplitude.

As we know that the amplitude is measured from a reference point, so according to it there are different types of amplitude.

For example, The peak amplitude refers to the maximum changes of the variable from the zero or center point. The peak amplitude is measured if the wave is not sinusoidal and the measured swings above and below a reference point. In the audio systems, and radio communication systems, this type of amplitude is measured. The peak amplitude is generally termed as amplitude or semi amplitude(because it is half of the peak to peak amplitude).

Peak to peak amplitude can be measured between the maximum positive value and the maximum negative value. For a sinusoidal wave peak to peak, the amplitude can be measured easily because here the time period is equal.

Another format for measuring amplitude is Root Means Square Amplitude. The root means square amplitude is measured for complicated signals that have discrete waveforms such as noise signals.

**Understand Amplitude with Examples**

For example, in a sound wave, the amplitude is the maximum loudness or displacement of vibrating particles through the medium with respect to a mean point. So the loudness is directly proportional to the amplitude of the sound wave. As the sound wave is not sinusoidal so here mostly the peak amplitude or semi amplitude is measured.

**The formula of Amplitude of a Wave**

The simple equation or formula for amplitude is,

**x = A sin (Ï‰t + Ï•) or x = A cos (Ï‰t + Ï•)**

Here,

x = displacement of wave (meter)

A = amplitude

Ï‰ = angular frequency (rad/s)

t = time period

Ï• = phase angle

So, when finding amplitude, the above terms are very important. The time period is the time taken by the variable to complete a cycle. The number of cycles per second is known as frequency. Frequency is measured in Hertz.

Also, you should have knowledge about crest and trough. The crest is the maximum positive value whereas the trough is the maximum negative value.

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What is Amplitude of a Wave? Definition, Formula, Example
Reviewed by Author
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4/21/2022
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