## Amplitude Formula

Amplitude is referred to the maximum change of variable in the mean value. The Amplitude is symbolized as ‘A’. In a periodic function along with a bounded range, the amplitude is half the minimum and maximum values. The amplitude is usually the height from the centerline to the peak.

## What is Amplitude Formula?

In Simple words, Amplitude is regarded as the maximum displacement of a variable from its mean value. The amplitude Formula helps in recognizing the cosine and sine functions. The amplitude is represented as ‘A’ and the cosine or sine function is represented as

x = A sin (angular frequency × time + phase of angle) or

x = A cos (angular frequency × time + phase of angle)

Here, A – Amplitude and x = displacement of wave (meter)

The amplitude Formula is also defined as the average of maximum and minimum value of the sine or cosine function.

Amplitude = (max + min)/2

### Solved Examples

**Example 1 **

Y = 2sin (4t) is a wave. Now find out the amplitude

Given, that Y = 2sin(4t)

Applying the amplitude Formula,

x = A sin (angular frequency × time + phase of angle)

In comparison with the wave Equation,

A = 2

Angular frequency = 4

A phase of angle = 0

Therefore, we get amplitude= 2 units

**Example 2 **

The Equation of a wave has been given as x = 10sin (5πt + π) of the wave. Find its amplitude.

Given Equation of Wave is x = 10sin (5πt + π)

Using the amplitude Formula,

x = A sin (angular frequency × time + phase of angle)

A = 10

Angular frequency = 5π

The phase of angle = π

Therefore, the amplitude of the wave is 10 units.