# Amplitude Formula

Amplitude Formula – The maximum divergence of a variable from its mean value is known as amplitude. It is the greatest displacement from a particle’s mean location into to and from motion around that mean position. Amplitudes exist for periodic pressure changes, periodic current or voltage changes, periodic fluctuations in electric or magnetic fields, and so on.

Quick Links

Amplitude does not have a set formula. It can be determined using equations or graphical representations of such variations.

## Amplitude Formula

The amplitude of a variable is its highest deviation from its mean value. The amplitude formula may be used to compute the sine and cosine functions. Amplitude is symbolised by the letter “A”. The sine (or cosine) function’s formula is as follows:

x = A sin (ωt + ϕ)

or

x = A cos (ωt + ϕ)

where,

• x = displacement of wave (meter)
• A = amplitude
• ω = angular frequency (rad/s)
• t = time period
• ϕ = phase angle

The amplitude formula is also used to calculate the average of a sine or cosine function’s maximum and minimum values. The absolute amplitude value is consistently utilised.

## Amplitude Solved Examples

Example 1: If y = 4 cos (3t + 1) is a wave. Find its amplitude.

Solution: Given: equation of wave y = 4 cos(3t + 1)

Using amplitude formula,

x= A cos (ωt + ϕ)

On comparing it with the wave equation:

A = 4

ω = 3

ϕ = 1

Therefore, the amplitude of the wave = 4 units.

Example 2:  y = 3sin(2t) is a wave. Find its amplitude.

Solution: Given: equation of wave y = 3sin(2t)

Using amplitude formula,

x = A sin(ωt + ϕ)

On comparing it with the wave equation:

A = 3
ω = 2
ϕ = 0

Therefore, the amplitude of the wave = 3 units.

## FAQs (Frequently Asked Questions)

### 1. What are the Units of an Amplitude Formula?

The unit in an amplitude formula is the meter (m).

### 2. What is the Amplitude Formula in Maximum and Minimum Form?

The amplitude formula is also expressed as the average of the maximum and minimum values of the sine or cosine function. i.e.,

Amplitude = (max + min) / 2

### 3. What is the Formula to Find the Amplitude?

The sine function (or) cosine function can be expressed as,

x = A sin (ωt + ϕ)   or   x = A cos (ωt + ϕ)

Here,

x = displacement of wave (meter)
A = amplitude
ω = angular frequency (rad/s)
t = time period
ϕ = phase angle