Amplitude refers to the maximum change of a variable from its mean value (when the variable oscillates about this mean value). In to and fro motion of a particle about a mean position, it is the maximum displacement from its mean position. Similarly, amplitudes are defined for periodic pressure variations, periodic current or voltage variations, periodic variations in electric or magnetic fields etc.
There is no particular formula for amplitude. It’s available from the equations or the graphical representations of such variations.
If y = A sin ωt ampere.
What is the peak value of the current?
Options:
(a) 5 A
(b) 2.5 A
(c) 4.33 A
(d) 7 A
Answer: (a)
Let us understand what amplitude is before moving on to the amplitude formula. The amplitude is the maximum displacement of any particle in a medium from its state or equilibrium position. The letter ‘A’ represents amplitude. The amplitude of a bounded-range periodic function is half the distance between the minimum and greatest values. The amplitude is the distance between the centerline and the peak or trough. Let us look at the amplitude formula and solve a few examples.
What is the Amplitude Formula?
The largest deviation of a variable from its mean value is referred to as amplitude. The sine and cosine functions can be calculated using the amplitude formula. A is the symbol for amplitude. The sine (or cosine) function can be written as follows:
x = A sin (ωt + ϕ) or x = A cos (ωt + ϕ)
Here,
The amplitude formula is also expressed as the average of the sine or cosine function’s maximum and minimum values. The absolute value of the amplitude is always used.
Example: A wave is y = 2sin(4t). Find out its amplitude.
Solution:
Given: wave equation y = 2sin (4t)
using the amplitude formula,
x = A sin(ωt + ϕ)
When compared to the wave equation,
A = 2
ω = 4
ϕ = 0
As a result, the wave’s amplitude is 2 units.