Amplitude Formulas - Equations for Wave Amplitude
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,
x = displacement of wave (meter)
A = amplitude
ω = angular frequency (rad/s)
t = time period
ϕ = phase angle
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.
FAQs on Amplitude Formula
1. What is Meant by 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 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.
x = A sin (ωt + ϕ) or x = A cos (ωt + ϕ) is the formula.
2. 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
3. What is the Amplitude Formula in Maximum and Minimum Form?
The amplitude formula is also known as the average of the sine or cosine function's maximum and minimum values. i.e.,
(max + min) / 2 = amplitude
4. What are the Units of an Amplitude Formula?
Meter(m) is the unit in an amplitude formula. The maximum disturbance or displacement of the medium from its equilibrium position is the amplitude of a wave.
5. Where can I find Amplitude Formula questions?
You can find questions on Amplitude formula on Vedantu. It defines amplitude and the amplitude formula, as well as explaining how it works. To gain a clear knowledge of the idea, practise questions relating to the amplitude formula available on vedantu. Apart from this, Vedantu offers study materials for students in grades 1 through 12 as well as a variety of competitive exams. Notes, important topics and questions, revision notes, and other materials are included in the materials. All of these resources are available for free on Vedantu. Students just need to register on the Vedantu website to gain access to all of these resources. Vedantu also has a mobile app where you can register.