Destructive Interference
- Waves overlap out of phase (crests align with troughs).
- Individual wave amplitudes partially or completely cancel each other out.
- Resultant wave has a smaller amplitude.
- Decreases intensity or loudness of the resultant wave.
Let us consider two waves that are travelling at the same velocity. Since these two waves travel at the same velocity and meet at a particular point. Let’s analyze the resultant amplitude of the wave which originates after the superposition of these waves. Assuming that the equations for displacement produced by both the waves are the opposite this time and are given by,
y1 = acos(ωt)
y2 = acos(ωt + 3π)
y = y1 + y2
y = acos(ωt) + acos(ωt + 3π)
y = acos(ωt) – acos(ωt)
y = 0
So, this time two displacements in opposite directions resulted in zero amplitude and zero intensity. This is called destructive interference.
Note that the case of zero amplitude is only when the two waves are of the same amplitude but in opposite directions.
However, this is not mandatory case to have waves of the same amplitude. Hence, the below figure represents a general concept of destructive interference for waves of different amplitude and opposite directions.
Condition for Destructive Interference
We know that the Intensity of the resultant wave is given using the formula,
I = I1 + I2 +2√(I1I2)cosθ
For constructive Interference, I is the minimum which is possible if
cosθ = -1, then θ = π, 3π,…., (2n-1)π i.e.
Phase Difference is the odd multiple of π
Also,
△x = λ/2π (θ)
△x = λ/2π ((2n-1)π)
△x = (n – 1/2)λ
Thus, for Destructive Interference
- Phase Difference: (2n-1)π
- Path Difference: (n – 1/2)λ
Principle of Superposition of Waves
When two waves propagating in the same medium interfere with each other the amplitude of the resultant of the two waves is the vector sum of the amplitude of the two waves, this is called the Principle of Superposition of Waves.
Waves are disturbances that transfer energy between two points without there being actual contact between the two points. We are completely surrounded by waves and these are used for performing a variety of tasks in our daily life.
We encounter different types of such as Radio waves, Light waves, Microwaves and others on a regular basis. The superposition of waves is the process of adding different waves together and finding their results.
In this article, we will learn about the Superposition of Waves and others in detail.
Table of Content
- What is Superposition of Waves?
- Principle of Superposition
- Types of Superposition of Waves
- Constructive Interference
- Destructive Interference
- Resultant Intensity in Interference of Two Waves
- What is Interference of Light?
- Solved Examples on Superposition of Waves