Destructive Interference occurs when two waves of the same frequency meet and overlap in a way that causes their amplitudes to cancel each other out, resulting in a wave with zero amplitude at specific points.

Interference occurs when two waves meet. This phenomenon includes superimposing the waves into a wave that can either be bigger, smaller, or the same magnitude. Wave interference can be categorized into two different types i.e., Constructive and Destructive Interference. In this article, we will discuss the nature of interference and describe destructive interference.

What is Destructive Interference?

Destructive interference is a type of interference that happens when two waves with opposite displacements meet anywhere along the medium.

When amplitude of these two waves is equal to 180°, destructive interference occurs. In this way, a positive displacement of one wave is compensated for a negative displacement of another wave. This yields a null wave where the amplitude is zero, and dark areas appear when waves interact destructively.

Definition of Destructive Interference

When one wave is, in a position and the other wave is in a position their combined value becomes zero, then occuring interence of waves is called Destructive Interference.

Similarly when the first wave is in a position and the second wave is in a position their combined value also becomes zero. In fact at every point where they meet these two waves completely nullify each other’s effect resulting in no remaining wave. This characteristic of waves is truly remarkable. It’s worth noting that the sum of two waves can be lower than either wave or even become zero. This phenomenon is known as destructive interference.

Principles of Wave Interference

Interference works on the principle of superposition. Superposition principle states that the resultant displacement of a point due to multiple waves is the sum of the displacements caused by each individual wave at that point. In simpler terms, when two waves meet, their effects add up or subtract depending on their alignment.

In simple words, superposition principle states that when two waves meet, they interact and produce a new wave. When the waves are in phase, meaning that their peaks and troughs coincide exactly with each other they will form a big wave of amplitude.

But if the waves are out of phase meaning their peaks and troughs do not coincide, they will cancel each other out by subtracting amplitudes from one another creating a wave with lower amplitude.

Read More about Superpostion of Wave.

Destructive Interference in Waves

Destructive interference happens when waves intersect and essentially nullify each other. This happens where peaks and troughs of two separate waves coincide such that they partially tend to neutralize their intensity or amplitudes. It can be demonstrated as different types of waves, such as electromagnetic waves (lighting) and water waves.

Conditions for Destructive Interference

Certain conditions must be met for interference to take place.

• It requires two waves with amplitudes that move in opposite directions.
• The waves should have frequencies that travel through the same medium.
• However, the intensity changes in various points due to overlapping of each other.
• In some cases the effect of interference is insignificant.

Mathematical Representation

For any two waves of the same frequency, their combined displacement at a point can be described using the principle of superposition:

y(t) = y₁(t) + y₂(t)

Where,

• y(t): Combined displacement at time t
• y₁(t): Displacement of wave 1 at time t
• y₂(t): Displacement of wave 2 at time t

If both waves are sinusoidal, we can express them as:

y₁(t) = A₁ sin(ωt + φ₁) and y₂(t) = A₂ sin(ωt + φ₂)

Where,

• A₁, A₂: Amplitudes of wave 1 and 2
• ω: Angular frequency (same for both waves if destructive interference occurs)
• φ₁, φ₂: Phase angles

Destructive interference happens when the waves are out of phase by 180 degrees (π radians). This means:

φ₂ – φ₁ = π

Substituting into the combined displacement equation:

y(t) = A₁ sin(ωt + φ₁) + A₂ sin(ωt + φ₁ + π)

Using the trigonometric identity sin(α + π) = -sin(α), we get:

y(t) = A₁ sin(ωt + φ₁) – A₂ sin(ωt + φ₁)

Now, the terms with ωt and φ₁ cancel out, and we see that the combined displacement depends on the difference in amplitudes:

y(t) = (A₁ – A₂) sin(ωt + φ₁)

• If A₁ = A₂, then the sum becomes zero, resulting in complete destructive interference at that point.
• If A₁ ≠ A₂, the resulting amplitude is the difference between the individual amplitudes, leading to partial destructive interference.

Read More,

• Reflection of Light
• Refraction of Light 

Examples of Destructive Interference

Following are some examples of destructive interference:

• Anti-reflective coatings: These coatings on lenses or glasses use destructive interference to cancel out specific wavelengths of light, reducing reflection and glare.

• Diffraction gratings: These gratings utilize destructive interference to produce specific diffraction patterns that split light into its constituent colors, as seen in rainbows or holograms.

• Noise-canceling headphones: These headphones use microphones to pick up ambient noise and generate sound waves with the opposite phase, leading to destructive interference and noise cancellation.

• Soundproofing materials: These materials often contain structures designed to resonate with and destructively interfere with specific sound frequencies, reducing noise transmission.

Destructive vs Constructive Interference

Common differences between both destructive and constructive interference are: