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 

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.