Superposition and Interference of Waves

The principle of superposition states that when two or more waves overlap in space, the resulting displacement at any point is the algebraic sum of the displacements of the individual waves at that point.

Types of Interference

Superposition is the general principle describing how waves combine when they overlap, while interference is a specific outcome of superposition where the combined wave's amplitude is either enhanced (constructive interference) or diminished (destructive interference).

Constructive Interference: Occurs when waves meet in phase (crests align with crests and troughs with troughs), resulting in a wave of greater amplitude.
Destructive Interference: Occurs when waves meet out of phase (crest aligns with trough), resulting in a wave of reduced or zero amplitude.

This principle applies to all types of waves—mechanical (like sound or water) and electromagnetic (like light).

Key Characteristics

Superposition can be temporary or lead to a permanent pattern (as in standing waves).
Superposition explains phenomena like beats, standing waves, and interference patterns.
For multiple waves: \( y_{\text{total}} = y_1 + y_2 + y_3 + \cdots \)

Two waves of equal amplitude \( A = 3 \ \text{cm} \), same frequency, and in phase travel through the same medium. What is the resultant amplitude where they meet?

Solution:

Since the waves are in phase, their displacements add constructively:

\[ A_{\text{resultant}} = A_1 + A_2 = 3 + 3 = 6 \ \text{cm} \]

Answer: The resultant amplitude is \( 6 \ \text{cm} \).

Two sound waves of equal amplitude \( A = 5 \ \text{units} \), same frequency, and 180° out of phase meet. What is the resultant amplitude?

Solution:

Since the waves are exactly out of phase, their displacements cancel each other:

\[ A_{\text{resultant}} = A - A = 0 \]

Answer: The waves completely cancel each other out, and the resultant amplitude is zero.

Written by Thenura Dilruk