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📘 Lesson 6 of 7 · Waves

🌊 Interference

When two or more waves overlap, they combine according to the principle of superposition — sometimes reinforcing each other, sometimes canceling out, producing striking interference patterns.

Course progress: 86%

01 Key Concepts

The Principle of Superposition

When two or more waves overlap at the same point, their displacements simply add together to determine the resulting combined displacement.

Constructive Interference

Occurs when waves overlap in phase (crest meets crest), combining to produce a wave with LARGER amplitude than either individual wave.

Destructive Interference

Occurs when waves overlap out of phase (crest meets trough), combining to produce a wave with SMALLER amplitude, potentially canceling out entirely.

Path Difference and Interference Type

Whether interference is constructive or destructive at a point often depends on the difference in distance traveled by each wave to reach that point.

Young's Double-Slit Experiment

A classic experiment showing light passing through two closely spaced slits creates a pattern of bright and dark bands (fringes) on a screen, providing strong evidence for light's wave nature.

02 Solved Examples

Example 1 Two identical waves meet perfectly in phase (crest aligns with crest). What type of interference occurs?
  1. Waves aligning crest-to-crest reinforce each other, producing a larger combined wave.
Answer: Constructive interference
Example 2 Two identical waves meet perfectly out of phase (crest aligns with trough). What type of interference occurs?
  1. A crest and trough of equal magnitude cancel each other out when added together.
Answer: Destructive interference (potentially complete cancellation if amplitudes are equal)
Example 3 In noise-canceling headphones, a microphone detects incoming ambient sound and the headphones produce an 'opposite' sound wave. What principle allows this to cancel out the noise?
  1. The headphones generate a wave that is the inverse (out of phase) of the incoming ambient noise.
  2. When these two waves combine (superimpose), they destructively interfere, canceling much of the noise.
Answer: Destructive interference cancels the ambient noise when combined with the inverted sound wave

03 Practice Questions

1What happens when two waves meet crest-to-crest (in phase)?
Constructive interference (amplitudes add)
2What happens when two waves meet crest-to-trough (out of phase)?
Destructive interference (amplitudes subtract or cancel)
3What principle states that overlapping wave displacements simply add together?
The principle of superposition
4What classic experiment demonstrated light's wave nature through interference patterns?
Young's double-slit experiment
5What does 'path difference' influence in an interference pattern?
Whether constructive or destructive interference occurs at a given point

📄 Interference — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.

🗒 Cheat Sheet ⬇ Download PDF 🖥 Interactive Worksheet