Interference Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Interference.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

The phenomenon that occurs when two or more waves overlap in space, combining their displacements at every point according to the principle of superposition.

When waves meet, they add up or cancel out at each point depending on whether their crests and troughs align.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Constructive interference (waves in phase) = larger amplitude. Destructive (out of phase) = cancellation.

Common stuck point: Waves don't 'destroy' each other—they pass through and continue on.

Sense of Study hint: When solving an interference problem, first determine the path difference between the two waves arriving at the point of interest. If the path difference is a whole number of wavelengths (m\lambda), interference is constructive. If it is a half-integer number of wavelengths ((m + \frac{1}{2})\lambda), interference is destructive.

Worked Examples

Example 1

easy
Two speakers emit identical sound waves in phase. A listener stands equidistant from both speakers. Does the listener hear constructive or destructive interference? What about if one speaker is moved half a wavelength farther away?

Solution

  1. 1
    When the path difference is zero (equidistant), the waves arrive in phase and interfere constructively — the listener hears a louder sound.
  2. 2
    If one speaker is moved \frac{\lambda}{2} farther, the path difference becomes \frac{\lambda}{2}.
  3. 3
    A path difference of \frac{\lambda}{2} means the waves arrive exactly out of phase, causing destructive interference — the sound is much quieter.

Answer

\text{Equidistant: constructive (louder); } \frac{\lambda}{2} \text{ offset: destructive (quieter)}
Interference occurs when two or more waves overlap. Constructive interference (waves in phase) increases amplitude; destructive interference (waves out of phase by half a wavelength) decreases amplitude.

Example 2

medium
In a double-slit experiment, light of wavelength 500 \text{ nm} passes through slits 0.2 \text{ mm} apart. A screen is 2 \text{ m} away. What is the spacing between adjacent bright fringes?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
Two coherent light sources create an interference pattern. The third bright fringe is observed at an angle where the path difference is 3\lambda. If \lambda = 600 \text{ nm}, what is the path difference in meters?

Example 2

hard
In a double-slit experiment, the slit separation is 0.5 \text{ mm} and the screen is 1.5 \text{ m} away. If the fringe spacing is measured to be 1.9 \text{ mm}, what is the wavelength of the light?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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