Interference Physics Example 1

Follow the full solution, then compare it with the other examples linked below.

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 λ2\frac{\lambda}{2} farther, the path difference becomes λ2\frac{\lambda}{2}.
  3. 3
    A path difference of λ2\frac{\lambda}{2} means the waves arrive exactly out of phase, causing destructive interference — the sound is much quieter.

Answer

Equidistant: constructive (louder); λ2 offset: destructive (quieter)\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.

About Interference

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

Learn more about Interference →

More Interference Examples

Example 2 medium

In a double-slit experiment, light of wavelength [formula] passes through slits [formula] apart. A s

Example 3 medium

Two coherent light sources create an interference pattern. The third bright fringe is observed at an

Example 4 hard

In a double-slit experiment, the slit separation is [formula] and the screen is [formula] away. If t

← All Interference Examples Interference Concept