3.4 Interference of Waves

3.4 Interference of Waves

Constructive and Destructive Interference:

Interference occurs when two or more waves overlap in space, leading to a new wave pattern. The resulting wave depends on the phase relationship between the interfering waves.
- **Constructive Interference:** When the waves are in phase (crests align with crests, troughs with troughs), the amplitude of the resulting wave is the sum of the amplitudes of the individual waves.
- **Destructive Interference:** When the waves are out of phase (crest aligns with trough), the amplitude of the resulting wave is reduced or cancels out entirely.

Conditions for Interference:

For two waves to interfere constructively or destructively, they must be coherent (have a constant phase difference) and have similar frequencies.

Example Problem:

Two waves with amplitudes of 3 units and 2 units interfere constructively. What is the amplitude of the resulting wave?

Solution:

The amplitude of the resulting wave is the sum of the amplitudes of the individual waves:
A_resulting = 3 units + 2 units = 5 units
The amplitude of the resulting wave is 5 units.