## 1.7 Short Notes: Interference of Waves

Principle of superposition

• In Figure 1.27, wave A and wave B are travelling against each other. Both have the same amplitude and the amplitude of the wave doubles (A + B) when both waves interfered.
• After interference, both waves travel with the initial amplitude. This situation is called constructive interference.
• In Figure 1.28, wave A and wave B are propagating into each other. Wave A has positive amplitude while wave B has negative amplitude. During interference, the sum of the amplitude for wave A+B is zero [A + (-B)].
• After interference, both waves propagate with initial amplitude.

Definition of interference of waves

• Interference is the superposition of two waves that comes from two coherent sources.
• Two waves are said to be coherent if the amplitude and phase difference for both waves are identical.
• Figure 1.29 shows the interference of two coherent waves. The solid line shows the peak of the waves while the dotted lines shows the trough of the waves.
• The point where peaks and troughs intersects are called constructive interference. The line that passes through all the constructive interference is antinodal line.
• The point where peaks and troughs intersects are called destructive interference. The line that passes all destructive interference is nodal line.

Formula of wavelength

Example question

Figure 1.30 shows two speakers are set 1.5m apart from each other. Several audio detectors are placed 3m from the sources. The distance of the first audio detector and the last audio detector is 3.3m. Find the wavelength of the sound waves. Note that the waves are from coherent sources.

Answers:

Questions

1. What is interference?
2. Describe the concept of superposition.
3. Find the distance between two dark fringes.

Answers

1. Superposition of two waves that comes from two coherent sources.
2. When two waves with positive amplitude collides, the amplitude for combined waves is doubled. When a wave with positive amplitude and another wave with negative amplitude collides, the amplitude becomes zero due to the differences of the amplitude.
3. 4.5mm.

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