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Chapter 6: Problem 22

When a wave passes through two nearby gaps in a barrier, interference will occur, provided that there is also diffraction. Why must there be diffraction?

Short Answer

Expert verified
Answer: Diffraction is important for interference to occur because it allows the waves to bend and spread out after passing through the gaps, enabling them to overlap and interact. This interaction leads to constructive or destructive interference, which would not be possible without diffraction.

Step by step solution

01

Define Diffraction

Diffraction is the bending of waves around obstacles or when they pass through an opening (such as a gap in a barrier). When a wave, such as light, sound, or water waves, encounters an opening or an obstacle, it spreads out and does not travel in straight lines. The amount of bending depends on the size of the gap and the wavelength of the waves.
02

Define Interference

Interference is the phenomenon in which two or more waves combine to produce a new wave pattern. When the waves are in phase (meaning their peaks and troughs align), constructive interference occurs, and the waves amplify each other, resulting in a larger wave. When the waves are out of phase (meaning their peaks and troughs are misaligned), destructive interference occurs, and the waves cancel each other out, resulting in a smaller or non-existent wave.
03

Understand the connection between Diffraction and Interference

For interference to occur when a wave passes through two nearby gaps in a barrier, there must be diffraction. This is because, without diffraction, the waves would not bend and spread out after passing through the gaps. They would continue to travel in straight lines and would not overlap or interact, which is a prerequisite for interference to happen.
04

Explain the importance of diffraction in interference

In conclusion, diffraction is essential for interference to occur when waves pass through two nearby gaps in a barrier because it allows the waves to bend around the barrier and potentially overlap, creating the conditions necessary for interference – either constructive or destructive. Therefore, without diffraction, the interaction between the waves would not be possible, and interference would not occur.

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