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

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Answer: Diffraction is necessary 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 with each other. Without diffraction, the waves would not be able to overlap, and no interference patterns would be observed.

Step by step solution

Understand the Concepts of Diffraction and Interference

Diffraction is the bending of waves around obstacles or the spreading of waves when passing through a small opening (gap). Interference, on the other hand, is the phenomenon where two or more waves superpose to create a new wave pattern. This can result in the waves either reinforcing each other (constructive interference) or canceling each other out (destructive interference).

Analyze the Importance of Diffraction in Interference

For interference to occur, the waves need to overlap and interact with each other. This means that the waves must have traveled from their source or have been affected in such a manner that they are now able to interact. Diffraction is the phenomenon that allows this to happen: as waves pass through the gaps, they bend and spread out, overlapping with the waves from the other gap.

Understand the Wave Interaction

When the waves from the two gaps diffract and overlap, they create an interference pattern. Depending on the path difference (the difference in distance traveled by the two waves) and the wavelength of the waves, the interference pattern will be a combination of constructive and destructive interference. If there were no diffraction (meaning the waves wouldn't bend and spread out), the waves from the two gaps would not overlap, and no interference could occur.

Conclusion

In conclusion, for interference to occur when a wave passes through two nearby gaps in a barrier, there must be diffraction. Diffraction is essential because it allows the waves to bend and spread out after passing through the gaps, enabling them to overlap and interact with each other. Without diffraction, the waves would not be able to overlap, and no interference patterns would be observed.

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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

Step by step solution

Understand the Concepts of Diffraction and Interference

Analyze the Importance of Diffraction in Interference

Understand the Wave Interaction

Conclusion

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