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Question Video: Identifying the Correct Relationship between Gap Width and Wavelength for Maximum Diffraction Physics • 9th Grade

Which of the following statements most correctly describes how the wavelength of diffracted waves relates to the width of the gap that they pass through? [A] Waves are diffracted most strongly when their wavelength is equal to half the width of the gap that they pass through. [B] Waves are diffracted most strongly when their wavelength is equal to the width of the gap that they pass through. [C] Waves are diffracted most strongly when their wavelength is equal to double the width of the gap that they pass through. [D] Waves are diffracted most strongly when their wavelength is equal to the square root of the width of the gap that they pass through.

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Video Transcript

Which of the following statements most correctly describes how the wavelength of diffracted waves relates to the width of the gap that they pass through? (A) Waves are diffracted most strongly when their wavelength is equal to half the width of the gap that they pass through. (B) Waves are diffracted most strongly when their wavelength is equal to the width of the gap that they pass through. (C) Waves are diffracted most strongly when their wavelength is equal to double the width of the gap that they pass through. (D) Waves are diffracted most strongly when their wavelength is equal to the square root of the width of the gap that they pass through.

Clearing some space at the top of our screen, we’re considering a scenario where we have some wavefronts, say that they’re moving to the right, which encounter a barrier with a gap in it, which then leads to what’s called the diffraction of these waves. Wave diffraction means that waves bend when they reach a corner, like the two corners of this gap. If the waves passing through this gap diffracted a little, then the resulting waves might look like this, while if they diffract or bend a lot, they might look this way. The amount that a wave diffracts when it passes through an opening like this depends on the width of the opening compared to the wavelength of the wave.

We see in fact that our four answer options are only different in this way. Each one suggests a different relationship between the width of the gap and the wavelength of the wave. It’s possible to test each of these four claims experimentally. We can vary the width of the gap so that the wavelength of the waves is half the width of that gap, equal to that width, double that width, and equal to the square root of that gap width. What we end up discovering is that when the wavelength of the incoming waves is equal to the width of the gap that the waves pass through, then in that case, wave diffraction or bending is greatest. This corresponds to answer option (B). Waves are diffracted most strongly when their wavelength is equal to the width of the gap that they pass through.

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