How does the wavelength of a water wave affect diffraction?

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If I send a single wave toward a corner won't it bend around the corner? If so, how does the wavelength of that single wave (is wavelength defined for a single wave?) effect how much it bends?

Every picture/illustration I have found on diffraction shows a series of lines (plane waves) approaching a gap and shows how the waves bend more if the gap is made smaller. What I haven't seen is a picture keeping the gap the same and changing the wavelength. I don't see how the distance between crests has anything to do with how much each crest bends as it leaves the gap.
 

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  • #2
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What do you mean by a single wave? do you mean a single crest? If so than you have to understand that short wave packets such as your single crest wave can be Fourier expanded into a sum of multiple crest waves (Principle of superposition). Each component of that expansion will diffract according with its wavelength.
 
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  • #3
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I don't see how the distance between crests has anything to do with how much each crest bends as it leaves the gap.

Interesting that it does, isn't it?
 
  • #4
sophiecentaur
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If I send a single wave toward a corner won't it bend around the corner? If so, how does the wavelength of that single wave (is wavelength defined for a single wave?) effect how much it bends?

Every picture/illustration I have found on diffraction shows a series of lines (plane waves) approaching a gap and shows how the waves bend more if the gap is made smaller. What I haven't seen is a picture keeping the gap the same and changing the wavelength. I don't see how the distance between crests has anything to do with how much each crest bends as it leaves the gap.

What is the difference? If the geometry is described in units of 'a wavelength', the absolute size of things is not relevant. The scale of the picture that's drawn may alter but the angles don't, for a given ratio of gap to wavelength.
 
  • #5
Drakkith
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What I haven't seen is a picture keeping the gap the same and changing the wavelength.

Here you go. This video shows changing the wavelength of a water wave through an aperture.

 
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  • #6
olivermsun
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Here you go. This video shows changing the wavelength of a water wave through an aperture.



Great video! (Although some of the comments below it appear to be wrong.)
 
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  • #7
Drakkith
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Great video! (Although some of the comments below it appear to be wrong.)

It's youtube. I'd be surprised if you didn't find a reference to hitler or nazis in the comments.
 
  • #8
sophiecentaur
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One point that's easy to forget. If you go from a narrow to a wide aperture, for the same wavelength, you get more total energy passing through. The actual amount of energy flowing 'off axis' may not change significantly. It's just that more energy gets through and that energy goes in the forward direction.
You get very little light through a pinhole, compared with a porthole but the porthole is still diffracting some. The diffraction at the edges can be very relevant even when an object is very large. It must, for instance, be a consideration for Stealth designs, where they go to a lot of trouble to make sure that specular reflections are angled away from the horizontal - yet there will be some energy reflected (due to diffraction) right back at the transmitter, unless they eliminate / reduce it in some way.
 
  • #9
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Thank you for all the comments. The video did clearly show the change in refraction as you changed wavelength.
 

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