For the last half hour or so I’ve been thinking about it.

The light from the left half of the slit overlaps the light from the right half, but to each side one of them is delayed. Straight ahead you get one cycle of light and then a cycle of darkness, repeated. That would turn into some harmonic series.

Off to the side enough that normally you’d get a dark gap because the right side comes in half a cycle behind, now you get a crest, and a half-cycle of darkness, and then a trough and a half-cycle of darkness, repeated. I imagine that would turn into a different harmonic series.

Where you would normally get your first constructive interference band, you would reconstitute the original wave.

So at each place you’d normally get destructive interference you’d get half cycles separated by blanks, and at the places you’d normally get contructive interference you’d alternately get reinforced cycles separated by blanks, versus the original wave.

But then I thought, what if you tried this with water waves? Water waves maintain themselves by pressure and height differences in a medium. If you cut out every second cycle, a water wave would quickly reform itself into just a wave with half the frequency and double the wavelength. Wouldn’t it?

What would actually happen? Do light waves move independent of what’s around them, or does each section of the wave depend on the rest of the wave to maintain its integrity, like water waves? Or is this an example where they behave like particles instead?

I tried to imagine actually doing the experiment. With a 1 hertz radio wave my slits would have to be 186,000 miles wide. Not very practical. Make the wavelength smaller. The outside edge of the disk has to move at 1 wavelength/cycle, Is that lightspeed? Maybe there’s some other way to do it.

Now that I’m awake, here’s the idea I’d like to find a way to explore. Water waves retain the shape their medium demands. Pressure waves in an incompressible liquid turn into vertical height, and the high water goes downhill, and it turns into a minimum-energy shape. Does light behave like that? Or does the source of the light make electric and magnetic fields that then propagate independent of each other and independent of their own preceding and following components?

I guess the question kind of answers itself. To the extent that Maxwell’s equations fit reality, electric and magnetic waves can’t have a sudden cutoff like I described. Do they immediately form a shape that fits ME if they get distorted away from that shape? Or is matter that emits EM radiation forbidden to move in ways that would generate a different shape? There may be no way to tell between those. If I can’t move matter in ways that would make perverse waves — if my beam-splitter and everything like it is impossible, then I’m left with an unsatisfying argument about some alternate reality.

It was a nice dream.

Ah… this is exactly either my point, or the point of my confusion.

The reason I think “the barn” example is confusing is that most people’s experience with sound is that it does not travel in straight lines. Air acts like a scattering medium, and I am not sure you would call such scattering a diffraction effect.

Hmm. I’m not sure what you mean. How would they have heard each other anyway? I think you’re making things too complicated. I consider diffraction to be effects associated with non-rectilinear propagation, e.g. light bending around corners. Non-line-of-sight propagation in a homogeneous medium is always diffraction, to the best of my knowledge.

The example I give isn’t really any different than examples in optics. Edge diffraction (light bending around an edge of a ‘black screen’, or corner) is well known and understood. The so-called Poisson or Arago spot, in which a bright spot appears in the center of the geometrical shadow when illuminating an opaque disk, was the experiment which really confirmed the wave theory of light for people.

You’ll have to clarify what you mean by ‘heard each other anyway.’ I chose the ‘big barn in a field’ example to avoid two specific complications: 1. penetration of the wave directly through the barn, and 2. reflection of the wave off of other objects.

You can, of course set up an acoustic scenario that demonstrates diffraction, but you would probably want to use a more controlled acoustic source, like a parabolic speaker, to create a more directional sound wave. I think a better example of diffraction in every day life would be ripples on the surface of the water (basically a 2D version of the string cases you have used throughout this tutorial). If a ripple hits a wall with a small opening, you see exactly the diffraction effects you are discussing.

What??!! You doubt me??!! You are so gonna get banned!!!

Seriously, though, I think my analogy works just fine. Mathematically, the air pressure satisfies an ordinary wave equation, provided one is dealing with relatively small pressure changes (to avoid nonlinear effects). This is similar to the reality that vibrations on a string satisfy a wave equation as long as the vibrations aren’t too large. Within these limits, the diffraction theory of sound is mathematically identical to the scalar theory of light diffraction. (I broke out my copy of Theoretical Acoustics, by Morse and Ingard, to make sure of this.)

Concerning your example, I suspect you’re confusing primary sources with secondary sources, which is a common slip-up in optics. Primary sources are the generators of the wave, while secondary sources are modifications of already generated waves (such as passing a wave through an aperture). Mathematically, a primary source and a secondary source have different Green’s functions representing them – primary sources are spherical waves, while secondary sources are the Huygens wavelets. A person screaming something is essentially a primary source, with some imperfect directionality created by their mouth and body, I would say.

These complications are exactly why I chose my example of ‘farmhouse diffraction’ very carefully, with no regard as to the generator of the sound. My only concern was that the source and receiver did not have direct line of sight, which means the only way that sound could get from one to the other is by waves bending around corners.