[FRIAM] Diffracton: minding the gap

Sat Aug 14 12:39:03 EDT 2021

The images in my initial email may have not come through. Attached is a PDF
of the message
_______________________________________________________________________
Stephen.Guerin at Simtable.com <stephen.guerin at simtable.com>
CEO, Simtable  http://www.simtable.com
1600 Lena St #D1, Santa Fe, NM 87505
office: (505)995-0206 mobile: (505)577-5828
twitter: @simtable
z <http://zoom.com/j/5055775828>oom.simtable.com

On Sat, Aug 14, 2021 at 10:17 AM Stephen Guerin <stephen.guerin at simtable.com>
wrote:

> At yesterday's Virtual Friam I asked a question on diffraction and said I
> would send more background.
>
> The gist of my question is:
>
> *Even though I completely understand the micro-level rules that generate
> diffraction in the wave model described below,  I still don't have an
> intuition **how** the gaps in an obstacle have the emergent effect of
> diffracting waves when wavelengths >= gap width. Can anyone help?*
>
>
> Background:
> The question arose from my mentoring NM School for the Arts high school
> students in the NM Supercomputing Challenge
> <http://nmsupercomputingchallenge.org> where the students simulated
> spatial acoustics by appropriating Saint-Venant equations used for shallow
> water waves to instead model acoustic pressure waves. We wrote a
> Netogo agent-based model with Python extension for reading / writing
> the sound files and simulating spatial acoustics.
>
> [image: image.png]
>
>
> The students explored the effects of different room configurations on
> acoustics.
>
> One configuration of interest was a wall gap illustrated below in the top
> right under Madelyn's video below. The wall gap is hard to see on right
> side.
>
> [image: image.png]
>
> They simulated microphones in Netlogo by recording amplitudes at a patch
> (red dot below in top-right visualization of room) and simulated speakers
> (hard-to-see blue dot below red dot on other side of wall) by driving
> amplitudes at a patch from the time series of amplitudes in  .wav files
> (recordings of a singer and viola performance). They could hear, and
> through Fourier analysis, see the gap acting as a low-pass filter on the
> acoustic signal. ie, only the low frequencies were "bending" around the
> wall to reach the microphone.
>
> You can see and listen to this effect and the spectrogram visualization at
> time 33:11 in their presentation <https://youtu.be/61p97NWJiQ8?t=2117>.
>
> [image: image.png]
>
> It took me a few weeks after their presentation in the NM Supercomputing
> Challenge - they got second place - to connect the low pass filter behavior
> to the concept of diffraction. Had this been a light model and I saw the
> rainbow effects I would have clued in much faster.  Their presentation was
> a month after finals and they added this epilogue in the presentation
> above to identify the effect as diffraction.
> <https://youtu.be/61p97NWJiQ8?t=2761>
>
> Their presentation included this physical wavepool video demonstration
> <https://youtu.be/BH0NfVUTWG4> which was helpful to me to begin to
> understand the diffraction relationship with frequency and gap width.
>
> Note: my question is not about "describing" the behavior with
> macroscopic equations or geometric models but fundamentally how does the
> gap become a point source ala Huygens Principle at the micro-level of the
> patches interacting with the emergent waves. To help with the distinction,
> I consider this interactive model
> <https://www.olympus-lifescience.com/en/microscope-resource/primer/java/diffraction/> a
> great macroscopic description of the phenomenon that nicely illustrates the
> relationship of frequency and gap width but doesn't help me interpret the
> micro-level interactions giving rise to the diffraction effect in our
> simple shallow-water model.
>
> The students describe the details of the shallow water model at this
> point in their presentation <https://youtu.be/61p97NWJiQ8?t=870>:
> [image: image.png]
>
>
> Here is my simplified Netlogo wave model
> <https://anysurface.com/sguerin/models/shallowWaterDoubleSlit.html> of
> the same shallow water equations without the acoustics. It's set up to
> explore double slit but you can change it to single slit and mess with
> frequency and gap and watch the wave propagations, diffractions and
> interference patterns
> https://anysurface.com/sguerin/models/shallowWaterDoubleSlit.html
> [image: image.png]
>
> As a related aside, with some follow-up discussions with Ed Angel and
> Steve Smith I am also trying to understand how the gap might be considered
> a sampling function on the signal. My intuition is that the diffraction of
> the wave creates a spreader Sinc function and the gap is Rect
> function which are Fourier duals. In some way, i see Nyquist-Shannon
> Sampling Theorem
> <https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem> related
> to the gap. Note that diffraction creates a spreader function on the back
> wall in single gap experiments and the gap may be considered a Rect pulse
> when smaller than the wavelength.
>
> [image: image.png]
>
>
>
> _______________________________________________________________________
> Stephen.Guerin at Simtable.com <stephen.guerin at simtable.com>
> CEO, Simtable  http://www.simtable.com
> 1600 Lena St #D1, Santa Fe, NM 87505
> office: (505)995-0206 mobile: (505)577-5828
> twitter: @simtable
> z <http://zoom.com/j/5055775828>oom.simtable.com
>
>>
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