[FRIAM] Diffracton: minding the gap

Sat Aug 14 12:17:07 EDT 2021

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

>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210814/c4afb2b3/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 163674 bytes
Desc: not available
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210814/c4afb2b3/attachment-0006.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 205035 bytes
Desc: not available
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210814/c4afb2b3/attachment-0007.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 58992 bytes
Desc: not available
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210814/c4afb2b3/attachment-0008.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 88718 bytes
Desc: not available
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210814/c4afb2b3/attachment-0009.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 54829 bytes
Desc: not available
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210814/c4afb2b3/attachment-0010.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: image.png
Type: image/png
Size: 68777 bytes
Desc: not available
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20210814/c4afb2b3/attachment-0011.png>