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I came across a previous question regarding how soundproof foam absorbs sound: How does foam "absorb" sound? where the answer explains the properties of the foam itself rather than the shape.

However, in analyzing audio spectrogram images (and messing around with Chrome Music Lab), I noticed a similarity in structure between acoustic foam and 3-dimensional spectrograms. The first two images are spectrograms and the latter two are two different acoustic foam designs.

Spectrogram 1

eSpectrogram 2

Sound foam 1

Sound foam 2

It appears that, depending on the kinds of soundwaves (music recording, conversation, etc.), the foam would be designed to replicate similar shapes and fit together almost like a puzzle piece.

My question is: Are soundfoam shapes designed to sort of "mirror" the incoming soundwaves?

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The primary purpose of the shape of the surface of acoustic panels is to diffuse the acoustic reflections.

This diffusion helps the audio in the room sound better because without the diffusion, it can sound like the reflected sound is coming from a specific location, and when these accumulate off the different walls, it can be difficult for the brain to sort out the sound. It also reduces interference between the incident and reflected waves. Diffusing the reflections, therefore softens the sound and makes sources become more intelligible.

I think the shape of the panels matching the shape of spectrograms shown in the question is interesting but just a coincidence. (It's reasonable to think these could be related, like some type of Fraunhofer diffraction grating, etc, but I don't think it works out that they are.)

(I have also heard of specialized acoustic panels creating interference such that reflections are cancelled, similar to anti-reflective coatings on lenses, which seems feasible, but I can't find a reference to these now. I even remember the shape of the panels as being an unusual stepped structure, and the inventor, a prominent academic, saying they "made walls disappear", but I haven't found the reference yet, so maybe that was an invention that didn't work out. References to the diffusion benefits of panels are all over the place though.)

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    $\begingroup$ I think your answer of sound diffusion is pretty much what I was after. It makes sense to have wedge- or pyramid-shaped foam so that a range of frequencies can be scattered so as to not bounce back directly. I found that this is similar to the F-117 stealth fighter having pyramidal design to scatter incoming radar pings in multiple directions to evade directly reflected waves. Thanks for the feedback! $\endgroup$
    – jinks908
    Apr 29 at 0:49
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I did a bit of search engine searching with the following search string

shape of sound absorbing material physics

In that search I did not encounter information about the shape of the sound absorbing material. The informative pages I found had information only about the properties of the material itself, such as elasticity, size of internal bubbles and what have you.

Hypothesis:
the purpose of the wedge shape is to increase surface area. The same material would already perform well when applied as flat panels, but the walls of a room have only so much area. The surface area of the wedge shapes is larger than the backing tile.
More surface area => more absorption.

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Some of the sound is absorbed and some is reflected. A flat surface would reflect more sound than the shaped surfaces which are designed to make more of the reflected wave hit the foam again so more is absorbed.

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