Archive for category Diffusion
For this installment of “Similar, yet Different”, we will be going retro – The Barrel Vs. The Pyramid! These two shapes are the historic foundations for modern acoustic treatments. How did they come about? Why do they work? How are they different?
These two shapes have origins before written history. The pyramids of Egypt may not have been renowned for their acoustic properties, but they certainly show the historical age of this shape. The barrel is also an ancient shape, born from the pillars of historic temples and gathering places. Both of these shapes have been used in architecture for the expanse of human history, and their acoustic properties have been studied in numerous environments, in many different applications.
These shapes are often referred to as “primitive.” The barrel, in its basic form, is a truncated cylinder – basically a segment of the cylinder. The pyramidal is, in this case, a modified/offset pyramid… a pyramid without equal sides. Their differences begin with this fundamental variable – the pyramid has angled planes and the Double Duty™ is a large curved surface.
Symmetry vs. Asymmetry
Another simple difference is the fact that the Double Duty™ is symmetric and the offset pyramid is asymmetric. The barrel primarily scatters sound across the curve of the face – sending acoustic energy in a wide arc. However, the pyramid’s facets are all angled slightly differently – reflecting in different directions. This allows the pyramid to be installed in complex arrays which create more “random” reflections due to their different facet angles. The Barrel is primarily a one-dimensional diffuser, and installs either horizontally or vertically.
There is another phenomenon that helps to contribute to diffusion – and that is diffraction. Diffraction is what happens to sound when it hits a corner or edge. Unlike light, acoustic energy is the physical fluctuation of pressure changes – which gives sound the ability to travel around corners. This bending varies by the wavelength of the sound and the size of the object in encounters. Both barrels and pyramids have facets which introduce diffraction, and while both can be made in different sizes, the offset pyramid has different sized facets on each device – contributing to more randomized diffraction at different frequencies.
Inverse Square Law
Without getting too heavy into math, as sound travels it decreases in intensity. This is due to the fact that sound “spreads out” as it travels. It is produced with a finite amount of energy, so intensity drops as it covers more space. Both the barrel and pyramid increase the rate that sound “spreads out,” which diminishes the intensity of the sound – however, they both do it slightly differently, however..
The Double Duty’s™ curvature leaves the wave primarily intact, but it increases the rate of expansion across the curve. This redirection is very smooth and predictable, where the random facets of the offset pyramid break up the sound into sections which travel in different directions. At the intersection of those facets, diffraction takes the reigns and scatters sound even further.
By increasing the rate of expansion of the wave, you decrease its intensity while also breaking up the wavefront which helps to reduce echoes and flutter. Both the barrel and the pyramid are perfect for larger spaces, as those massive surfaces do a great job of controlling reflections from large wave fronts. Also, due to their simple shapes, they can be made really big, which helps!
There is one more feature which is sometimes overlooked. Because of the material of their construction, and the large volume of air behind them, these diffusers exhibit a certain amount of “bass trapping.” The Double Duty™ diffuser got it’s name due to this characteristic. It’s not just a diffuser, but also a bass trap. The Pyramidal diffuser also exhibits bass absorption, though it is slightly less.
So there it is… the battle of the classics! Sometimes, keeping it simple is the way to go!
Today on, “Similar, yet different…” we are going to analyze two more of our acoustic diffusers and compare/contrast their designs and functionality… and this one is a doozy; The Model D vs. The Aeolian®. These two diffusers have some very interesting similarities and some surprising differences – so lets get started!
We have discussed the Aeolian® construction before, so we will start here with a quick recap as a reference point. The Aeolian® started life as a blocky-looking diffuser – just like the Model C, but the implementation is different. While the Model C retains its “blocky” appearance, the Aeolian® has run through a mathematical process called “bicubic interpolation.” This smooths the transition from one block to the next, creating the wavy appearance of the Aeolian® diffuser.
So, keep that in mind: The diffuser was tuned with different height blocks and then the transitions were smoothed.
The Art Diffusor® Model D has multiple layers of math below its curved surface. While the Aeolian® started life as “Blocks” of different heights… the Model D started life as “Rings” of different sizes and heights. The calculation for the heights is identical to the mathematics used in tuning the Aeolian®, but why different sized rings?
There is an older diffuser design known as a Maximum Length Sequence (MLS) diffuser. These were tuned to different frequencies using a specific depth, and different spacings of “lands and valleys.”
The Model D started with the concept of twisting the MLS spacings into rings, and changing the size of the rings. Then to break the “MLS mold” of having the same depth, this MLS ring structure is raised to different heights using Quadratic Residue calculations… effectively combining the rings of MLS spacings with different QRD heights. While this could have been where this stopped, we wanted to interject more randomness into the equation.
Wherever the rings of different heights intersected, we decided to change the heights by values relative to the difference between the two rings. This height variation is what is responsible for the “random” waviness. This was accomplished with different Boolean Functions, to either add or subtract height where the rings intersected.
This method of using Boolean Functions inserts a known-height randomization into a hybrid MLS/Quadratic system. (That’s a mouthful.) The final step, after refining the ring size, height, position and intersection parameters… was to smooth the whole geometry with “Bicubic Interpolation.” That’s right. This final step smooths all the transitions from the heights, just like the blocks of the Aeolian®.
So onto the Simple Similarities!
Both diffusers use a quadratic residue calculations to get the main heights of the diffusive elements. Both diffusers are finished off with a helping of “Bicubic Interpolation” to smooth it all out. This gives them both a very organic look… The Aeolian® looks a bit like rolling waves, and the Model D resembles droplets of rain in a puddle…
They do perform quite a bit differently though.
The Aeolian® has great lower mid-band performance… while the Model D is a beast in the upper mid-bands starting about 2.5K. The difference is in the severity of the geometry. The Aeolian® is a gently rolling surface which redirects the waveforms uniformly through a wide range of frequencies. The Model D has a very irregular surface. With the different ring sizes, heights, locations and boolean functions… it’s meant to target and shred mid to high frequencies. Both diffusers are asymmetric – and affect different frequencies in different ways.
The Aeolian® is also deeper than the Model D – and this depth is a single resonant cavity… allowing it to be a great bass absorber as well. The Model D is useful in environments where you have bass control in place, but really need to diffuse the upper mid range and bring those frequencies to life… or maybe shred some flutter echos or comb filtering. There are scenarios where both are used in the same environment – but for different reasons.
While both the ArtDiffusor® Model D and the Aeolian® both look like liquids frozen in time, they have some other similarities in the math behind them… Yet they are still as different as rolling waves versus droplets of rain in a puddle.
While these two diffusers look very different, there are a fair amount of similarities between them. Their physical size and depth allow them both to be great mid-frequency diffusers, but did you know that the Aeolian® started life as a blocky-looking diffuser – just like the Model C? It’s true!
The mathematics behind the two diffusers is similar, but the implementation is different. While the Model C retains its “blocky” appearance, the Aeolian has run through a mathematical process called “bicubic interpolation.” Without turning this into a math-heavy post, if you take a “blocky” design like the Model C and run its geometry through bicubic interpolation, you get a “curvy” surface like the Aeolian® – It “smooths” the transition from one block to the next in a 3 dimensional matrix.
While they did not begin as identical geometries, they were similar in their height ratios – with the Aeolian® starting with fewer blocks in a more random distribution, and a slightly taller maximum height. They both effect similar frequency ranges, with the Aeolian® going slightly lower and higher due to its depth and interpolated surface. The pattern and type of the diffusion is also different because of the different geometries – the Model C has blocks, and the edges of those blocks introduce a great deal of edge “diffraction” – which is what happens when a wave interacts with an edge, or corner, of a surface. It bends and shears around the edge, which helps break up the continuity of the waveform, where the Aeolian® takes the approach of redirecting most of the energy off a randomized and continually-curved surface.
It is important to note that the two are similar, yet different in their absorption numbers as well. With the Aeolian® being deeper with a single large cavity, it provides a bit more absorption in the low frequencies than the Model C, which is a more rigid geometry containing smaller elements. Depending on the space, this may be a useful addition to the diffusive properties. While some spaces need the extra absorption, some are pretty well balanced already and are just looking to “sweeten” the sound a bit.
On the surface, they are both a nominal 2’x2′ square of thermoformed Class A plastic with lightly textured surface. That is the extent of the visual similarities, and we cannot hide the aesthetic differences between the two devices. The ArtDiffusor® Model C is a “classic” diffuser. Many have been looking at these for the better part of 3 decades now. It’s a classic design at this point with no need for introduction – it is what the quintessential diffuser “looks” like. In fact, when many people think of a diffuser – the Model C is what they visualize! The Aeolian® is a modern rendition of the classic design. Using modern calculation techniques, we can now present the type of diffusion the Model C is famous for, in a different way.
While the two geometries look entirely different, and perform a bit differently, they have a common heritage as mathematical, 2-dimensional diffusers. You could say that the Model C is the grandparent of the Aeolian®, and that pedigree has been passed on – having a similar foundation, but a different final interpretation.
We often get asked about the functionality of the different diffusers, and one of the frequently asked questions is about the differences between the ArtDiffusor® Model C and ArtDiffusor® Model F. We will cover some of similarities and differences in the design, functionality and use of these two devices.
The Model C and Model F use identical math to come up with their basic structure, they even have angled faces – the main difference between the two is that the Model F elements are ½ of the Model C’s height, length and width – and then it is duplicated 4 times in the same footprint… The Model C is nominally 2’ x 2’ x 4” deep. The Model F is four quadrants that are nominally 1’ x 1’ x 2” deep – like little scaled down Model C’s… This makes them visually similar and aesthetically compatible. This low profile design makes the Model F more desirable for ceiling installs in spaces with very limited headroom – like basement studios that have low ceilings.
Due to the different size of the elements on the two devices, they have very different frequencies at which they are most effective. The Model C is a mid-frequency diffuser by design… having larger elements and deeper wells than the Model F. The Model F is primarily a high-frequency diffuser, due to the small elements and lower profile. Both diffusers are tuned to different frequencies as their “primary range,” and while they do affect lower and higher frequencies than they are designed for – it is to a lesser degree, or the product of absorption.
What does this mean?
The Model C has a primary design range of 1KHz to 4KHz. This is where it is primarily designed to work. It can and does diffuse below 1KHz and over 4KHz – just to a lesser degree than its primary design range.
The Model F has a primary design range of 2KHz to 8KHz, and again, it does diffuse outside of that range, but to a lesser degree.
The angled caps of both the Model C and Model F help to extend their high frequency range by reflecting sound in different directions at higher frequencies – causing the sound to scatter spatially. The different heights of the elements cause sound reflections to be offset “temporally,” or in time. The sound that hits the higher elements is reflected sooner than the sound that hits the lower elements – travelling further before it is reflected. This time offset, changes the “Phase Coherency” of the reflection; the larger the difference in the heights, the greater the offset in time.
The size of the elements matters as well. The shorter wavelengths of high frequencies can diffract and scatter off of the smaller elements of the Model F more readily than low frequencies, which see the Model F as a slightly angled & mostly flat surface. However, the lower frequencies are more affected by the larger and deeper elements of the Model C.
How do these differences help define their use?
The Model C is a great all around diffuser – it covers a wide range of frequencies, throws a very predictable 2D diffusion pattern, and it is tuned to a very musical range.
The Model F is a great high-frequency diffuser. It targets a few very specific, yet important issues. High frequencies are responsible for some nasty problems in rooms. Flutter echoes, ringing, comb filtering, and other artifacts are particularly noticeable in higher frequencies. If your room is otherwise performing well acoustically, the Model F can help tackle that last hurdle to make a good room into a great room.
Adding Nouveau™ wood diffusers to a home theater is not as daunting a task as it may seem, and can be done with a little planning and a few tools. This install used an ingenious mounting method to ease the final install. Instead of mounting the z-track to the wall directly, it was mounted to sheets of plywood which were hung with Gorilla/Hercules hooks.
The first task was to pick a stain. You can use the back of a plank to get an idea of how the poplar will respond to the different options. Poplar has a very interesting and varied structure that will take stain differently than some other woods. Darker stains may be more consistent, but don’t reveal the character and variation in the wood. This install chose a Smoke Gray which grayed out soft areas and browned the harder heart wood. A semi-gloss clear coat was used to finish.
While the stain dried, the mounting plywood was cut down to hide behind the planks. Four hanging straps with eye-loops were then added to the top edge of each of the plywood sections, and spaced to avoid studs.
The Z-track that would normally be installed on the wall was installed on the opposite side of the plywood. This will make it easy to hang the Nouveaus onto the sheet after it’s on the wall.
After the Nouveau™ planks are finished with the staining, and left to cure for a few days, they are ready to have the mating Z-bars attached to the back. They are installed with the same spacing as the Z-tracks on the plywood sheets. This will make it easy to align them after the plywood is hung on the wall.
The Gorilla/Hercules Anchor hooks are rated to around 50-60 lbs each. The Nouveau™ planks are roughly 25lbs each (at 48 inches) and each section has 4 hooks supporting 4 planks plus the weight of the 3/8″ plywood. The hooks are installed so that the plywood will hang level – with the weight distributed evenly across all four hooks.
Finally, the Nouveau™ planks are installed into the Z-Tracks on the plywood, and moved into position. Because the z-bars were installed square and level, there is no shifting, and they hang true. The undersized plywood sections disappear behind the planks leaving the impression that the planks are floating slightly off the wall.
While this mounting method may not be ideal for every scenario, this was an effective way to install 8 Nouveau™ planks with only 8 small hook holes in the wall. These can now be installed in apartments or temporary environments with minimal damage to the existing walls – and once you are done, they’re easy to take down and reinstall somewhere else. You just need a level!