Posts Tagged Model Q
Similar, yet different: Angled QRD vs. Standard QRD
Posted by Acoustics First in Diffusion, Product Applications, Products on August 19, 2025
In this installment of “Similar, yet Different,” we explore the similarities and subtle differences between a classic, standard 1D QRD and a modern, angled 1D QRD. While being based on the same mathematic function for their design, there are a couple subtle differences in the performance of these devices.
Quick review. A Quadratic Residue Diffuser is based on a mathematic equation that states that the Well Depth is decided based on the square of the position of the cell and the remainder of when it is divided by a prime number. (We know it sounds really complex… but this is how the ratios of the wells are calculated to maintain a balance of magnitude across the face of the device.)
The equation looks like this:
Well Depth = (n² modulo p)
(Note: there will not be a quiz!)
As it was stated, both of the devices use the identical calculation when coming up with their wells… but there is one important change – the well bottoms are flat on the standard QRD and angled on the angled quadratic. This change makes this diffuser perform differently in 2 key ways:
- The Diffusion Pattern is wider on the angled QRD.
- There is a more subtle transition from one frequency to the next on the angled QRD.
When you look at the two sets of polar pattern above, you will notice that the Angled QRD has a wider pattern, as shown in the first-column, horizonal polar pattern (at 2000Hz especially), where the standard QRD is a more forward-focused pattern.
What does that mean in practice?
Both of these diffusers have a 1D pattern, but the flat bottoms of the standard QRD primarily use diffraction and incidence angle to widen the diffusion… the rest of the diffusion works on the principal of phase offset from the depth of the wells and the time of travel. The Angled QRD introduces an angle which means that one side of the well is deeper than another. This changes the reflection angle, time of travel, and, in turn, degrees of phase shift depending on where the sound strikes the inside of the well. This modification smooths the transition of phase from well to well – as the wells themselves have a range of phase change. This angle also causes the sound to be redirected toward the inner walls of the wells, causing it to change direction from the angle of incidence – widening the pattern further, changing the travel time, and basically bouncing sound around more.
There are some situations where the standard QRD‘s narrow pattern and well-defined transition frequencies may be preferable. In some practice rooms or larger listening spaces, there may be a need for the diffusion to be a little more directional, maybe to hit (or avoid) a certain position in the room. In these scenarios, the standard quadratic may be the recommended choice. In other spaces where you want the reflections to spread out more rapidly – maybe in smaller rooms or spaces where you need to get more coverage from ceiling reflections – then the angled quadratic may be more appropriate.
In closing, while these two devices have a nearly identical design, a small difference can have a big effect on the performance of the diffuser – and how you use them.
Eight very different 2′ x 2′ sound diffusers.
Posted by Acoustics First in Diffusion, Product Applications, Products, Recording Facilities on June 30, 2025
Acoustics First® has maximized the idea of adaptable designs. One of the most common modular architectural elements is the 2′ x 2′ ceiling grid. While standard, fiber ceiling tiles have their uses, specialized acoustic environments require higher-performing materials – for both absorption and diffusion. While Acoustics First® excels with its Sonora® and Cloudscape® Ceiling tiles, today we are going to focus on the wide range of 2’x 2′ diffusers that have been developed over the several decades.
Sound diffusers in a 2′ x 2′ format have several advantages, other than just being placed in a ceiling grid to help diffuse the ceiling. They integrate well on walls and in arrays, where they can help break up large flat surfaces and help minimize flutter and standing waves from parallel surfaces. While they provide many different aesthetic options, there are also many different functional types of diffusers available in this form-factor to address different acoustic issues, from flutter, bass issues, targeted frequency absorption, and geometric scattering. Let’s look at some of these devices and their uses.
Geometric Diffusers.
Geometric diffusers have been around a long time. These devices break up large flat surfaces and redirect or “scatter” those reflections in different directions. They work great in environments where you need to redirect acoustic energy in a predictable way, and redistribute a specular reflection over a wider area. In a 2′ x 2′ size, you can also get a fair amount of bass absorption, due to the large cavity behind the geometric shapes creating a space that can be stuffed with absorbent material to tune it.
Quadratic/Mathematic Diffusers
Mathematic diffusers are devices that use specific calculations to design their size, shape, and structures to effect their performance. A common type is called the Quadratic Residue Diffuser (sometimes called a Schroeder Diffuser, after its pioneering inventor, Manfred Schroeder). This type uses a Quadratic Residue Sequence that optimizes uniform sound diffusion at specific design frequencies. There are different ways to implement these designs, but two common designations are based on their diffusion patters – 1D or 2D. A 1D Quadratic diffuser mostly spreads energy in one plane, and a 2D provides a hemispheric pattern.
Organic Diffusers.
Organic diffusers are a variation on the classic mathematic diffusers which use different mathematic functions to optimize the diffusion further by creating a smooth transition. Once such method is called Bicubic Interpolation. Instead of having the math restricted to having blocks at certain heights, the interpolation bridges these heights using a function that provides a smooth transition to the next target height. This transition creates unlimited resolution in the frequencies within it’s functional range, providing expanded uniformity throughout its range, and increasing its capabilities. As different frequencies are affected differently depending on their wavelength – the organic diffusers have no hard edges to define their pattern and look differently to different frequencies and energy from varied sources.
These diffusers all have the ability to be used in different types of installations for different reasons. Many of these diffusers are mixed and matched in the same room. You will see these on the walls or ceiling, and placed in different locations. There are rooms with Double-Duty diffusers for low frequency control, Model C for Mids, and Model F for flutter, while other rooms may have Aeolians™ on the rear wall and Model C’s and Model F’s to control the ceiling.
Keep in mind, these aren’t even all the diffusers we have available, these are just the ones specific to the 2′ x 2′ format. The Aeolian™ has a 1′ x 1′ version called the Aeolian™ Mini. There are flat panel diffusers that are hybrid absorbers and diffuser like the HiPer Panel® and the HiPer Panel® Impact. There are even large format versions of the Double Duty™ diffuser, Pyramidal, and even the Quadratic Diffuser.
For more info about these diffusers, read some of our, “Similar, Yet Different Series,” where we go into more detail about our products… and how some of these are similar, yet different!”
If you have any questions as to which products you need to optimize your space, reach out to Acoustics First® and we can help you find which products will be best for your application. Remember that Acoustics First’s® full line of sound diffusers are all made in the USA, with many available in stock for quick shipping.
Similar, yet different: Quadratic vs. Itself?
Posted by Acoustics First in Diffusion, Product Applications, Products on July 6, 2023
For this installment of “Similar, yet different,” we will take a classic welled-quadratic sound diffuser, The Model Q, and compare its performance to itself – only installed backwards!
Taking “similar” to the extreme in this case, we are testing the difference in performance of a 1-dimensional, welled-quadratic diffuser installed in the standard welled configuration, and then installed reversed – with the sound impeding on the back side of the wells. For a bit of history, the Classic Quadratic Diffuser (or Schroeder diffuser) was designed with a grid separating the reflectors – creating wells of different depths proportional to the remainders of n2 (mod N). This design has some interesting facets.
- They are inherently symmetric if left in the original sequence.
- They are periodic (i.e. they repeat.)
- The discrete Fourier transform of the exponentiated sequence has constant magnitude.
The design principal is simple if you tear apart the math, and it’s simply wells that have a different effect on different frequencies, depending on the geometry of the wells. The Model Q is an advanced 1D-Quadratic with angled well-bottoms, which assist in smoothing out the performance and widening the 1D polar radiation. So if this design is relying on the wells to be effective, why would we reverse it?
An acoustically diffuse environment develops due to many factors, and while the frequency focus of the wells is useful, there are other scenarios where different methods may be preferred. If the geometry of the elements were flipped around, you would get the same (albeit reversed) ratio of distance, but you lose the containment and channeling that the wells provide. This imparts a diffraction on the unrestrained elements. This also allows for a different interaction between the elements, as the face of the unit is no longer planar.
Let’s look at the effect this has on the performance of the device at some different frequencies – starting low and moving up…
First, we will look at the 1150Hz performance of the devices… standard welled-install on the left, reversed on the right.
At 1150Hz, there is a little variation in the performance. Both are front focused, with a strong 1D horizontal polar response, but they are not identical. The welled-design (left) shows a broad frontal response, while the reversed design has a smoother vertical response, sharper front lobes, and stronger side performance. Overall, this difference is relatively small at this frequency.
Now, we will look at 2300Hz.
Again, we have two similar looking balloons, but there seems to be a bit more variation. The welled-design (left) shows a smoother 1D pattern in the front as the wells release sound within the same plane – at the front face of the wells. On the right you will notice sharper and more discreet lobes, but you will also notice that it has wider horizontal performance again, as it isn’t as front focused due to its free standing elements. The vertical performance is also a bit different – the welled design is broad and smoother vertically, while the reversed installation shows sharp lobes again.
Step up to 2800Hz, and we see some more drastic differences.
The performance of the standard welled-install (left) stays smooth and front-focused, while the lobes of the reversed install (right) have become even more distinct. Interestingly, the side lobes are even larger, showing an even wider polar pattern than before. These two instances show a marked difference between the smooth front-focused wells and the wide sharp scattering of the unrestrained elements. These two configurations are both very different, but are still both very effective at helping to disperse the incoming energy. Remember that the room develops diffusion through sound travelling in many different directions – these are not simple reflectors sending the specular energy in a single direction.
Now at 3650Hz we see a shift toward the reverse installation.
At around 4K the welled-installation (left) begins to move back front and center. It’s primary method of diffusion uses the wells to channel the energy, and at higher frequencies sound becomes much more directional. This directionality is used to create a temporal shift in the sound, as the reflections will occur out of phase from the source, and controlling that reflection is paramount to tuning this method of diffusion. However, as stated before, there are other mechanisms contribute to diffusion. The unrestrained elements on the right balloon, have hit their stride and still maintain a wide 1D polar pattern. The lobes are still sharp, showing the interaction of the elements with sound. This installation is showing the strength of its spatial dispersion, which will send acoustic energy in more directions and use the travel through the space to create a diffuse environment. It loses some of the frequency tuning of the wells, but makes up for it in the wide polar pattern.
Now for the super high frequencies – we jump straight to 10Khz.
This final set shows two diffusers pushed to the limits. The welled-installation (left) is a very narrow focused beam now. You will note that it has some variance due to the interactions with the walls of the wells but all of its work is done through phase shifting at this point. In contrast, the exposed elements (right) are still allowing for a bit of diffraction to occur, and the angled faces are still allowing for a bit of spatial redirection. Also note that these polar patterns were generated with a sound source directly in front of the device at 0° incidence, and the exposed elements would offer more exposure to its surface area than a welled design at wider angles of incidence.
In summary…
Diffusion develops using many different variables, including the untreated walls of the space. While both of these installations are functioning in nearly identical frequency ranges due to their geometry, the mechanisms which they work are slightly different and have different strengths. The welled-design (in classic temporal Schroeder configuration) uses the wells to channel sound and address the frequencies in a tuned and controlled fashion. By simply flipping the device around, however, you change its performance from a controlled time shift, to an unrestrained spatial redirector, which imparts time shift through dispersion, diffraction, and distance travelled – further reducing intensity by having a wide 1D diffusion polar pattern. Both have scenarios which one configuration would be preferable over the other, making the Model Q diffuser a very versatile device.
Both configurations are literally two sides of the same coin… they work in different ways, over the same frequencies, providing results – no matter how you flip them.
Acoustics First® makes sound Visible!
Posted by Acoustics First in Diffusion, Product Applications, Products, Uncategorized, Video on November 18, 2016
As many of you know, Acoustics First® invests a great deal of energy in the development of the science of acoustics. Here are three ways that we are making advances that help people learn and actually Visualize acoustics!
Those interested in sound diffusers have certainly noticed that Acoustics First® has produced a Diffuser Data book, containing all kinds of test data about how our diffusers contribute to the sound in your space. This information is a great advancement and we have worked closely with the ASTM committee developing this test method. Some people wonder exactly how the test produces the data that we report, and we have developed a simulation to show exactly how the sound energy is sampled during this test.
If you download the Diffuser Data booklet, you can see a picture of the gigantic test arc at NWAA Labs which is used for the real world tests.
Acoustics First – Diffuser Data Test Demo from Acoustics First®.
We have also made leaps and bounds in using simulations to show the different ways that diffusion develops in a space. Depending on the type and placement of the diffusers you install, the diffuse field will develop at different speeds, at different frequencies. We can now show a couple of simulations of the development of a diffuse field to help you visualize how sound moves in room without treatment and with two different sets of diffuser treatments.
Acoustics First – Room Simulations from Acoustics First®.
Bonus video! Imagine being able to see the Untreated room and the Model D room from a different angle – To be able to move around the outside of the room and see how the sound field develops from a different perspective. Imagine no more! Here it is!
Acoustics First – Sound Field Development Simulation – 3D Panning from Acoustics First®.
If you prefer to use YouTube – you will find the videos uploaded at our YouTube channel here.
We hope these helped you to “look” at acoustics in a whole new way, and stay tuned – more advancements are coming soon!
Contact Acoustics First® for a high bitrate, presentation quality version of the videos – as well as permission and terms of use.
Bonus! Simulations! Now in stereo – and with absorption! Click Here!
Acoustics First BLOG 
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