# Sound Diffusion Physics: How to Design Sound Diffusion Paneling

### The Importance Of Diffusion

Most of us have seen the science demonstration of how sound waves work – a pebble dropped into the calm surface of water in a tank, the slowly-radiating concentric peaks and troughs in water corresponding to cycles of compression and rarefaction in air.

But the analogy of waves on water to sound waves in air can be misleading. While it’s convenient to think of acoustical energy as radiating evenly in all directions like the pebble’s waves, sound is not evenly distributed in all directions at all frequencies. Sound waves are directional, with three-dimensional radiation patterns that vary by frequency.

Likewise, flat-surfaced rooms do not distribute sound energy evenly. Sound waves reflect off flat surfaces at the same angle as they arrive, proceed to bounce off the next flat surface at the arrival angle, and continue on until dissipated by friction. These discrete single reflections result in wide variations in tonal balance and reverberation times at different room positions even a few inches apart. Parallel flat surfaces also create destructive flutter echos.

If left untreated, these two issues – sound wave directionality and flat-surface reflectivity – make for bad acoustics in rooms where sound is created, monitored, or recorded.

A common solution is to use sound absorption panels on walls and ceilings, but too much absorption causes “dead-sounding” rooms and loses the essential feeling of “live-ness”.

Creating consistent-sounding and useful acoustics is much simpler when source radiation patterns are evenly distributed and sound energy arriving at surfaces is scattered – exactly what diffusion does. With proper diffusion (ideally polycylindrical diffusors) balancing the right amount of absorption, a room will sound like it has an indefinite number of random reflections and proportional decay times, resulting in a sense of natural spaciousness.

There is another problem – when low-frequency wavelengths are whole multiples of room dimensions, they destructively cancel or add together at different positions (room modes). Where wavelengths are longer than the room’s dimensions, they cannot be diffused, and standard absorption panels attenuate only mid and high frequencies. Absorbing low frequencies (20-200Hz) requires a large amount of thick absorbent material, causing space issues. The best solution is to absorb low-frequency energy with mass-loaded vinyl (MLV) membrane absorbers – these have proved to be cost- and space-efficient.

This is the most effective combination of acoustical solutions:

• Diffuse mid to high frequencies with polycylindrical diffusers
• Moderately attenuate mid to high frequencies with panel absorbers
• Attenuate low frequencies with MLV membrane absorbers

Proper diffusion is necessary in creating natural-sounding acoustics. The right combination of diffusion and absorption results in much better tonal balance and smoother reverberation times throughout the room.

## How to Design Sound Diffusion Paneling

Understanding diffusion is like understanding women, with the only difference being that diffusion makes sense to SOMEBODY. Maybe we’ll get a little closer with this article.

I’ve embarked on my journey to figure out this diffusion business.

I want to point out right now that I’m NOT an expert on this. The point of this article is more of a hook up with a buddy and figure it out together kind of thing. I’ve learned a few things along the way and am confused about a few others.

I’ve made a note anytime I’m in “hypothetical mode”.

Please share what you know! I wouldn’t give this article any more clout than anything else you read online, BUT my idea is to be comprehensive with everything I know and this sure beats trying to gain anything useful from a 279 post forum thread from 2006.

## To DIY Or Not

Is a DIY diffusor the way to go? I’m assuming that you are like me, a lot better at audio than construction, but you probably have some kind of Tim-The-Tool-Man-Taylor magnet pulling you towards the circular saw and plywood section at Lowes.

If you come from a not-as-much testosterone stock, that’s okay. Save yourself the trouble and buy the diffusors.

Realtraps, GIK, RPG, Prime Acoustic, and many others all make diffusors. I’m going to go out on a limb and say all these are fine diffusors. None of them are cheap.

I’m going out on a limb here when I say that the kind of difffusor that you manufacturer for efficient shipment isn’t the exact diffusor you build at home. Whether weight and size is an issue is up for discussion.

### Go Big!

I want to make sure you realize how the scope of this thing. It’s covered best in Recording Studio Design, but if you want to notice any real changes in your room, you need to be applying your changes to 20-25% or so of the surface area.

Placing a pencil on a shelf does nothing. Those people who post DIY threads and blogs where they cover 1% of their room and rave about the “amazing difference” are suffering from the confirmation bias. Nothing more.

One pencil does nothing. 10,000 pencils may get you somewhere. When thinking in terms of acoustics, I’ve learned that it’s preferable to think in terms of atom bombs or at least dump trucks.

GO BIG!

You have to in order to cover ¼ the damn room. If you are expecting a proof-of-concept type of benefit from a 2’x2′ thingy you will be disappointed.

## Schroeder Diffusors Are What I Want

It’s explained in Alton Everest’s Master Handbook Of Acoustics as well as in Acoustic Absorbers and Diffusers: Theory, Design and Application by the RPG guys (The QRD chapter is free on Google books, actually.).

Basically, there was a time when sound diffusion just wasn’t happening. Pretty much all the designs out there were sorely lacking. The notion of livening up a room without direct reflections was pretty much a dream. We are talking about the 1970s here.

Then this Bell Labs genius dude, named Schroeder, stormed in and cracked the code. He basically figured out a way with math to get into the panties of room acoustics at will. It’s the closest thing to the Orgazmo Ray imaginable for what we do.

I’ve done little more than research this diffusion business for the last week and I’ve not found anyone with any clout that has a better idea than the Schroeder Diffusors. It’s THE diffusor…although there are variations. All other wannabe diffusors just aren’t.

All the crap they teach you in all the living home recording books and articles most of you stumble upon (the kind of bullshit that motivated me to dedicate 2 years to create Killer Home Recording ) tell you that bookcases and random crap in the room are diffusion. These aren’t even close to diffusion. It’s disgusting that they aren’t prosecuted for fraud.

If you shoot a bullet into a thick, metal wall it will bounce off pretty much at the angle of incidence. (There are a few exceptions to this rule, but ignore all that.) That’s what sound reflection is.

When you fire a gun into a wall and the bullet busts into a thousand pieces forming a half-circle force field resembling something aliens most likely have, you have diffusion.

As far as I’m concerned, this phenomenon is a miracle. It shouldn’t happen. Kinda like a 30-ton metal thing shouldn’t be able to flow through the air. It does because of some physical and mathematical awesomeness. Hooking wings to your Jeep is not an airplane and a bookcase is not a diffusor.

Diffusion sounds badass. Just some crude, angled thing doesn’t. They don’t even do the same thing. So if you are considering trying diffusion in your studio, consider nothing but Schroeder diffusors or some kind of mathematically sound equivalent.

End of story.

Just to make this perfectly clear, the rules for making a Schroeder-type diffusor are specific. There is a purpose for each little slat, block, or peg. It’s shown in the Master Handbook of Acoustics that if you cover just one well with the wrong size, the whole diffusor is rendered useless.

When the math is wrong, you are done for. That’s why random wood and stuff around the house, while possibly reflective, do not reach this holy grail we call diffusion.

If you are broke and need to bust up some standing ways, using some reflectors is a doable approach. Just remember that diffusion is the silver tuna that you’ll want some day.

### Which Schroeder Diffusor?

There are several different “styles” of diffusor associated with Schroeder and it gets pretty hazy trying to make heads or tails.

My view (yes, this is an opinion…I’m still learning here and prefer to be honest about what I’m sketchy about) is that the same basic concept is applied to all Schroeder-type diffusors and it’s simply the way the math is done that changes.

Alton Everest doesn’t help a bit in Master Handbook Of Acoustics with this confusion as he lists Reflection Phase Grating Diffusors, Quadratic Residue Diffusors (QRD Diffusors), and Primitive Root Diffusors (PRD Diffusors) without really stating if they are the same thing or not. Bla blah blah. All big words that don’t mean anything to me.

I do see a few Primitive Root Diffusor designs out there, but it seems that the Quadratic Residue Difffusors (QRD) are the overwhelming winner, at least in terms of popularity. They can be seen at Skywalker sound. (Sold! That’s good enough for me.)

Some acoustic specialist may have qualms with this (and I’d love to hear what they have to say). From what I’ve gathered PRD diffusors never repeat themselves (no lobing….see below) and are a little better at diffusing.

The problem is to build one correctly means cutting “pegs” that are never the same length. This adds tremendously to the time required for the project. If you can cut 169 different sized pieces x 10 diffusors knock yourself out. For my time, QRDs seems to be acceptable and allow me to cut 12 different sizes in as close to “mass production” as I can get. Again, they use them at Skywalker sound.

So from here on out, I’m going to be talking specifically about the Quadratic Residue Diffusors (QRD Diffusors). There are many, many QRD diffusors products out there so that’s a good sign that the design is effective. Ethan Winer, from Realtraps and I traded emails. He basically said that QRD diffusion is the only way to go. That guy has tested them all and designed his own.

### Forget Figuring Out QRD Diffusors

If you want your Ph.D. in physics, learn the math for QRD diffusors. If you are just a recording guy, don’t bother.

There are gadgets out there that do all the work for you. I’ve learned the hard way that it’s very easy to try to figure this stuff out, spend 10 hours on the laptop, and at 4 am it suddenly occurs to you that you no longer want to live anymore.

I did this for a week straight. I came out with what felt like a combination of my brain oozing out my ears (in the way a melting marshmallow oozes), and a good ol’ chainsaw to the frontal lobe.

In the end, I don’t feel like I walked away with much. If your goal is to make better recordings and not become a math major, do yourself a favor and skip the tech jive. It’s optional.

1D QRD Diffusors (1-Dimensional)

2D QRD Diffusors (2-Dimensional)

#### 1D vs 2D

While these diffusors look dramatically different, they work along the same principals. They are both Schroeder QRD diffusors.

I feel a little sketchy giving advice on this one so fair warning.

The general idea is that the 2D diffusors, which look amazing, will shoot sound both left, right, up and down (assuming it’s mounted on a vertical wall…not on the ceiling).

1D diffusors (assuming they are arranged vertically…up/down) will spit the sound left and right only, give or take.

Some people have made the claim that you don’t want to “waste” that energy by dividing it by 2 dimensions and that the 1D design will shoot more sound to the areas you want it.

Others seem to be content with sound going all over the place as long as it doesn’t bounce straight back (direct reflection). I’ve not found a good answer for this one and probably will not.

2D QRD diffusors definitely give the “mad scientist” effect and are client pleasers. (Purists dismiss this, but many of us in the studio BUSINESS must embrace it. I cover this in detail in my half-written book on the studio business, Surving And Thriving In This BS Recording Studio Business) Focus energy in all four directions.

All those little pieces require quite a bit of labor to cut and glue. We’ll get into that. This isn’t to say that the 1D diffusors aren’t time-intensive. Just be prepared for an adventure with 2D diffusors.

There’s probably something big I’m missing here. If you know, speak up. If you don’t believe me so far, that’s probably a good sign that YOU are on the right track.

## A Shortage Of Premade Plans

After going into shock and considering becoming a nun, I decided to simply look for some premade plans. There are a few out there. The Tape Op plan is super simple. It’s a PRD diffusor.

That particular design is heavily quantized, meaning they’ve rounded all those unique sizes to four. This makes the diffusor useful, but the word on the street is this increase in design simplicity/ construction efficiency makes for a less effective diffusor.

Not sure.

All I know is I go big so I wanted something that the nerds would give a thumbs up to. I can’t be rethinking this in 5 years.

The depth of 4” means that its design frequency is going to be pretty high. Do we want low-frequency diffusion? I never found any good info on this one. I can’t think of any ANY frequency I wouldn’t want scattered around as opposed to a direct reflection. That’s an easy one.

A harder one is whether absorption would be a better choice. More importantly at what point is absorption a better choice? Don’t know.

Besides the Tape Op version, which is a spinoff of the BBC Diffusor I don’t find too many ready to rock plans. Now I see they are unnecessary.

## Design Considerations

### Lobing

This is what happens when too many identical QRD diffusors are used in a row. The tech jargon for a single diffusor is “period”.

You can clearly see this pattern when looking at QRD diffusors in various images. Even when multiple diffusors are hooked together to look like a single unit, this pattern/period is quite obvious.

If you repeat a bunch of periods, you can get into a mess. It makes sense that diffusors are going to diffuse certain frequencies better than others. When you use a bunch of diffusors that all peak at 2k, guess what. You’ll get a heavy peak at 2k. Duh! That’s a problem. The solution to this is to throw in a different design to bust this up. How?

Note: Most diffusors have peaks are multiple frequencies. It’s not important to know the details. Just know that if you use the same period 200 times, you’ll end up with very peaky response. This is like eating only vegetables and grains. You start to look like Moby after a week.

This is where things get pretty damn technical. I’d love for a real guy to step up and speak in mostly-plain English. I’ve not found a guy to explain this that I trusted AND could understand. Feel free to correct me. If you ARE that guy, step on up.

The idea is to use “barker codes” to fight the forces of peaky lobing. This is a mathematically sound way to randomize these diffusors to get them to all work together in harmony. If you read the wiki for barker codes , you’ll see that they are used for pulse compression radars. I have no idea what that is, but I assume it’s a toy on the Call Of Duty games. Either way, I don’t recommend going there without a physics degree. I barely made it out alive.

I wouldn’t overthink the Barker Codes. You’ll see the Barker Code for 4 units is +, +, -, +. The best way to handle this, based on my research, is the + version is your standard diffusor and the – is the inverse of the difffusor. Hold off on the inverse business until you read about phase.

For more on lobing, see http://www.subwoofer-builder.com/qrd…uide-lobes.htm

## Diffusor Phase

This is optional but when I understood it, this diffusion business made a lot more sense. I’m going to try to make a confusing topic pretty simple.

We are getting into phase bs so that means we need to think in terms of clocks with hands. Noon is 0 degrees. 12:15 is 90 degrees. 12:30 is 180 degrees. 12:45 is 270 degrees.

Now let’s say we’ve got a random “peg” from a 2D skyline diffusor. These things are tuned to be a certain length to diffuse certain frequencies. I won’t get into those details because I don’t understand them either. Let’s just say our smallest peg is 1” tall. It represents 90 degrees (or 12:15 on the clock). Our next peg is 2” tall and it represents 180 degrees or 12:30 on the clock. The next is 3” and it represents 3”.

Can you guess what the next peg height is going to be?

If you said 4” you’ve just wasted some wood, although it is kinda correct.

The real answer is 0”. Why? When you add one second to a clock that says 1:59:59, everyone on earth (at least in your time zone) will say it’s officially 2 o’clock…or 0 degrees.

No one refers to that thing after 359 degrees as 360 degrees. They call it 0 again. If you said 4”, you are basically saying it’s 1:60:00. That isn’t wrong, but it’s the same thing as starting our cycle over again. This diffusor depth business is a cyclical function determined by the wavelength of the design frequency….I think.

In our overly simplified example here, if we needed to add 90 degrees for our diffusor. (See Optimizing Your Diffusor Depth below), all pegs at 0” (which are essentially using the base as the peg) will now need to be 1”. All 1” become 2”. All 3” become….0” which is the base/foundation thing.

It’s no different than adding 15 minutes to a clock. When it’s 3:45 pm and we add 15 minutes, we start a whole brand new hour at the beginning. Why is this important?

Note: These 1”, 2”, 3”, etc are totally arbitrary. I used them as a simple illustration of the concept. Real QRD diffusors use very specific math obtained from prime numbers and I’ve not seen one yet that was this simple or that used these dimensions.

## Optimizing Your Sound Diffusor Depth

Due to limitations in wood use and the amount of space in your room, we can only make diffusors so deep.

When you play around with this phase business (which is made SUPER obvious and easy to do in QRDude….we’ll talk about him later) you find that in certain designs, you can use dramatically less wood and space simply by shifting the phase.

Using our bs example above, if the design has a disproportionate number of 3” pegs, if we can phase shift those so they end up at 0”, we’ve officially saved ourselves a bunch of wood, space, and work. You can leave it like that if you choose. OR……..you can use that wood to your advantage and increase the max depth of the diffusor as a whole, which in most designs will increase the low-frequency diffusion. Pretty cool!

In other words, since we’ve moved that large quantity of 3” pegs to 0” pegs and our smaller quantity of 2” pegs to 3” pegs, we now have a diffusor that is using less wood and, on average, less depth. With all this new wood, we can say, “Hey, let’s make the max depth of this thing 5 inches instead of 3 inches” and that will allow diffusion to lower frequencies.

Note: As you’ll see in QRDude, when you need to include an inverse via Barker Codes (remember: +, +, -, +) in your diffusor array, you get a bit limited in how much you can optimize.

Ultimately, wood isn’t that expensive, and few commercial diffusors go down to super low frequencies. It seems that it’s more important to utilize Barker Codes, avoid lobing, and maybe not get to optimize your diffusor’s wood/space usage. Let me know what you figure out.

### Rounding

By necessity, most DIY dudes like to round the multitude of lengths down to a handful of numbers. (This seems to occur more in PRD designs than QRD designs.) I see that in many DIY designs and these guys seem to be happy with their diffusors….whatever that is worth.

I haven’t figured out how detrimental it is to round 4.23 inches to an even 4”. I’m a wimp when it comes to this stuff, which means I have to be REALLY tough when building them.

I did zero quantization and ended up with 12 different sizes for my diffusor pegs. It’s my guess that quantization is a part of the QRD design and in my gut, I feel more comfortable going with a diffusor that is designed to be quantized than simply quantizing a PRD diffusors which was never meant to do so.

The idea of doing self-quantizing with this stuff is a little unnerving to me. As mentioned above, one wrong well and the whole thing can be ruined.

## QRDude: The Solution To Designing All Of This Diffusion Business

There’s a freeware app called QRDude. I’d gladly donate my woman for a night or two to the guy who wrote this.

Wow!

My advice is to IMMEDIATELY read their guide. It covers everything that this article doesn’t. If you haven’t gotten to the Advanced Mode part where you can automatically optimize the depth of the diffusor for max low-frequency diffusion, you haven’t lived.

The “manual” for this thing isn’t really a manual at all. It’s more of a “Diffusion: How To” kinda sorta like this one, but I think I take a more layman-type approach. The combination of this guide here and the pages found along with the QRDude should pretty much cover all your info needs.

I highly recommend you spend a few hours getting familiar with QRDude. It’s amazingly powerful and extremely well-written software. It’ll handle the entire design for you. Make sure to view the exports. They’ll show you the exact dimensions you need to cut, how many you need to cut, how heavy your design is with a number of materials and much more. I used the MaxGraph function on my laptop when gluing the pegs to the foundation.

Pay particular attention to the advanced features. They are extremely powerful and come in handy for optimizing your diffusor array to work with the inverted versions that you’ll need to follow the Barker Codes.

I’d gladly pay \$200 for this software. Very impressive!

## QRD 1D vs 2D…Again

I went back and forth over which design I should start with. I say “start” because I know my control room and live room will most likely need plenty of diffusion and variety seems to be an important part of good diffusion. (Again, think like a dump truck, we need 25% coverage). So I liked the idea of just jumping in and trying out a method.

As of this writing, I just finished my 4th QRD 2D N13 diffusor. It’s been a RIDICULOUS amount of work, but I am getting better and faster each time.

My biggest reason for going with 2D diffusors first was I knew I could build them without a table saw. I have a miter saw and circular saw, but I didn’t buy a table saw until midway on this project.

Another issue was I was concerned about the divider thickness (often required or at least highly recommended with 1D diffusors). Locally, I couldn’t find anything under 1/4” in thickness. Later in the project, I found some 5mm thick plywood (.19 inches) which will probably work okay.

I never found any definitive numbers on divider thickness. (Everyone said the thinner and stiffer the better.) I considered plexiglass, but never found what I was looking for at the right price. Now I THINK I would be content with 5mm dividers, but further research is required.

I’m noticing when playing with QRDude that it’s much easier to get high-frequency diffusion with 1D QRD by using 1” wide wells. This, of course, means quite a bit of work as a 36” by 36” period would require 31 wells (if my memory is correct….don’t trust it….I don’t).

31 wells is some work in terms of cutting wood and assembling the diffusor, but it’s nothing compared to the work in a 2D design. At least that’s what I’m saying after the 2D experience. (I’ll probably be bitching about 1D construction when I’m doing that!)

The biggest difference is the 2D diffusors are very specific about the periods being square. A mod 13 design of 2”x2” pegs will be 19.5” x 19.5”. That same design using 1D will still be 19.5” wide (assuming no dividing fins are used) but the length dimension seems to be a crapshoot.

Make it whatever you want. (Again, check me on this.) It seems you could start at the floor and go to the ceiling with this design. If this is correct, other than having to deal with 1” by 8′ strips of plywood, it really doesn’t take significantly longer to make a 2′ long diffusor than it does an 8′ long diffusor.

I haven’t encountered the numbers, unfortunately, that directly compare the diffusion coefficients (is that the right phrase for it?) of 1D diffusors and 2D diffusors.

My gut says that on a per square footage basis, the 1D diffusors are dramatically more efficient from a construction time standpoint. I’ve worked from Tuesday to mid-day Saturday to construct 4 19.5”x19.5” QRD 2D diffusors. This includes a multitude of mistakes. Not counting the sanding, staining, and polyurethane processes I was able to construct a single 2D diffusor today in about 3.5 hours, give or take.

## My First Design

The images don’t fit well in full-size mode so just right click and open them in your browser to see the in their entirety.

As you can see, this design scatters down to 350Hz, is designed to diffuse down to 700Hz, and quits working at up 4.5k.

I’ve been asked why I made the diffusors nearly 9″ deep. Changing to 4″ deep diffusors gets me a diffusion frequency of 1.5Khz. Whether I need the low mids diffused is still up in the air, but I went for it. The additional cost of wood was minimal.

QRDude makes it easy to come up with the inverse for the Barker Codes. Just push one button. Awesome!

Here’s QRDude in 2D mode.

## Conclusions

So far, my research seems to conclude that QRD diffusors are the way to go because QRDude makes it easy to calculate what you need, the quantization appears to be math based and a part of the design, lobing can be avoided using Barker Codes, they are faster to build than PRD diffusors, and they are used at Skywalker Sound. (Again, I’d LOVE for someone who knows what they are doing to confirm all of this.)

The decision to go 1D vs 2D is still complex, but I suspect that 1D will be faster and cheaper to build. I’ll let you know soon. I start on those any time now.

We will be happy to hear your thoughts