Reddit mentions of Acoustic Absorbers and Diffusers: Theory, Design and Application

Frequency dependent treatments generally are for situations where a particular room mode is very problematic. Broadband absorbers are most often the best price/performance ratio by far.

As for references, it’s true that few other books cover the topics involved well, and generally they’re very expensive. This work by Cox and D’Antonio is one of the best, albeit not inexpensive. Also, the work of Helmut Fuchs has fundamentally changed room acoustics almost from the ground up. I still hear consultants claim that the 1/4 wave rule is immutable while Fuch destroyed that quite a few years back. His VPN devices are amazing.

a reflection phase grating is a type of diffraction grating or geometric device that will spatially (in space, across a given hemisphere) and temporally (delayed in/over a period of time) disperse sound.

while a flat, planar surface (whose size is large with respect to wavelength) will reflect an incident pressure/sound wave geometrically (angle-of-incidence = angle-of-reflection), a diffusor's intent is to equally disperse energy across a plane regardless of the angle of incidence.

this is accomplished via a constructed geometric device that consists of a series of wells of same width but varying depths. due to the speed of sound being constant, some energy will be reflected and emerge out of the shorter wells prior to that of the longer (deeper) wells. this path length differences results in phase changes for a given frequency (wavelength). as a result of huygens principle and diffraction, an interference pattern emerges when the phase-shifted signals from all of the wells are superposed (combined).

the claim to fame of RPG's was via that of Dr Manfred Schroeder who posed quadratic residue number theory (n^2 mod P) to dictate the depth sequence of the wells - which subequently yield equal energy diffraction lobes. that is, the dispersion/scattering of the reflections from the diffuser would be equal in gain at the diffusion frequency and multiples there-of.

quadratic residue diffusers (QRDs) are one form of RPGs - but do have their own limitations and inherent "distortion" and frequencies that are not correctly "diffused" (thus, "flat plate"). primitive root number theory (PRDs) is another psuedo-random number sequence used to construct RPGs that offer slightly different polar response (more flat power response vs individual diffraction lobes).

you can explore superposition/summation of multiple-spaced signals (which yield polar lobes and nulls) via a 2d wavetank model: http://www.falstad.com/ripple/

a good friend took the time to construct QRDs in the wavetank to illustrate the development of the equal-energy diffraction lobes via that of a 3x N7 QRD array: https://vimeo.com/7507997

notice too how there is less scattering/diffusion at the lower frequencies (longer wavelengths), where the depth of the well is not deep enough to cause significant phase shift and thus "steering" of energy - while the higher frequency waves (shorter wavelengths) form a distinct interference pattern with the "lobes" being dispersed across the given plane/hemisphere.

another wavetank example he constructed was a QRD vs a flat wall (planar surface): https://vimeo.com/6461707

you can clearly see the flat wall yields a reflection in the "geometric/optical" direction - much like that of a pool/billiards ball bouncing around the table. this is the "specular" nature of indirect energy where wavelength is small with respect to boundary. now compare to the QRD where regardless of angle of incidence, energy is dispersed in all directions on that plane.

QRDude is a software based GUI QRD calculator: http://www.subwoofer-builder.com/qrdude.htm

the author also formed a concise tech guide that should be easily digestible for the novice: http://www.subwoofer-builder.com/qrd.htm

much of the information was taken from the authoritative source on the subject: Acoustic Absorbers & Diffusers (Peter D'Antonio of RPG Inc, and Trevor Cox): https://www.amazon.com/Acoustic-Absorbers-Diffusers-Theory-Application/dp/0415471745/

pdf can be found here for you to explore: https://www.sendspace.com/file/pqgxx8

there is also a nicely written presentation by D'Antonio regarding the subject at conception and his collaboration with Schroeder: https://www.sendspace.com/file/acgjeh

a higher order "N" panel (prime number root) will yield more varied depths of wells, thus more phase shifts, thus more "complex" diffused returns. a deeper diffuser will yield a max depth = 180* phase shift for a lower frequency (longer wavelength), lowering the effective diffusive frequency bandwidth. nested or "diffractal" diffusers can be constructed to increase the overall bandwidth of the array. there are numerous design flaws of QRDs and subsequent mitigations that can be used to optimally design a device for a given application.

it helps best if you think of a 1D or 2D reflection phase grating as a phased array just like a loudspeaker/PA line array (or AESA/PESA radar array). in the case of the line array, the individual drivers all produce the same signal, but are delayed from each other physically (ie, curved or "J" array) and/or electrically (phase delay from the controller), which results in constructive interference to "beam steer" the signal (ie, towards the rear of the crowed), and destructive interference to that where sound is not wanted to radiate.

a good illustration of beam steering via that of phase shifts can be found here: http://www.radartutorial.eu/06.antennas/pic/if3.big.gif

plenty of videos available on youtube that illustrate huygen's principle - which should shore up a lot of the basics.

a RPG converts a single "sparse" reflection into many "signals" (reflections) who have a phase shift dictated by the depths of the wells - and subsequently "beam steer" in multiple directions of equal energy to "diffuse" or scatter the sound. it should help to imagine a small loudspeaker/driver at the bottom of each well, all of which radiate the same signal, but due to the varying depths, some wells emit out away from the diffuser before others. when all of these signals from the individual wells are layered on top of each other, constructive interference form the diffraction lobes to manifest the spatial dispersion.

bit brief and overly high-level but i hope that helps. their design, optimization, application, and the "why" they are needed are further topics of discussion.

Recording Studio Design. Philip Newell

Acoustic Absorbers and Diffusers. Cox/D'Antonio

Room Acoustics. Heinrich Kuttruff

Sound System Engineering. Davis/Patronis.Jr/Brown

Home Recording Studio. Rod Gervais

Master Handbook of Acoustics. F.Alton Everest

Some are heavy on the acoustic theory some are more practical but all really good resources. I'd also second the John Sayers forum.

Great that you're putting together ideas for acoustic treatment, as it really does make a huge difference in your listening enviroment.

• 1. Roxul is pretty popular and will do well just as long as you have the right amount. (a minimum of 4inches deep is needed for bass frequency reduction.)
     2. Rockwool works well in most cases and when you throw panels up you can usually control a fair amount of the bass. Though some situations require "bass-traps" in wall corners. Usually work pretty well just as the foam, though getting ones made of rockwool is preferable in most cases.
     3. Yes, simply put.
     

• • • 
      Now the difficult part.
      Acoustic treatment varies from room to room, as a common saying in the industry "In the beginning sound was perfect, and then man created rooms". This is because every setup is a little different, and every centimeter makes a whole new world of reverberations possible.
      First I would suggest doing a bit more research on the subject as it is a science all in itself, learning a bit more will definitely help you make the best use of your space.
      From personal experience I've found that a combination of live 'Diffusers' in couple with 'isolation' and 'absorption' creates pleasing results, but that's my room and my purpose as a recording studio.
      Look into some wooden diffusers as they will help balance the high end, isolation keeps the sound in and the cops from being called ;P and absorption pads (rockwool gobos) help take out some of the built-up frequencies.
      Here is a great book on the subject.
      Hope that helps a bit ;D
      Cheers!~
      Check out speaker risers as well!
      

Interesting project. You want to consider the mathematical relationships of wavelengths and notes. You'll quickly find that each note and each chord has a unique set of associated harmonics. Maybe you could construct an item based on the fundamental key the instrument is tuned to, but it seems that would be fairly limiting.

The attached show something that would certainly resonate (because everything does) but the circular items would support frequencies relative to their dimensions while the larger item would be diffuse over a larger frequency range.

The book you want to read is this: https://www.amazon.com/Acoustic-Absorbers-Diffusers-Theory-Application/dp/0415471745

>"What was (or still is) your audiophile journey??"

QRDude:
http://www.subwoofer-builder.com/qrdude.htm

Acoustic Absorbers & Diffusers (Cox & D'Antonio):
http://www.amazon.com/Acoustic-Absorbers-Diffusers-Theory-Application/dp/0415471745/

http://books.google.com/books?id=jYBR-aL2vJMC&printsec=frontcover&dq=Acoustic-Absorbers-Diffusers&hl=en&sa=X&ei=6AHxTvumPMaJgwed0rCKAg&ved=0CEsQ6AEwAA#v=onepage&q=Acoustic-Absorbers-Diffusers&f=false

http://www.amazon.com/Sound-System-Engineering-Third-Davis/dp/0240808304