# Perspectives in Control for Multiple Frequency Regions: Part III



## ejbragg (Dec 13, 2009)

*Part III: Interior Acoustic Design (Treatment)*
*CHAPTER 1: MODAL TREATMENT*

The practices of this section are specific to the completion of the studio construction or remodeling process. In other words, we assume the space has already been treated for soundproofing. *It is important to know that interior acoustic treatment will do very little, if anything, toward soundproofing one room from another. If you hope to absorb enough sound out of a room to make it sound quieter in an adjacent room by putting extra absorbent material on the walls, you’d be making a mistake. Sound proofing is only reliably done using heavy materials in the wall construction, and such walls must be assembled carefully. (Please refer to Part II: Soundproofing.)*

*Section 1: Finish Construction First!*

The first problem to deal with is the one we originally tried to circumvent in Part II; room modes. These problems will exist the instant your (bare, painted) walls are in place. It is wise to complete construction and install all cabinetry, desks, furniture, and flooring before continuing. These objects will change the sound of the room, affecting every aspect of our list. For simplicity, pictures and other wall hanging objects should be left out – you may not know yet where you will have to place treatment.

*Carpet*
Popular belief, even common sense, tells us that placing carpet in a room is good for the acoustics. To our ears, it may sound quieter, especially with thick, plush carpet. However, carpet tends to cause more harm than good, because it throws the room acoustics off balance by absorbing a great deal of high frequencies, a modest amount of middle frequencies, and practically NO low frequencies. The result is a room that must be treated more extremely to get all frequencies in balance, and the final result may very well be an extremely dry listening environment. This is most certainly not ideal for critical listening, for reasons that will be covered later. The best flooring is some form of hard surface; wood, stone, tile, concrete, etc. Each of these hard surfaces has its own merits and downfalls, which is again, outside the scope of this discussion. Nevertheless, for a commercial studio environment, a hard surface is usually deemed an imperative starting place. Sectional rugs can always be added later, if necessary.

*Section 2: Modal Analysis and Treatment at the Low End*

This is the point where some form of testing equipment is a must. All the details of acquiring and setting up the test equipment cannot be covered here, but room modes must be measured using a single point source (preferably one of your main monitors, if the space is the control room) and a qualified test microphone calibrated to that monitor. Using appropriate software generating tones and noise, the room dynamics are to be measured in many different places. The number of sampling positions is subjective, but 1 microphone test position per 16 sq ft (4 ft x 4 ft square) is my “ballpark suggestion”, making sure to include placement close to the corners. For metric users, that’s 1 mic every 1.5 sq m (1.2 m x 1.2 m). I generally like to position my microphones at console position ear height when shooting the control room, but sometimes extra points at various heights throughout the room will provide a more insightful overall result. During testing, be sure to number your sample positions and name them so you know where in the room it was placed. _(Certain results will prove that position matters, especially if something looks strange in the results.)_

The resultant responses should be analyzed using one of many available frequency analysis software applications. Where peaks are present, especially those that show themselves at many test points, those frequencies are likely caused by room modes, and are hopefully close to the ones estimated during the Acoustic Architecture computations, *Part I, section 2*. Of these room modes, the lowest and strongest should be dealt with first. In fact, during treatment, depending upon the type of treatment used, it is possible to remove the harmonics of the low frequencies in the upper registers of the problem areas. Note that larger peaks require heavier treatment over smaller peaks, and peaks that occur over many test positions have higher requirement over peaks that occur in fewer positions, unless those few peaks are large enough (or wind up in a critical listening position). If the modal problems lie at 20 Hz or below, treatment at those frequencies is subjective, since they may not be noticeable or reproducible.

There are many ways to absorb these modal frequencies. Bass traps and panels based off differing principles can be constructed to pull out what is needed. Some models are stronger than others at treating these problems. Some require more cubic space than others. (Often the larger cavities absorb more energy than smaller ones.) Specific bass trap design is deferred to other threads on this forum, as well as the *Home Studio* forum. There is no difference between "commercial" or "home" studio acoustic treatments, as long as the treatments are based on sound acoustic principles and constructed with care. Note that bass traps and acoustic resonators must be air tight in order to work correctly. Some different trap models that are appropriate for treating low frequency room modes are:


Simple quarter wavelength tuned cavity
Hemholtz resonator
Slat absorber

Treat the lowest and strongest frequencies first, using the corners of the room, especially the corners in which the modes were created. The second lowest and/or strongest peaks should be treated next, and so on. The amount of square footage required for each trap is a product of the combined hard surfaces of the room and the required attenuation in sabins added or removed from the room by such treatment. "Total Sabins" (Sa) can be broken down into units of:

"S": total surface area in room, sq ft; and
"a": average absorption coefficient of surfaces in room.

The easiest (although most tedious) method for computing this is shown in the following example...

A 15 ft X 25 ft rectangular room w/ an 18 ft flat ceiling, and concrete floor:
Wall area: (15 ft X 18 ft X 2 walls = 540 sq ft) + (25 ft X 18 ft X 2 walls = 900 sq ft)
Ceiling area: 15 ft X 25 ft = 375 sq ft
Total drywall area: 1815 sq ft
Total floor area: 375 sq ft
Room Volume: 6750 cu ft

The coefficient of absorption for drywall and concrete differ across the spectrum...

FREQ: 125Hz, 250Hz, 500Hz
-------------------------------
drywall: 0.29, 0.10, 0.05 (S)
concrete: .01, 0.01, 0.015 (S)

Multiplying the coefficients by the wall areas...

FREQ: 125Hz, 250Hz, 500Hz
------------------------------
drywall: 526, 181, 91 (Sa)
concrete: 3.75, 3.75, 5.6 (Sa)
--------------------------------
total: 530, 185, 97 (Sa)

Note that the energy absorbed out of the room is likely to be stronger at 125 Hz than at 500 Hz, according to the numbers given by the material manufacturers. For a well made bass trap, the amount of absorption per square unit of space can be estimated as being close to 1.0 (which is 100 %). It has actually been shown in practice that a good acoustic trap can actually absorb _more than_ 1 sabin, which makes no theoretical sense! Nevertheless, if our bass trap is to absorb mode problems at, say, 125 Hz, if we cover 160 sq ft in the corners in 125 Hz trapping, we replace the sabins at that frequency that used to belong to the drywall sabins:

FREQ: 125Hz, 250Hz, 500Hz
------------------------------
drywall: 0.29, 0.10, 0.05 (S)
concrete: .01, 0.01, 0.015 (S)
bass trap: 1.0, 0.20, 0.08 (S)

Multiplying the coefficients by the wall areas (drywall = 1655, bass trap = 160)...

FREQ: 125Hz, 250Hz, 500Hz
-----------------------------
drywall: 480, 166, 83 (Sa)
concrete: 3.75, 3.75, 5.6 (Sa)
bass trap: 160, 32, 12.8 (Sa)
------------------------
total: 644, 202, 101 (Sa)

In this example, we have successfully absorbed more bass frequencies at 125 Hz (if the spectrum analysis proves so after treatment). However, as an example of balancing the room, this example is far from accurate. The problem with the sabin formula is that it only allows limited insight for the treatment of a room - modal problems are not estimated using the formula, which is why we must rely upon spectral tests. However, by estimating the area of the walls creating a given room mode, one can obtain a rough estimate of the area of treatment needed to remedy the problem. The best method is to treat each of the bottom modal frequencies one at a time, measuring the room response at the same positions used earlier to measure the progress. As earlier noted, certain frequency problems may diminish during treatment.

*Section 3: Modal Analysis and Treatment at the Middle and Upper Frequencies*

One of the primary differences between commercial studio space and home studios is that of the space available. While home studios are generally limited to bedrooms, living rooms, garages, etc., commercial venues often have more space available to use. The most major advantage of a large space is in the amount of modal treatment required. Because modal frequencies are based on the frequencies of resonance of a room, it follows that larger rooms primarily resonate at lower frequencies. By the time the middle and upper frequency spectrum is reached, most modal problems for these rooms has been greatly diminished. A small room, however, may be plagued with modal problems no matter how much treatment is used. Such small rooms are often best treated to be extremely dry and let modern electronics offer the virtual space desired, adding reverb or other delays. Such strong treatment also assists in avoiding comb filtering and phase problems associated with hard walls close to the microphone.

Often, modal frequencies in commercial spaces are not a problem above 400 Hz. In the event that a small room has been constructed, the above method for bass traps still applies, but there are also some other absorbers that may be used to stop specific frequencies in these bands, including:


Diaphragmatic absorber
Polycylindrical absorber

Ideally, all room modes are to be treated until peaks in these frequencies no longer exist. This does not mean that the room is yet balanced. It merely means we have successfully knocked down the extruding "sore spots" in the audio. If there are sharp peaks or valleys existing in the test results, and if those peaks are not very repeatable throughout the room, they are usually problems caused by lack of diffusion, which will be addressed in the final treatment. Some of these will always exist, and when narrow enough, not very discernable by the ear. Such minor problems are generally ignored. The next section deals with overall reverberation, which can be treated in similar fashion to modal problems, but with a different strategy in mind, and a different test signal...


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## ejbragg (Dec 13, 2009)

*Part III: Interior Acoustic Design*
*Chapter 2: REVERBERATION TREATMENT*

There is a program available at this site called Room EQ Wizard which is a great program for measuring reverberation. Because modal analysis and reverberation times are both measurements of the time it takes for a particular frequency (or band of frequencies) to dissipate within the room, both CAN be conveniently measured using the same technique. An impulse response is the signal of choice for many, although different signal types provide different environments revealing different characteristics.

The best type of signal to use for a given test can be a subjective argument. My personal choice is to use slow frequency sweeps and pink or white noise for modal analysis, merely because it provides time for the room to respond and show resonances, if they exist. Transient signals don't allow time for these frequencies to build, if this is something the room has a tendency of doing. However, transients do show resonances, nonetheless.

So what are transient signals?

*Section 1: Transient Test Signals*

A transient signal, simply stated, is a signal that provides a sudden “transition”. We can identify a cymbal strike as a type of transient signal. When a music waveform is viewed on a time line up close, it can be quite obvious where the transition from _no cymbal_ to _cymbal strike_ occurs. Because a cymbal continues to ring after being struck, this transient is only “transitional” on one side – the attack side.

A transient test signal sounds a lot like a “click”. It’s there, and it’s not there, just as suddenly. In theory, a perfect transient has infinite amplitude and is infinitesimally short – having no actual length. In practice, a signal so short it has no length would be like referring to an object, say a baseball, having no mass! But if someone hands you a baseball that has no mass at all, guess what? There’s no baseball! Furthermore, infinite amplitude is also a ridiculous request.

However, there’s an interesting phenomenon pertaining to this theoretical extreme. In digital signal processing theory, engineers use what they call “*transforms*” to _transform_ signals from one dimension, mathematically, into another dimension. A short piece of an audio signal, which is sampled along the time line for say, a few milliseconds, can be routed through a complex mathematical formula – a _transform_ – and the outcome is a different form altogether, still representing the music, but no longer providing the same apparent properties (overall amplitude change along a time line). If a certain type of transform (Laplace, Z, Fourier, to name a few examples) is applied, the outcome is the amplitude of particular constituents of the music along the frequency domain. The “domain” is the _dimension_ in which the data exists. Engineers and physicists love converting things from one dimension into another! If we leave the data in the frequency domain for a bit and make adjustments, then send the data BACK through the same doorway (called reverse transforming), we wind up with the original signal (or something closely resembling it), with some slightly shifted properties. This device would be a digital equalizer. What we take for granted as a “simple digital E.Q” is actually a bona fide example of the application of “worm hole” technology that has been referred to in sci-fi shows, and is actually being applied to space travel research now!

Back to earth: the astonishing phenomenon about a purely transient signal (as described in theory) is that when translated into the frequency domain, the result is a flat line at amplitude “1”, from 0 Hz to Infinity Hz! In other words, the signal contains ALL frequencies that could ever exist. Because in practice, we must be able to actually create and use such a signal, we can only get as close as we can in the real world. So we create a short burst of high amplitude. Amazingly, if the burst is short enough, the transformed result is a flat line along the frequency domain to well outside our range of hearing. The signal is thus most certainly usable for testing our room(s) accurately.

*Section 2: Room Balance*

Assuming Modal problems have already been handled, we turn our efforts to the overall frequency balance of a room. Transient response room analysis must be performed, and the resulting graphs assessed for an overall room characteristics.

Reverberation Time

Reverberation is appropriately measured for a specified frequency band, and is shown in units of dB per unit of time. RT60 is the popular variable used to represent this measurement, whereas the “60” represents the number of decibels of sound pressure change over time. The idea is to determine how long it takes for a particular frequency band to diminish by 60 dB. All frequency bands are tested and compared. If the entire audible spectrum diminishes at the same rate, your room is said to be in balance. This is true, no matter how long or short the reverberation time is. For example, let’s say we enter a large hall with concrete walls, ceiling, and floor, and we clap our hands and find it takes 10 seconds for the sound to die out (by 60 dB). Such is an extreme case of reverberation. In this room, it is very difficult to understand speech or music. If a transient response test shows that all frequencies die out at the same rate, the room is still said to be _in balance_!

This, in fact, is the preferred place to be at this stage of room treatment, with the exception that it would be nice if the room wasn’t quite so reverberant. After treating the room modes, if all surfaces are hard, this should, to some degree, be the present case. However, there are always rooms that have certain frequency bands that seem to be heavier or lighter than the others.

There is only one goal in balancing a room: bringing all frequencies to the same RT60 time, using the least amount of treatment possible. If, for example, we have the following room characteristics (assume one octave bandwidths, with center frequencies shown):

*FREQ -- RT60*
-------------------------------
31.3 -- 1.8 (seconds)
62.5 -- 1.6
125 -- 1.7
250 -- 1.2
500 -- 1.1
1K -- 0.95
2K -- 0.90
4K -- 0.85
8K -- 0.80
16K -- 0.80
32K -- 0.65

…. the first thing to note is that the high frequencies in this room are naturally attenuated the quickest. If the goal is balance the room (as in a control room), we do nothing to the upper frequencies, but rather decrease the reverberation times specifically in the lower frequencies, using band-specific absorption. In the above case, 32KHz is above the threshold of hearing, so we ignore it. We might also ignore the 31 Hz band, unless we’re designing a sound-for picture room where sub frequencies are sometimes mixed in sound effects for films.

In light of this data, then, we would look at the 0.80 sec decay as the goal for all (audible) frequencies, without trying to adjust the upper frequency band from about 4 KHz on up.

The Sabine Equation

The formula used for estimating the amount of wall space needed is:

RT60 = (0.049 * V) / Sa, where
V = room volume cu ft
S = total surface area of a room, sq ft
a = average absorption coefficient of room acoustics (see Part III Chapter 1)

Estimating that your wall, ceiling, or corner treatment is an excellent absorber for the frequencies you have designed it for, estimate an absorbent coefficient of “1” for the amount of wall space covered for those frequencies, and you’ll (hopefully) land close to your goal.

One good plan of attack is to add semi-wide band absorbers to the room. Assuming we aren’t trying to get extra precise, we might use a set of wide band absorbers that are active for the frequencies between 250 Hz – 2 KHz, then another set of wide frequency bass traps to treat the frequencies at around 125 Hz and below (note that you’ll need more treatment in the low end to bring the room up to balance).

Without getting off into the science of building these devices (which is a DIY Projects project), let’s assume we have successfully built and placed these absorbers in the room such that the following transient responses are the result:

*FREQ -- RT60*
-------------------------------
62.5 -- 0.75 (seconds)
125 -- 0.81
250 -- 0.85
500 -- 0.88
1K -- 0.75
2K -- 0.70
4K -- 0.65
8K -- 0.78
16K -- 0.80

Although not ideal, this room actually holds a fairly decent profile. The wavering RT60 measurements are common and realistic. While a more exact profile is possible, the effort to bring a room toward a perfectly flat response grows exponentially, the closer you get. The above results reveal the following statistics:

Mean: .77 sec
Standard Deviation: .072 sec (not bad)

At this point, let’s assume we’re balanced enough to continue to the next step.

_Note that it is not necessarily everyone’s goal to balance a room according to the flat response profile. Historically, the most famous tracking rooms in world class studios are renowned for their particular frequency profiles. As earlier noted (Part II, Section 5), these profiles are particular to the purpose of the room._


*Section 3: Reverberation Decay Goals*

So what is the overall reverberation time (or decay rate) we want for this room? Is the room to be used for speech? Music? Film (a cross between the two)? And what genre(s) within the appropriate field? For example, speech generally sounds more crisp and pleasant in a fairly dry room, and the “dryness” of the room naturally diminishes with the expansion of the room volume; greater spaces cause greater travel through air before striking reflective / absorptive surfaces. If we based our room on the dimensions of the wall in Part III, Section 2 (15 ft X 25 ft X 18 ft), we have 6750 cu ft. In such a room size, a decay time of approximately 40 ms is a good rule of thumb. However, if we decided this room is for music, we might decide to allow a little more time – around 68 ms. If the room is designed for recording horns, we might have made it unbalanced, first of all, absorbing more in the upper mid frequencies (where horns tend to sound harsher) and maybe tightened down the overall decay time due to unpredictability in music tempo – allowing for electronic delays to be added when necessary. Or if a room is used predominantly for string swells, perhaps the room would slightly accentuate the mid low end high ends, as well as be more reverberant (1.2 seconds). Whatever the goals, they should be in your design well before getting to this point, because if 1.2 seconds is the ultimate decay time, we’ve already blown it with the average decay of 77 ms! Such walls would have to be extra hard, and the space would likely need to be larger to meet this need. Otherwise, by the time we treated for room modes and balance, we’d already be in trouble.

Assuming we are creating a listening room, such as a control room, we probably want to stick with the 68 ms profile goal. If the present mean is 77 ms, according to section 2, then we need full spectrum (40 Hz – 16 KHz) absorbers on more surface area, as computed by the sabin formula. We need just enough to absorb all frequencies by about 9 ms. Actually, it might be a good idea to treat most of the problem now, then wait until the next step is finished to complete this process, since the materials used in the next step might have some absorbing properties. Nevertheless, once the decay rate goal is basically met, we have only one remaining goal to meet: diffusion.


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## ejbragg (Dec 13, 2009)

*Part III: Interior Acoustic Design*
*Chapter 3: DIFFUSION*

This is the part of the project where we smooth out all the sharp peaks and valleys in the frequency spectrum, and even cure many comb filtering effects. In fact, this part of the project may even prove to tame some modal problems that weren’t completely curable via absorption panels. Diffusion allows us to prevent slap-back echoes and cure phase problems without muffling the sound qualities of a room into a lifeless, dry cell. It is a treatment which, like modal and reverberation treatment, is managed by placing objects on the flat surfaces of a room, especially where the space is large and the surface is hard.

A properly constructed diffuser is made of hard material, to prevent its surface from absorbing any more sound. After all, once reaching the decay goals of a room, adding more absorbent materials will detract from the design goals.

*Section 1: Loose Definition for Diffuser*

So what does a diffuser do? The best explanation is possibly in the comparison with the hard flat wall on (in) which it is placed. When an airborne wave front strikes a flat, hard object, most of the energy is reflected. The angle of reflection of the wave upon the surface is roughly the same as the angle of incidence. But a diffuser is made up of many small compartments of different depths. The same wave front striking an array of such compartments will not be able to reflect in the same manner. Where the wave strikes the highest peaks (first), the wave either breaks or bends, as it begins to reflect immediately. The deeper cells begin to be struck next, and so on. By the time the entire wave front has contacted all the surfaces of the diffuser, reflections are chaotic and do not all follow the angle of incidence. They are scattered throughout the room, and those arriving back at the source do so at different times, “softening” the reflection from an echo to a reverb. Frequencies below the design specifications of the diffuser are not affected much.

Diffusers have a tendency of scattering wave fronts along the plane of design. There are one- and two- dimensional diffusers, and the shape of their diffusion properties differ. One dimensional diffusers tend to scatter in a half column shape. Two dimensional diffusers tend to scatter sound in a half spherical shape.

For example, if a 1 dimensional diffuser covers an 8 ft X 8 ft space on a wall, and if the diffusers are placed such that the cells are opened vertically, all sound striking the diffuser from any direction parallel to the floor or ceiling will be spread in all directions along the ceiling or floor, in a semi-circle or “hemidisc” – thrown into the side walls. If the 1-dimensional diffuser is placed with the cells open horizontally, any sound striking the surface will be thrown evenly in all directions (in a hemidisc) from the floor to the ceiling, but NOT in the direction of the side walls. If a 2-dimensional diffuser is erected on a wall, any sound from the room striking the surface will be thrown in all directions on both planes – both vertical and horizontal hemidiscs.

Diffusers are peculiar objects. If they are to perform as described, they must be designed using a particular approach. There is more than one approach; however, changing the dimensions from the computed version for your design criterion will most certainly affect the frequencies diffused and / or the shape of diffusion.

Diffusers were officially invented by Manfred R. Schroeder of the University of Gottingen, Germany. The Quadratic Residue Diffuser (QRD) is one of the models he invented that has been popularized for acoustic treatment. Its popularity is contributed partly to its proven effectiveness in laboratory testing, but also toward its symmetrical layout. It looks appealing to the eyes, and especially where symmetry in a room such as stereo mixing or listening is concerned, is hailed as the model of choice for most designers.

There is another asymmetrical model which also has proven quite effective, called the primitive-root diffuser (PRD). Both the QRD and the PRD diffusers are contained in the family of diffusers known as “Diffraction Grating Diffusers”. There are many companies that make such diffusers. However, there are also programs presently available to help others design these devices and build them. Note that designing and building a diffuser likely takes more time and energy than building absorbers, but this part of the acoustic treatment process that should not be bypassed. Especially in a control room, the sound environment must be dominated carefully, and the diffusion of sound is a basic necessity of such a controlled environment.

But how much surface area should be covered in diffusers? This is a tough question to answer. The acoustic ideal would be to cover every single square inch of untreated flat surface area with a diffuser. On planet earth, such an array might look rather crazy, and perhaps not so appealing. You must be the judge. Do some research, draw up the plan, and decide the most practical amount of treatment for your own purposes.

*Section 2: Hybrid Absorbers / Diffusers*

There are certain companies that build diffusers overlapped by a layer of absorbent material. The entire device is then covered in cloth material (for aesthetic appeal). Such a device is known to have diffusive and absorptive properties. However, these devices are also very likely to absorb more of the high frequencies than the low frequencies, much like carpet. Furthermore, their effectiveness at actually diffusing sound are thereby limited to some mid-range and mostly lower range diffusion. In rooms requiring strict acoustic properties, these objects might be most wisely saved for emergency use only – that is, if wall space is necessarily limited. On the other hand, if the properties of such a device has been tested thoroughly, and its properties known, and if those properties are shown to positively contribute to the room’s acoustic properties, then use of such devices is quite acceptable.

*Section 3: Modular Treatment*

There are times when certain rooms need to be adjustable for different applications. What should be done in these cases?

Acoustic treatments can be made to mount on walls over treated areas to counter the treatment with other acoustic properties. For example, if a drum room needs to be more live for a particular project, diffusers can be made to fit over the absorbing units on the wall and hung accordingly, masking the absorbent properties from the room and replacing them with reflections. Likewise, absorbers may also be constructed to fit over diffusers (or any blank wall space) and absorb the sound energy from a room.

These objects could also be placed on the floor on coasters and rolled around into the rooms where needed, placed strategically where they might block treatment already in place. There are also such designs existing in which individuals have constructed devices which are absorbent on one side, diffusive on the other. These can be as tall or short as deemed necessary, stacked side by side, and even used to create smaller compartments within a room.

Refer, of course, to the DIY Projects Forum for ideas and building suggestions.


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