minimizing acoustic distortion in project...

____________________________________________________________________________________________Listen to the Music, Not the Room!

1

By

Dr. Peter D’AntonioRPG Diffusor Systems, Inc.

Recording studio design has changed dramatically since Ifirst entered the audio industry back in 1971. In thoseJurassic days project studios were called “semi-pro”studios, because they did not possess the electronic andacoustical performance of the professional 16 trackstudios. In the intervening 27 years, the hardware gap hasbeen narrowed, if not erased, by new electronic digitaltechnology. On the other hand, the acoustical gap haswidened. This is due to the fact that the professionalstudio designers have made extensive use of advancedcomputerized acoustical measurement tools, computermodeling and simulation, room acoustics andpsychoacoustics research and innovative acousticalproducts. Until recently, project studios haveconcentrated primarily on the electronic “gear” andessentially ignored or worked around acoustical issues.As the project studio format becomes more and morepopular and finds more and more acceptance on theBillboard charts and in post-production, acoustical issuesbecome the most sonically glaring omission.

In view of the way Project Studios have evolved, anemphasis on electronic hardware is understandable.Project studios have historically grown by sequentialaddition of gear. The owner would initially purchase thenecessary gear to get started. When the budget allowed, anew microphone, signal processor, or loudspeaker wouldbe added. In this scenario, at some point a critical mass ofgear is installed and the project studio owner would thenhave to decide whether he wanted to add new bells andwhistles or actually hear what he or she is doing moreaccurately. With the amount of hardware in masscirculation, many owners are in this position and studioacoustics is a very real issue. A more contemporaryscenario for the Project Studio is to include a basicacoustical package at the inception. There is moreawareness of the importance of accurately hearing what isattempting to be accomplished in the studio at the expenseof that special bell or whistle that can be added later.Also, as the cost of acoustical materials for ProjectStudios has dropped and more choices have been madeavailable, including acoustics does not necessarily have tobe an either-or choice. Additionally, as computerizedmeasurement programs have become more affordable,Project Studio owners can determine for themselves theimprovement even modest acoustical design can offer.

In this article I hope to address the relevant acousticalissues facing project studio design, make some

suggestions about addressing these problems and the realworld limitations of these suggestions.

The most relevant point is transferability. The audioproduct created in a recording studio needs to soundsimilar in a wide range of listening rooms. Thus, theaudio product must be transferable to these differentlistening environments. The first step in this process is tounderstand the sonic ramifications of potential acousticalproblems in the room in which the audio product iscreated. This means that a recording engineer must beaware of the acoustical signature of the room he/she isworking in, so that the room’s signature is not embeddedinto the audio product. A simple example of this ismixing in too little low end in a room with significant lowfrequency modal emphasis. When played back in a roomwith uniform or deficient low frequency response, the mixwill sound thin, but more importantly it will sounddifferent. Another example is mixing with near fields in aconsole arrangement with strong console reflections. Themixer will unconsciously and unsuccessfully try toequalize the resulting comb filtering. When the audioproduct is played back in another listening environment,timbre and imaging corruption will be heard. Since wehave little control over the acoustical design of theenvironments into which the audio product will betransferred to, we should make every effort to providegood acoustics in the creation environment so that we canhear and execute the necessary imaging and signalprocessing adjustments. An engineer needs to feel securethat the countless hours spent creating an audio productare not wasted. We don’t want to build the proverbialboat and not be able to take it out of the basement. Theinteraction between the room, the loudspeaker and listenermay produce what I call “acoustic distortion”. Everyonein the recording industry is conscious of electronicdistortion, but acoustic distortion sometimes is overlookedin the pursuit of more electronic gear.

[1] ROOM REFLECTIONS CAUSEACOUSTIC DISTORTION

Acoustically we can divide rooms depending on whetherthey are used as music production rooms, like concerthalls where the room contributes to the character of thesound auditioned, and music reproduction rooms, likecritical listening rooms where the room is neutral andallows the spatial and spectral content to be auditioned.

Minimizing Acoustic Distortion in Project Studios


2

The recording control room or project studio is essentiallya “small” room acoustically. The volume isapproximately 2,000-3,000 cubic feet (57-85 cubicmeters). The decay time is roughly 100 to 400 ms. Theroom’s acoustical signature is strongly characterized by itslow-frequency modal response and speaker-boundaryinterference, strong early reflection interference fromsurfaces, consoles and equipment racks, flutter echoesfrom untreated parallel reflective surfaces, sparse latereflection density and spatiality leading to poor sounddiffusion and envelopment.

When the sound from a loudspeaker encounters theboundaries of a room, a very complex series of reflectionsoccur. It is very difficult to isolate the direct sound alone,because these reflections interact with it and amongthemselves to produce a wide range of effects, which wewill call acoustical distortion. If proper acoustic design isnot utilized, a room may introduce sonic distortion thatprevents the listener from hearing all of the detailedinformation the loudspeakers and electronics are capableof delivering. We need to be as mindful of acousticdistortion as we are about electronic distortion and reduceboth of them to appropriate levels.

The sound that we hear in a critical listening room isdetermined by the complex interaction among the qualityof the electronics, the quality and placement of theloudspeakers, the hearing ability and placement of thelistener, the room dimensions (or geometry if non-cuboid)and the acoustical condition of the room’s boundarysurfaces and contents. All too often these factors areignored and emphasis is placed solely on the quality of theloudspeakers. However, the tonal balance and timbre of agiven loudspeaker can vary significantly, depending onthe placement of the listener and loudspeaker and theroom acoustic conditions. In some cases the differencesbetween different loudspeakers located in the samelocation in a room can be less than the differencesintroduced by moving the same loudspeaker to differentlocations in a room.

The acoustic distortion introduced by the room can be soinfluential that it dominates the overall sonic impression.The causes of acoustic distortion are:1. Modal Coupling- the acoustical coupling between

the loudspeakers and listener with the room’s modalpressure variations or room modes

2. Speaker-Boundary Interference- the coherentinteraction between the direct sound and theomnidirectional early reflections from the room’sadjacent boundaries

3. Comb Filtering- the coherent constructive anddestructive interference between the direct sound andearly reflections

4. Sound Diffusion- the spatial and temporal reflectionpattern due to mid and late arriving reflections

When you stop and realize that the loudspeaker/roominterface is your acoustical microscope, it seems prudentto strive for the ultimate sonic resolution. Remember,dollar for dollar the acoustical treatment of your room willmake more of an audible difference than any piece ofelectronic hardware, speaker, or cable. The goal of thisarticle is to collect all of this information in one place andattempt to raise the reader's awareness of potentialacoustical problems in the rooms they work in so that theycan take measures to compensate for these sources ofacoustical distortion.

[2] ACOUSTIC DISTORTION AFFECTSPERCEPTION OF SOUND

Despite the marvelous electronic advances in digitalhardware, sound must eventually travel the acousticanalog path from loudspeaker to our ears. Since we alsohave a brain attached to our ears, a very complexpsychoacoustic process is involved in sound perception.Therefore, since we are dealing with acoustical distortion,we should first attempt to minimize the problemacoustically, before sophisticated electronic equalizationis used. In general, a combination of the two may producethe best result, but we should attempt to minimize theacoustic problem before reaching for the equalizer.

Acoustic distortion affects threepsychoacoustic perceptions,shown in Figure 1, namelyFrequency response or timbre,Imaging, and Spatial Impression.Frequency Response or Timbrerefers to the perception of theharmonic content of the musicand its spectrum. Imaging refersto the size of sonic images ofvoices and instruments, i.e. theirapparent width, height and depthand their apparent location ofsonic images, i.e. their phantomposition between stereo left and

right or between center/left, center/right, left front/leftrear, right front/right rear, left rear/right rear inmultichannel formats. Spatial Impression is the sense ofspatiality, envelopment or sense of immersion in the sonicevent we experience.

BASS RESPONSE

SPATIAL IMPRESSION

IMAGING

Figure 1. Threepsychoacousticareas affected byacoustic distortion


3

[3] HEARING IS BELIEVING

Acoustic Distortion is difficult to describe. Hearing isbelieving! Some of the effects we describe can besimulated using hardware that recording engineerstypically have on hand. In Figure 2 we describe anequivalent circuit for acoustical distortion. The signalfrom a DAW or mixer is fed to a parametric or graphicequalizer, then to a digital delay unit and finally to anamplifier and loudspeaker. Wouldn’t it be a rather badtrick to secretly insert this circuit in the signal path priorto a critical mix? The circuit would boost 71, 142, 213Hz by 10 dB, and introduce 4ms, 7 ms, 9 and 10 ms ofdelay. The engineer would mix the sound product andsubconsciously attempt to adjust for these effects.Imagine the surprise when they were informed of this dirtydeed and they played back the mix with the equalizer anddigital delay switched off!

This is not a practical joke, because the room is playingthis trick on engineers all the time. Everything you recordand mix is being “heard’ through the “lens” of the room.It’s like looking at the world wearing “rose colored”glasses. You are listening to your music wearing “roomcolored” ear muffs.

0ms

4ms

7ms

9ms

10ms

Figure 2. Equivalent circuit for acousticaldistortion


4

[4] SOURCES OF ACOUSTICDISTORTION

[4.1] Room Modes

All mechanical systems have natural resonances. Theseresonances are one aspect that differentiates acousticinstruments. In rooms, sound waves coherently interfereas they reflect back and forth between hard walls. Thisinterference results in resonances at frequenciesdetermined by the geometry of the room. In completelyreflective rectangular (cuboid) rooms, where the normalcomponent of the particle velocity is zero at the surface,the modal frequencies, associated with the eigenvalues ofthe wave equation, fn n nx y z

, are determined by Eq. 1.

fc n

L

n

L

n

Ln n nx

x

y

y

z

zx y z

=

+

+

2

2 2 2

(1)

nx, ny and nz are non-negative integers, Lx, Ly and Lz arethe length, width and height of the room and c is the speedof sound. These modal frequencies are distributed amongaxial modes involving two opposing surfaces (e.g. nx=1,ny=0, nz=0), tangential modes involving 4 surfaces (e.g.nx=1, ny=1, nz=0), and oblique modes involving allsurfaces (e.g. nx=1, ny=1, nz=1).

For an axial mode between two opposite boundaries, thisfrequency is equal to the speed of sound, c, divided bytwice the room dimension in that direction. For example,for c = 1,130 ft/sec, a 15’ wall to wall dimension results ina first-order fundamental room mode of 37.6 Hz.

As an example, in Figure 3 we present the measuredmodal frequency response of a room whose length is 15’.The loudspeaker was located in a corner and the

microphone was placed against a wall perpendicular to the15’ dimension, in order to record all axial modes. Thefirst-order (100), second-order (200) and third-order (300)modes are identified in Figure 3 at 37.6 Hz, 75.3 Hz and113 Hz, respectively. Notice the (100) mode has onenodal plane, the (200) has two and the (300) has threeperpendicular to the 15’ length x-axis. As the frequencyincreases, room modes are still present, but their numberand density increase and are not perceived as a problem.

Each of these modal frequencies has an associated 3-dimensional pressure distribution in the room. In Figure 4we present a 2-dimensional illustration of the pressuredistribution perpendicular to the length of the room, whichis normalized to one. The numbers nx, ny and nz indicatethe number of nodal planes of zero sound pressureperpendicular to the x-axis, y-axis and z-axis. In thisexample, ny and nz are zero and nx takes the value 1, 2 and3. Thus, in addition to choosing dimensional ratios thatuniformly space the modal frequencies, we must considerhow the listener and loudspeakers couple with the modalpressures that exist at the locations of the listener andloudspeakers.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Fractional Room Dimension

Nor

mal

ized

Sou

nd P

ress

ure

Leve

l

First-Order Mode Second-Order Mode Third-Order Mode

Since conventional closed or ported dynamicloudspeakers are pressure sources, they will couple mostefficiently when placed at a high pressure region of themodal or sometimes called standing-wave pressuredistribution. The loudspeaker placement will accentuateor diminish the coupling with the modal pressurevariations at each of the modal frequencies. Similarly, alistener will hear different modal emphasis depending onwhere he or she is seated. Figure 4 illustrates how thesound energy is distributed along a room dimension. Theroom dimension is shown as a fraction ranging from 0 to1. 0.5 would be in the center of the room and 1 would be

Figure 3. Measured modal frequency response ina room 7.5’(W) x 15’ (L) x 9’ (H). The (100),(200), and (300) modes are identified.

Figure 4. Normalized energy distribution of the firstthree modes in a room.

(100) (200) (300)


5

against a wall. Examining Figure 4 reveals that thefundamental has no energy in the center of the room.Physically this means that if you were sitting in the middleof the room you would not hear this frequency. The firstharmonic, however, is at a maximum. It can be inferredfrom this plot that, in the center of the room all oddharmonics are absent and all even harmonics are at amaximum.

Sound waves are longitudinal waves. While oftenpictured as a sinusoidal transverse wave, sound waveactually oscillate (expand and contract) in the direction ofpropagation. As the sound waves expand and contractthey cause high-pressure regions and low-pressureregions. The instantaneous pressure on opposite sides of apressure minimum has opposite polarity. The pressure onone side is increasing while the pressure on the other sideis decreasing. The position of a loudspeaker and listener’sear with respect to these pressure variations will determinehow they couple with the room.

[4.1.1] Non-Rectangular RoomsMost project studios are rectangular simply because theyare converted bedrooms, offices, garages, etc. Since theyare rectangular we can calculate the modal frequenciesand pressure distributions. Once they become non-rectangular, none of this simple math applies and we mustrely on finite element method (FEM) or boundary elementmethod (BEM) analysis, which we will discuss later. Thesimple nodal planes become nodal surfaces!

FEM and BEM simulations are used extensively in theaerospace, automotive and underwater acousticscommunities, but the cost of the programs precludes theirevery day use in architectural acoustics. At RPG we use aprogram called SysNoise to carry out FEM/BEM analysesas well as an in-house proprietary code to optimizesurface shapes using iterative BEM calculations. In BEMcalculations a mesh of the enclosure, consisting ofhundreds or thousands of small elements, is created. Theelement size is typically 1/6 of the upper frequency limit.There exists an equation for each element over which thepressure is assumed constant. These equations are solvedfor each frequency of interest and the sound pressure levelat any observation point can be determined. While this isa horrendous calculation, it is doable for any shapeenclosure. The FEM approach determines theeigenmodes and the frequency response is determined bysummation of the modes.


6

[4.2] SPEAKER-BOUNDARYINTERFERENCE RESPONSE

Room modes develop as reflected sound interferes withitself. This next type of acoustic distortion is due to thecoherent interference between the direct sound of aloudspeaker and the reflections from the room, inparticular the corner immediately surrounding it.

This distortion occurs across the entire frequencyspectrum, but is more significant at low frequencies. Werefer to it as the Speaker Boundary Interference Responseor SBIR. The room’s boundaries surrounding theloudspeaker mirror the loudspeaker forming virtualimages. When these virtual loudspeakers (reflections)combine with the direct sound, they can either enhance orcancel it to varying degrees depending on the phase

relationship between the reflection and direct sound at thelistening position. In Figure 5 a loudspeaker is located 3’from each room surface with coordinates (3,3,3). Thefour virtual images on opposite sides of the main roomboundaries that are responsible for first order reflectionsare also shown. A virtual image is located an equivalentdistance on the opposite side of a room boundary. Thedistance from a virtual source to the listener is equal to thereflected path from source to listener. In addition to thefour virtual images shown, there are 7 more. Three virtualimages and 1 real image in the speaker plane and 4 virtualimages of these above the ceiling and floor planes.Imagine that the walls are removed and 11 additionalphysical speakers are located at the virtual imagepositions. The resultant sound at a listening positionwould be equivalent to the sound heard from one sourceand 11 reflections!.

The effect of the coherent interference between the directsound and these virtual images is illustrated in Figure 6.The SBIR is averaged over all listening positions with thespeaker located 4’ from one, two and three wallssurrounding the loudspeaker. It can be seen that as eachwall is added, the low frequency response increases by 6dB and the notch, at roughly 100 Hz, gets deeper. It isimportant to note at this point that once this notch iscreated, due to poor placement, it is virtually impossibleto eliminate without moving the listener and loudspeaker,since it is not good practice to electronically compensatefor deep notches. Thus the boundary reflections eitherenhance or cancel the direct sound depending on the phaserelationship between the direct sound and the reflection atthe listening position. Initially, the direct sound andreflection are in phase and they add. As the frequencyincreases the phase of the reflected sound lags the directsound. At a certain frequency the reflection is out ofphase with the direct sound and a cancellation occurs.The extent of the null will be determined by the relativeamplitudes of the direct sound and reflection. At lowfrequencies there is typically very little absorptionefficiency on the boundary surfaces and the notches canbe between 6 and 25 dB! The conclusion is obvious,never place a speaker’s woofer equidistant from the floorand two surrounding walls.

The low frequency rise in Figure 6 illustrates why one canadd more bass by moving a loudspeaker into the corner ofa room. Actually one has two choices. Either move theloudspeaker as close to the corner as possible or as faraway from the corner as is physically practical. As youmove the speaker closer into the corner, the firstcancellation notch moves to higher frequencies, where itmay be attenuated with porous absorption. This can beseen in Figure 6 for the last condition in which theloudspeaker is positioned 1’ from the floor, rear andsidewalls. In addition, the loudspeaker’s own directivitypattern diminishes the backward radiation thus reducing

ORIGIN OF SOUND SOURCE(3,3,3)

(3,-3,3)VIRTUAL IMAGE

(3,3,14)VIRTUAL IMAGE

(-3,3,3)VIRTUAL IMAGE

(3,3,-3)VIRTUAL IMAGE

CEILING

WALL

FLOOR

Figure 5. Sound from real and virtual speakerscombine to create the speaker/boundaryinterference response.

-25

-20

-15

-10

-5

0

5

10

15

20

0 200 400 600 800 1000

Frequency, Hz

Pre

ssur

e, d

B

1 Boundary X=4'

2 Boundaries X=4', Y=4'

3 Boundaries X=4', Y=4', Z=4'

3 Boundaries X=1', Y=1', Z=1'

Figure 6. Speaker-Boundary Interference Responsefor several loudspeaker positions near a corner.


7

the amplitude of the reflection relative to the direct sound.This principle is the basis for flush mounting loudspeakersin a corner soffit. The bad news is that with theloudspeaker in the wall-wall dihedral or wall-wall-ceilingtrihedral corner, the loudspeaker very efficiently coupleswith the room modes. If the dimensional ratios are poorleading to overlapping or very widely spaced modalfrequencies there will be significant modal emphasis.Professional loudspeaker manufacturers usually providethe low frequency roll off equalization to compensate forthe added emphasis of flush mounting the speaker.

We can also move the loudspeaker farther away from theadjacent corner. In this case the first cancellation notchmoves to lower frequency, hopefully below the lowercutoff frequency of the loudspeaker or the hearingresponse of the listener. To obtain a 20 Hz firstcancellation notch one needs to position the loudspeaker14’ from the rear wall!

Clearly, some happy medium needs to be found and withthe myriad alternatives available the most effectiveapproach is to start with a multi-dimensional computeroptimization (described later) and tweet to taste.


8

[4.3] Comb Filtering

Another form of acoustic distortion introduced by roomreflections is comb filtering. It is due to interferencebetween the direct sound and a reflected sound. In criticallistening rooms, we are primarily concerned with theinteraction between the direct sound and the first-order(i.e. single-bounce) reflections. Reflections cause timedelays, because the reflected path length between thelistener and source is longer than the direct sound path.

-20

-15

-10

-5

0

5

10

0 500 1000 1500 2000 2500 3000

Frequency, Hz

Leve

l, dB

0 dB3 db6 dB12 dB

Thus when the direct sound is combined with the reflectedsound, we experience notches and peaks referred to ascomb filtering. The reflections enhance or cancel thedirect sound to varying degrees depending on the phase(path length) difference the reflection and the direct soundat the listening position. An example of comb

10

100

1000

10000

100000

0.1 1 10 100

Total Delay, Feet

Fre

quen

cy, H

z

First NullSecond NullThird NullFourth NullFifth Null

-6

-4

-2

0

2

4

6

8

10

12

0 500 1000 1500 2000 2500 3000

Frequency, Hz

Leve

l, dB

filtering between the direct sound and a reflection delayedby 1 ms is shown in Figure 7. Four conditions areillustrated. 0 dB refers to the theoretical situation inwhich the reflection is at the same level as the directsound. The remaining three interference curves indicatesituations in which the reflection is attenuated by 3, 6 and12 dB. In Figure 8 the locations of the first 5 interferencenulls are indicated as a function of total delay. A delay of1 ms or 1.13’ produces a first null at 500 Hz withsubsequent notches 1000 Hz apart. The constructive

interference peaks lie midway between successive nulls.When the reflection is at the same level as the directsound the nulls theoretically extend to infinity. This nameevolved, because comb filtering resembles a series ofequally spaced notches like the teeth of a comb. Thelocation of the first notch is given by the speed of sounddivided by 2 times the total path length difference. Thespacing between subsequent notches is twice thisfrequency. In Figure 9 the comb filtering due to a seriesof regularly spaced reflections separated by 1 ms (flutter

Figure 7. Comb filtering with 1 one reflection delayedby 1 ms with attenuated of 0, 3, 6 and 12 dB relative tothe direct sound.

Figure 8. Comb filter destructive interference nullfrequencies for a single reflection delayed 1 ms fromthe direct sound. Constructive interference peaksoccur midway between adjacent nulls.

Figure 9. Comb filter due to equi-spaced flutter echoes1 ms apart.

Reflection Control

Direct Sound Only

Figure 10. Time and frequency response of the directsound from a loudspeaker.


9

echo) is shown. Note how the peaks are much sharperthan the single reflection.

The audible effect of comb filtering is easy to experienceusing a delay line. If you combine a signal with a delayedversion, you will experience various effects referred to aschorusing or flanging, depending on the length of thedelay and the variation of the delay with time. Shorter

delays have wider bandwidth notches and thus removemore power than longer delays. This is why microsecondand millisecond delays are so audible.The effect of a reflection is illustrated in Figure 10 andFigure 11. In Figure 10 we illustrate the time andfrequency responses from the right speaker only. Theupper curve shows the arrival time and the lower curveshows the free-field response of the loudspeaker. InFigure 11 we show the effect of adding a side wallreflection to the sound of the right speaker. The uppercurve shows the arrival time of both the direct sound andthe reflected sound. The lower curve shows the severecomb filtering that a single reflection introduces. If yourspeaker had a free-field response like this lower curve,you probably would not have purchases it. Yet, manyrooms are designed without reflection control. In realityour ear/brain combination is more adept at interpreting thedirect sound and reflection than the FFT analyzer, so thatthe effect may be somewhat less severe.

Comb filtering is controlled by attenuating the roomreflections or by controlling the loudspeaker’s directivityto minimize boundary reflections. If the loudspeaker hasconstant directivity as a function of frequency, then broadbandwidth reflection control is necessary. Since thedirectivity of conventional loudspeakers increases withfrequency, low frequency reflection control is important.For this reason, one would not expect to control low

frequency comb filtering effects with a thin porousacoustical foam or panel.

Comb filtering can be controlled by using absorption,which removes energy from the room, or diffusion, whichdistributes the reflection over time, without absorption.Both approaches are valid and produce differentpsychoacoustical reactions. Using absorption to reducethe effect of a specular reflection, will produce pin pointspatial phantom images. On the other hand, diffusion willproduce sonic images with more spaciouness (width,depth and height). The degree of this effect can becontrolled.

Comb filtering usually results in image and timbrecorruption. The effect of comb filtering at low frequencyfrom the speaker’s constructive interference with thesurfaces surrounding it have been discussed in theSpeaker-Boundary Interference section. Reflections fromsurfaces between the loudspeaker and the listener give riseto constructive and destructive interference as shown inFigure 7. Floor, ceiling, and sidewall reflections are causefor acoustic distortion. The floor bounce can produce lowfrequency problems, which are difficult to deal with sinceit is difficult to provide any passive absorption ordiffusion on the floor. However, this is one area wherethat large obstacle with many knobs on it can actually bebeneficial in diffusing these floor reflections. Just whenyou felt secure in using near field monitors, I have theunfortunate task of informing you that console reflectionsmay create comb filtering at a level equal to or greaterthan room effects caused by the interaction of mid/farfield loudspeakers. Another phenomenon to be consciousof is the sequence of notches caused by the reflection offthe wall behind the listener. This first notch occurs at thespeed of sound divided by 4 times the distance betweenthe listener and the rear wall. Thus a 5’ distance wouldcause notching at 57, 170, 283 Hz, etc. Low frequencyabsorption is probably the best approach to minimizingthis effect. Low frequency diffusion has the addedadvantage of increasing the modal density, but at theexpense of consuming a lot of real estate.

Reflection Control

Direct Sound &1st Reflection

Figure 11. Time and frequency response of the directsound combined with a side wall reflection. The combfiltering is apparent


10

[5] ACOUSTICAL SOLUTIONS

We now discuss some practicalsolutions. Since real worldlimitations have a nasty habit ofgetting in the way of ourbeautifully conceivedmathematical models, we will alsomention the limitations of thesesuggestions. We can think of atool kit of Bass Tools to improvebass response, Imaging Tools tocontrol imaging and Spatial Toolsto improve sound diffusion andour sense of envelopment.

[5.1] Bass Tools

The perceived bass response in a room is controlled by thefree-field loudspeaker response, the room dimensions, theacoustic coupling of the listener/loudspeakers to themodal pressure variations, the speaker-boundaryinterference between the direct sound and adjacentreflections, the internal contents of the room, theacoustical nature of the boundary surfaces and surfacetreatment and the hearing response and training of thelistener.

Any absorption or amplification over a frequency range,which is introduced by the room, will color the sound thatwe hear. The room will thus introduce its own signaturerather than having a flat frequency response. Since mostof today’s speakers are of high quality and we may nothave any control over the room's dimensions, we canfocus our attention on proper speaker placement andacoustical treatment. Proper speaker placement canoptimize the coupling with the room’s standing wavepattern and the interference between the speaker andreflected sounds from the nearby corner. This can resultin severe cancellations if the speaker is located an equaldistance from all boundaries. After locating the speakers(and the listener) properly, we may choose to utilize lowfrequency absorbers to damp room resonances andminimize the speaker/boundary interference. Followingall of this you may want to fine-tune the bass responseusing electronic equalization.

[5.1.1] Room DimensionsIf one is building a new room, it is useful to considerdimensional ratios. One might wonder if there is an idealroom. As usual the answer is yes and no. If the room isrectangular there are various approaches to choosedimensional ratios that uniformly distribute the modalfrequencies. One of these determinations by Louden,illustrated in Table 1, yields the following dimensionalratios in order of preference. As an example, a room with

a 10’ ceiling height would have a 14’ width and a 19’length. At RPG we have also developed an automatedalgorithm to minimize the standard deviation of the modalpressure response, which may also prove helpful.

Table 1. Room dimensions in order of preferenceaccording to Louden.

ORDER LENGTH WIDTH1 1.9 1.42 1.9 1.33 1.5 2.14 1.5 2.25 1.2 1.56 1.4 2.17 1.1 1.48 1.8 1.49 1.6 2.110 1.2 1.411 1.6 1.212 1.6 2.313 1.6 2.214 1.8 1.315 1.1 1.516 1.6 2.417 1.6 1.318 1.9 1.519 1.1 1.620 1.3 1.7

Rectangular Modal Prediction Limitations:The modal frequency calculations based on rectangularroom dimensions assume that the room is rectangular andthat the walls are perfectly reflecting. Real rooms are attimes non-rectangular, wall surfaces and windows mayabsorb low frequencies due to diaphragmatic vibrationand also transmit low frequencies, and internalfurnishings can scatter and absorb low frequencies.These effects will cause an error in the calculated modalfrequencies. At low frequencies small perturbations, likealcoves and soffits, which are small compared to the longwavelengths may introduce only small changes. Also anyprediction should properly weight the axial, tangentialand oblique modes in this order. Another thing that isassumed is perfect acoustical coupling between sourcesand modes, in which all modes are uniformly energized.The actual locations for loudspeakers may only energizea subset of the modes and the listeners may be inlocations, which do not permit them to hear the effects ofeven those modes that are excited.

One might wonder if making a room non-rectangular is abenefit. The first thing to understand is that making theroom non-rectangular does not make modes disappear anddoes not make the modal behavior less pronounced than inan equivalent rectangular room, just different. The

BASSTOOLS

SPATIALTOOLS

IMAGINGTOOLS

Figure 12. Acoustictools improveimaging,spaciousness andbass response.


11

magnitudes in the pressure variations do not varysubstantially, but the changes in frequency distributionand nodal lines are non-intuitive. Splaying of sidewalls orceiling to reduce high frequency flutter effects, hasminimal effect on modal problems and the mid-dimensionof the tapered wall may be used for rectangular analysis.

Beneficial low frequency modal mixing leading toincreased diffusion may be introduced even by makingone wall non-rectangular. However, one should have anacoustician carry out FEM calculation to verifyperformance to insure the effort is producing a beneficialand useful effect, since non-rectangular construction isoften more expensive and introduces non-symmetriceffects, which may affect imaging.

BEM/FEM Limitations:The limitation of these approaches is that the acousticalproperties of the enclosure must be precisely known. Atlow frequencies many structures exhibit panel orHelmholtz resonances, with associated large changes inimpedance, over small frequency ranges. Data for theacoustic properties (complex impedance) of commonlyused structural and decorative materials are notavailable. Data may be obtained from impedance tubetesting, but this too may lead to errors because samplescannot be tested at full scale. Once these data becomemore widely available progress in non-rectangular roompredictions may play a more active role in architecturalacoustics.

[5.1.2] Optimize Location of the Listenerand Loudspeakers Since the modal coupling andspeaker-boundary interference are position related,optimizing these effects seems like a good way to start.Especially, since they involve a cost-free remedy. Onecould start by placing the loudspeakers in a given locationand listening to the response. Then moving theloudspeakers and listener locations in a systematic trialand error manner until a satisfactory response is achieved.This may be practical for mono, or maybe even stereo, ifyou have enough patience and your monitors are notextremely heavy, but for multichannel 5.1 digital formats,this may prove impractical. At RPG we considered waysof letting the computer do the moving! We can describethe necessary steps by the acronym DESIRE.

Describe- How do we mathematically describe thesystem?To accomplish this one needs to be able to predict theroom response at hundreds or maybe thousands oflistener/loudspeaker locations. For rectangular rooms,which fortunately model many project studios, one canaccurately calculate the room response for a givenlistener/loudspeaker location using either the modesummation method or by a reflection summation

method and Fourier transforming the resulting room’simpulse response.

Mode Summation Method- The pressure at the listeningposition from a group of loudspeakers in a rectangularroom can be modeled by a rather complex expression ofsix cosine terms containing the integer mode identificationand room dimensions, the damping factors of the modes,etc. The calculation is time intensive and care must betaken to include all of the modal frequencies contributingin the frequency range of interest, plus corrections forthose modes lying outside this range. This systemdescription is available for use in the program.

Reflection Summation Method- Since we will beevaluating many possibilities, the equivalent reflectionsummation impulse response approach using an imagemodel is more efficient and is the default approach used inthe program. The image model includes only thoseimages contributing to the impulse response and providesappropriate weighting of the contribution of each mode.It has the advantage that it is a transient calculation, inwhich one could use any desired amount of time. It offersthe additional benefit that having determined the impulseresponse by following the reflection history of raysreflected around the room, we could extract the effects ofthe speaker-boundary interference from the early timeportion and the modal response from the entire timehistory.

Since modes can only exist if reflections are specularlyreflected over many orders. You may wonder how thesurfaces of a relatively small room can produce low-frequency specular reflection, when the wavelengthsassociated with low frequencies are larger or comparablewith the extent of the boundary surfaces. In a free field awall of say 10’ would produce diffusion at 113 Hz, whichhas a wavelength of 11.3’. However, in a rectangularroom, the virtual images as described in the SBIR section,effectively extend the boundary extent to infinity. Thus arectangular room acoustically consists of three sets ofintersecting infinite planes. Boundary absorption maypractically reduce the extent of these planes, but theeffective reflection is specular even though the physicalsurfaces are small.

Evaluate- How do we evaluate the calculatedperformance?Once the speaker-boundary and modal responses arecalculated, we must theoretically evaluate them. We mustfind a parameter that corresponds to what we might say ifwe were actually listening to this trial location. Toaccomplish this we adopted the flatness of the room’sfrequency response as a predictor. This was selectedbased on the extensive work of Floyd Toole and hisassociates in determining the importance of a flat andsmooth loudspeaker response on listener preference. To


12

evaluate the quality of the listener/loudspeaker locations,we sum the standard deviation of the room responsedetermined from a cosine squared windowed FFT of thefirst 65 ms of the impulse response and the standarddeviation of the entire impulse response. The standarddeviation has proven to be a reliable statistical indicator ofdeviations from a mean response. Therefore, we can nowlet the computer do the moving, by automaticallyevaluating as many trial listener/loudspeaker locations asis necessary to produce a satisfactory room response.

Search- How do we search the millions of possible triallocations?Out of the millions of possible locations for the listenerand loudspeakers, how do we automatically decide whichtrial locations to evaluate next. Fortunately,mathematicians have examined this problem anddeveloped intelligent search engines. These algorithmslearn as they go and hence find the optimum trajectorythrough the error space using multi-dimensional simplexminimization.

I teRate- How do we automate this trial and erroroptimization cycle?We then need to set up a cyclical iteration path in whichthe impulse response for new trial locations aredetermined, room response calculated, standard deviationdetermined and a comparison between desired quality andcurrent quality is made. If the quality is acceptable theprogram ends. If not another set of trial locations isdetermined and evaluated. This is accomplished using asimple If check.

End- How do we know when we are done?We now need a way to tell the computer it is finished.This is accomplished by storing the weighted standarddeviations for each trial position of listener andloudspeakers. When further movement does not produceany further benefit or if the number of iterations exceeds acertain number the program ends.

In 1997, we put all of this together and published the firstalgorithm to simultaneously minimize the effect of themodal coupling and the speaker-boundary interferenceusing an image model and multi-dimensional optimizationtechniques. The program allows a fast evaluation of avery large number of possible listener and loudspeakerlocations. It also indicates the first order reflectioncoordinates for application of mid/high frequency surfacetreatment to address imaging issues. We thus have amethod to optimize the placement of the listener andloudspeakers, within physically accessible or desirableregions of the listener and loudspeakers for any numberand type of loudspeakers. The Speaker-BoundaryInterference Response improvement between the worstlocations found for the listener and loudspeaker is shownin Figure 13. The improvement in the modal responses

between the worst and best locations of listener andloudspeaker is shown in Figure 14.

50

60

70

80

90

100

0 50 100 150 200 250 300

Frequency (Hz)

Best case

Worst case

Figure 13. Speaker-Boundary Interference Thestandard deviations are 4.67 and 8.13 dB for the bestsolution and worst case respectively.

50

60

70

80

90

0 50 100 150 200 250 300

Frequency (Hz)

Best case

Worst case

Figure 14. Modal Response- The standard deviations are3.81 and 6.28 dB for the best solution and worst case,respectively

Real World Limitations-Real rooms may not be perfectly rectangular, they may belarge bulky obstacles with lots of knobs in the room, like aconsole, walls may not be perfectly reflective (like onelayer of drywall), there may be windows, etc. At lowfrequencies, the wavelengths are very long (50 Hz being22.6’) that small perturbations are not “seen” and theprincipal dimensions may be satisfactory to describe theroom. In light of all of this, the multi-dimensionaloptimization should be regarded as a fast way to get closeand it is always advisable to measure the room usingimpulses, swept sine waves, maximum length sequencesor transfer function approaches. No directivityinformation is used for sources, but this is not a serious


13

limitation as woofers operating below 200-300 Hz areomnidirectional.

[5.1.3] Sub-WooferSo far we have discussed optimizing the location of thewoofers to find the best acoustical coupling with theroom’s modal pressure variations and speaker-boundaryinterference. While improving the bass response bylocating full range loudspeakers, there is the obviouschance to adversely affect the higher frequency effects ofimaging. There may be occasions where a choice has tobe made, since both may not be achievablesimultaneously. A convincing arguments for the use ofone or more separate sub-woofers is that they offer theopportunity to achieve good bass response by locating thesub-woofer independently of the mid/high frequencyloudspeakers. Multiple sub-woofers also offer theopportunity to increase modal mixing as well as offer lowfrequency spatial effects, which some argue are notperceivable. Optimum sub-woofer locations areachievable by physical trial and error or by multi-dimensional analysis. The obvious place to start is in thecorner, since the sub-woofer couples so efficiently in thislocation. The potential problem with this location is thatall of the modes will be excited and if the dimensionalratios are poor, this location will lead to severe low-frequency coloration. It’s best to predict the optimumperformance and then let your ears be the judge.

[5.1.4] Damp the ModesOne method to reduce the magnitude of these effects is toincrease the damping factors of all of the modes bysuitable use of low frequency absorptive materials. Byincreasing the damping factor, the maximum amplitude ofthe resonance is reduced and the range of frequencies overwhich it acts is widened. Most people are familiar withacoustical foam or other porous absorbers, which absorbsound by converting sound energy into heat. Theefficiency of a porous absorber is highest when the soundis traveling at its highest velocity. This point is reached at¼ of the wavelength and thus varies with the frequency.At low frequencies like 100 Hz, this distance is about 2.5’from the wall. Unfortunately at the wall surface where theporous absorber is usually placed, the particle velocity iszero. This is where the sound wave changes direction onreflection and hence the velocity is zero. Since porousabsorbers rely on particle velocity, they have limitedefficiency at low frequencies. The point to be taken awayfrom this discussion is that placing porous absorbers on awall or in a corner is pointless.

Fortunately, there is another mechanism that can beutilized. At the wall the particle velocity is zero, but thepressure is a maximum. To exploit this phenomenon, oncan employ a membrane with high internal losses and anair cavity with a porous material near the membrane. Themembrane can be tuned to sympathetically oscillate with

the pressure fluctuations at low frequency, thus creatingair movement through the internal porous material. These

0

0.2

0.4

0.6

0.8

1

1.2

10 100 1000

Frequency, Hz

Abs

orpt

ion

Coe

ffici

ent

BASS Trap

Figure 15. Low frequency membrane absorberresponse

Devices are called membrane absorbers and a typicalabsorption coefficient response is shown in Figure 15.Another approach to essentially create particle velocity isto make use of the pressure gradient between the insideand outside of a volume enclosed by a porous material.Another newly modeled mechanism is the pressuregradient absorption produced by reflection phase gratingdiffusors. When the pressure difference between adjacentwells, separated by dividers, equilibrates significantlyincreased particle velocities over the dividers introduceslow frequency absorption below the design frequency.Another approach is to use Helmholtz absorbers, whichconsist of a series of slots or holes in a panel placed overan air cavity with a porous material close to, but nottouching, the panel. New theoretical models for neckdesigns holds promise to increase the bandwidth of thesenew devices.

[5.1.5] Electronic EqualizationIn a small project studio the listener is typically located inthe direct field within the critical distance (that point atwhich the direct and reverberant sound are at the samelevel). In this case, full bandwidth electronic equalizationto compensate for room problems should be avoided as itwould corrupt the one thing that may be acceptable in theroom, namely the frequency response of the direct sound!Therefore, prudence dictates that mid/high frequencyequalization or time domain filtering be used by a trainedacoustician.

On the other hand, there may be valid reasons to introducelow frequency electronic equalization to complete theadjustment of the low frequency room response.Psychoacoustically, the effect of room modes on theeffective output power of the loudspeaker is essentiallyindistinguishable from a real departure of the loudspeakerfrom a level response. Low frequency equalization below


14

roughly 300 Hz is justifiable when, for practical reasons,one cannot relocate the listening position or loudspeakerpositions or to fine tune the room’s low frequencyresponse.

Low Frequency LimitationsAttenuation of excess peaks is acceptable, but one shouldavoid trying to raise the level of notches. Responsenotches are usually the result of nulls in the modalresponse or destructive interference. Therefore, theirextent may be limitless. Thus any gain introduced tocompensate will reduce the amplifier headroom andincrease distortion. When making corrections based onacoustical measurements, spatial averaging is prudent tonot only help identify the source of the problem, but allowfor practical movement.

[5.2] Image Tools

Imaging refers to our ability to perceive and accuratelylocate the instruments, voices and effects that comprisethe soundstage. The factors affecting localization and theacoustic soundstage are reflections from the room’sboundary surfaces that cause comb filtering. Thesereflections cause frequency response notches and peaksthat fool the ear/brain (auditory system) and degrade ourability to experience the sonic images as they wereintended to be perceived. Imaging is optimized by anImaging Tool that attenuates the room’s first orderreflections over a wide range of frequencies. Lets look athow we can evaluate absorbers and diffusors and how weperceive what they do to the reflected energy.

[5.2.1] Characterization of ScatteringSurfacesWhen sound strikes a surface or an object, a portion of theincident energy will be reflected. Energy that is notreflected is either absorbed by the surface or transmittedthrough it. If the wavelength is small in comparison to thedimensions of the surface, sound is reflected like lightfrom a mirror, in which the angle of incidence equals theangle of reflection. If the wavelength is similar to adimension of the surface then some of the reflected energywill be scattered and the intensity in the specular directionwill consequently be reduced. If a significant fraction ofthe reflected energy is scattered then the reflection istermed a diffuse reflection. Thus Figure 16 illustrateshow sound can be attenuated by absorption (transmission),re-directed by reflection and uniformly distributed bydiffusion..

We have recently celebrated the 100th anniversary of thefounding of architectural acoustics by W.C. Sabine. Hiswork linking the decay of sound in a room to the randomincidence absorption coefficient has formed the basis forearly room design. Standards for experimental

measurement and prediction of the random incidencecoefficient have been established and experimental datahave been tabulated. Transmitted sound has also beenstudied extensively and standards for its experimentalmeasurement and prediction has been established.

I

n the intervening 100 years and primarily the past 20,years significant research has been carried out tounderstand what happens to the sound that is scattered bythe boundary surfaces, surface-mounted scatteringsurfaces and objects within the room. This research hasbeen a personal passion of mine and several years ago Istarted what we called the Directional ScatteringCoefficient Project or DISC Project. The researchattempts to find experimental and predictive methods todetermine how uniformly a surface scatters sound for agiven direction of incidence and how much of the incidentenergy is scattered into non-specular directions. We havecoined the term diffusion coefficient to measure thedegree of diffusivity or how closely a polar responseresembles a semi-circle. The scattering coefficient is ameasure of how much of the randomly incident energy isscattered in non-specular directions. A few years after westarted the DISC Project I was asked to Chair the AES’sstandards committee for the Characterization ofAcoustical Materials. In 1997, RPG co-funded a three-year international research project with the BritishEngineering Physical Sciences Research Council todevelop a room diffusion coefficient and make these dataavailable to the industry.

Let’s now consider how to measure and evaluate soundabsorbing and diffusing surfaces.

[5.2.2] Absorption

The random incidence absorption coefficient isdetermined by two measurements in a reverberation

Figure 16. The Acoustical Palette


15

chamber, which has well behaved room modes and a well-characterized reverberation time versus frequency. After

100125

160200

250315

400500

625800

10001250

16002000

25003150

4000

Frequency, Hz

0

0.2

0.4

0.6

0.8

1

Abs

orpt

ion

Coe

ffici

ent

Legend1" Absorber Spaced From Wall1" Absorber mounted on wall

measuring the empty room, 72 square feet of the test

sample is either placed directly on the floor or spaced by adistance from the floor. This type of mounting has asignificant impact on the result and you should determinewhether the data were measured in an A mounting (on thefloor) or in an E mounting (off the floor). The numberfollowing the E in millimeters indicated the distance fromhe floor. Figure 17 illustrates the increased low frequencyabsorption that is there for the taking by creating an aircavity behind an absorbing panel. Comb filtering isusually controlled by the use of porous materials likefabric-upholstered fiberglass and foam. Since theefficiency of all porous absorption relies on the degree ofair movement at a given frequency, low frequencyeffectiveness depends on the thickness and the amount ofair cavity between the material and the mounting surface.Generally the thicker the material and the farther it isremoved from the mounting surface the lower thefrequency it will be effective. Ironically, most porousabsorptive foam and fabric wrapped fiberglass panels areplaced on the boundary surface for convenience, albeitthey have the least effectiveness there

The test uses the two reverberation times, room empty androom with test sample, to extract a random incidencecoefficient based on Sabine’s formula relating the two andthe volume and surface area of the test chamber. TheASTM C423 procedure is based on the fact that theabsorption in a room is proportional to the decay rate orreverberation time of sound in that room. Frommeasurements made of the decay rates for the empty roomand the room with the test specimen added, the absorptionof the test specimen can be calculated. A large number ofrepeated measurements are taken to ensure the precisionrequirements of the standard are met.

Limitations of the C423C

The major limitation of this test is that it often givesnumbers higher than 1, which should be the limitingvalue. This arises from edge effects and in samples,which have significant surface topology. The test yieldsabsorption coefficients for random incidence sound. Insmall room acoustics we are more interested in thedirectional absorption coefficient. That is how much anincident sound is attenuated for a given angle ofincidence and observation.

[5.2.3] DiffusionAs mentioned earlier both absorption and diffusion can beused to attenuate a reflection and reduce the depth of thecomb filter interference. In Figure 18 the steady statereduction of a specular reflection by a 2D diffusor isshown. The response of the diffusor is averaged overangles of incidence to depict a random incidencebehavior.

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 1000 2000 3000 4000 5000

Frequency, Hz

Leve

l, dB

2D DiffusorReflector

Figure 18. Relative attenuation of a specularreflection with a 2D diffusor

Figure 17. Increased low frequency absorption from avariable depth air cavity


16

In Figure 19 we compare the extent of comb filteringbetween a direct sound and a strong specular reflectionand between the direct sound and a diffuse reflection.Note that the diffuse energy is distributed over time andconsequently it decreases the depth of the comb filtering,introducing, instead a dense pattern of irregularly spacesfrequency notches characteristic of a diffuse sound field.

Figure 19. Diffusive attenuation of specularreflection and accompanying comb filtering.


17

[5.3] Spatial Tools

Diffusing surfaces have been used since antiquity in theform of statuary, coffered ceilings, columns and surfaceornamentation. In 1983 RPG introduced the firstdesignable diffusor based on mathematical number theoryand tens of thousands of diffusors have been used in themusic industry since then. Since they have become sowidely used it is important to know how to evaluate apotential diffusor. The method that is being evaluated as astandard is to automatically measure, under computercontrol, the scattered impulse responses 5 meters from atest surface at an angular resolution of 5 degrees, with thetest source at a given angle with respect to the normal and10 meters away. An illustration of the test geometry isshown in Figure 20. Once the impulse responses are

determined they are Fourier transformed to obtainfrequency responses at each observation angle. Fromthese data one can take a frequency slice averaged over1/3-octave to obtain the polar or angular response. Thediffusion spectrum is then defined by a plot of the

standard deviation of the 1/3-octave angular response indB plotted versus frequency. The diffusion coefficient isobtained by normalizing this curve from 0 to 1 by thescattering from an ideal polar response consisting of adelta function. In Figure 21 we see a plot of the diffusioncoefficient of a 2’ x 2’ diffusing surface plotted versus aflat panel of similar size. There are two mechanisms forsound diffusion- size diffraction and surface topology.You will notice that at about 565 Hz the two curves beginto deviate. This is a reality check on the experimentbecause size diffraction should end at a frequency roughlyequal to the speed of sound divided by the size of thepanel (1,130 ft/sec/ 2’= 565 Hz). As you can see up to565 Hz scattering from a flat panel and a diffusor ofsimilar size are equal as it should be. Above thisfrequency the wavelengths are small enough to “see” thesurface variation and begin to diffuse based on the natureof the surface topology. It is important to indicate that notany surface variation is acceptable. Diffusion involvesconstructive and destructive interference and this complexinteraction is often non-intuitive. One of the promisingaspects of this approach is that the diffusion performancecan also be predicted using BEM calculations

In the coming years you will be hearing more and moreabout modeling using geometrical computer modelingprograms. They have been reserved for larger rooms, butinclusion of diffusion algorithms and phase triangularbeam tracing has made them more applicable to smallrooms like project studios. The missing parameter in thistype of modeling is a random incidence diffusioncoefficient. As part of our research program we areevaluating a method suggested by Mommertz to measurethis quantity directly. This method is very much like the

random incidence absorption coefficient approach, exceptit uses a maximum length sequence stimulus instead ofpulsed noise bursts and an additional measurement isrequired. Thus one measures the reverberation time of thechamber empty, with the scattering sample stationary andwith the sample rotating. Rotation removes the incoherent

MICROPHONE(19TYP.)

SAMPLE

MIC BOOM

LOUDSPEAKER TRACKLOUDSPEAKER @ 45°

PLAN VIEW

ELEVATION

DIRECTION OF ROTATION

Figure 20. Measurement Goniometer to map thebackscattered hemisphere.

Figure 21. Diffusion coefficient for a 2D diffusor

Figure 22. Scattering coefficient for a quadratic residuediffusor

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

125

160

200

250

315

400

500

630

800

1000

1250

1600

2000

2500

3200

4000

Frequency, Hz

Diff

usio

n C

oeffi

cien

t

Diffusor

Reflector

Diffraction LimitWidth = λ

0

0.2

0.4

0.6

0.8

1

1.2

100 1000 10000

Frequency, Hz

Sca

tterin

g C

oeffi

cien

t

δα


18

scattering arising from the surface topology and yieldsonly the specular scattering. Thus one can obtain thefraction of the sound scattered in the specular direction.From this and the total sound power, one can obtain therandom incidence absorption coefficient, α, and thescattering coefficient, δ. In Figure 22 we show the firstmeasurements on a number theoretic diffusing surfaceshowing its random incidence diffusion and absorptionspectra.

The type of spatial scattering a diffusing surface offersdepends on whether the phase variation occurs in one ortwo dimensions. A 1-dimensional diffusor is formed fromextruding an optimized diffusing profile. The phasevariation occurs in only one direction, the direction of theprofile, and the other direction has constant depth. InFigure 23 we show the hemidisc scattering from a 1D

diffusor. When the phase varies in two perpendiculardirections the diffusor is called a 2D diffusor and itprovides hemispherical scattering. This is illustrated inFigure 24.

In 1995 I presented a review paper at the AES in NewYork on two decades of diffusor design and development.This research began with the seminal research of ManfredSchroeder and has progressed from simple number theoryquadratic residue diffusors, to diffusing fractals, additiveand multiplicative modulated QRDs, to the present stateof the art in which almost any desired shape surface canbe acoustically optimized using BEM optimizationtechniques. Over the past 20 years we have developed theability to predict, measure, quantify and optimize diffusorperformance.

Small rooms like project studios require a very efficientsurface to diffuse interfering wall reflections and providea diffuse sound field. For this application diffusors withphase variation in two perpendicular directions is ideal. Ifthe phase variation is calculated properly these 2-dimensional surfaces can scatter sound omnidirectionallyfor any given angle of incidence.

[6] EXAMPLE

In 1983, RPG introduced two new concepts in controlroom design, which were extensions of the LEDE designconcepts by Don Davis. One involved creation of atemporal reflection free zone (RFZ) by reflecting and/orabsorbing first order reflections between the listener andloudspeakers. Since flush mounted loudspeakers werepopular at that time, the RFZ also included flush mountedloudspeakers as close to the trihedral corner as wasfeasible. The sidewalls between the loudspeaker andlistener were typically splayed away from the listener inorder to deflect energy towards the rear of the room. Theaddition of broad bandwidth absorption on these splayedsurfaces further reduced the scattered sound level at thelistening position. Recognition of modal excitation withthis corner loaded loudspeaker mounting requiredpotential low frequency shelving to the loudspeakersignal.

The other idea was to use sound diffusing surfaces on therear wall to control interfering rear wall reflections,maintain a natural ambiance in the room, widen the sweetspot and create a sense of passive surround soundenvelopment. In concert hall research the sense ofenvelopment was linked to the amount of sound reachingthe listener from lateral directions around 55 degrees withrespect to the frontal direction. In music reproductionrooms like recording studios, strong lateral reflectionswould produce comb filtering and corrupt the imaging andtimbre of the reproduced sound. The use of sound

Figure 23. Hemidisc scattering from a 1D diffusor

Figure 24. Scattering hemisphere from a 2D diffusor


19

diffusing surfaces on the rear wall helps to acousticallycreate an impression similar to today’s surround soundsystems. We call it “passive surround sound”. Thus weuse a Spatial Tool to create envelopment, widen the sweetspot, add warmth and naturalness to the sound, anduniformly distribute the sound throughout the room. TheRFZ/RPG design quickly became a sort of defactostandard and photos of this approach are commonplace intrade magazines.

Figure 25 illustrates the results of applying Image andSpatial tools to an untreated room. The display at the topillustrates strong corrupting early reflections from thesidewalls, floor and ceiling between the loudspeakers andthe listening position. In addition, reflections arriving

after the rear wall reflection are sparse and do not follow alinear decay as would be found in a diffuse field.The RFZ/RPG design quickly became a sort of defactostandard and photos of this approach are commonplace intrade magazines.

Imaging Tools, in the form of broad bandwidth absorptionwere used to minimize the corrupting early reflections anda temporal Reflection Free Zone 24 dB below the directsound was created to improve imaging and timbre. Thendiffusion was added to the rear wall to minimize thecorrupting effect of isolated strong reflections and providea spatially and temporally dense reflection pattern. Notethe linear envelope decay of the diffuse reflectionsindicative of a diffuse sound field.

[7] SUMMARY

Today project studios are primarily using smallfreestanding powered monitors and subwoofers. Inaddition, the rooms are usually approximately rectangular.We can summarize ten steps to help create accuratelistening rooms that provide a transferable audio product.The ultimate goal would be to give recording engineersthe confidence that what they hear in their room willtransfer to other listening locations. When undertaking anacoustical analysis of a room, consult an acoustician.These professionals have a wealth of experience that theycan offer in the early stages that will save you time andmoney in the long run.

Below are Dr. Diffusor’s top ten tips that will help youListen to The Music, Not the Room!!

1. Listen to your recordings in a variety of listeningenvironments to convince yourself that the acousticsof the listening room play a vital role in what is heard.

2. If you are building a new room, use good dimensionalratios to provide uniform modal frequencydistribution. If the room already exists there is notmuch you can about this.

3. Design a symmetrical listening environment for goodimaging. Place speakers symmetrically and on axisfor best response.

4. Locate the sub-woofers, loudspeaker woofers andlistening position to optimize the acoustical couplingwith the room's pressure variations and speaker-boundary interference. I.e. optimize the bassresponse. Experiment with positioning the wooferabove or below the tweeter for optimal coupling withthe room.

5. Minimize first order reflections from the walls,ceiling and floor between the loudspeakers and thelistening position using absorption or diffusion. Beconscious of the effect of console reflections andminimize.

Figure 25. Time response comparison of an untreated andacoustically treated room.


20

6. Diffuse rear wall reflections over roughly 60% of thesurface area beginning 3' off the finished floor.

7. Provide low-frequency absorption on the rear wall tominimize low frequency cancellation effects.

8. If necessary, damp low frequency modes by applyinglow frequency absorption at maximum pressurelocations like dihedral and trihedral corners.

9. Electronically equalize remaining low frequencymodal emphasis. Reconsider equalizing frequencynotches in the room response. Consider time domainequalization.

10. Measure the room's time and frequency response atseveral listening positions using any of the excellenttransfer function or stimulus and responseapproaches. Analyze the results and tweak to taste.


21

TABLE OF FIGURESFigure 1. Three psychoacoustic areas affected by acoustic

distortion .................................................................. 2Figure 2. Equivalent circuit for acoustical distortion ...... 3Figure 3. Measured modal frequency response in a room

2.29 m (W) x 4.57 m (L) x 2.74 m (H). The (100),(200), and (300) modes are identified. ..................... 4

Figure 4. Normalized energy distribution of the first threemodes in a room. ...................................................... 4

Figure 5. Sound from real and virtual speakers combineto create the speaker/boundary interference response.6

Figure 6. Speaker-Boundary Interference Response forseveral loudspeaker positions in a corner. ................ 6

Figure 7. Comb filtering with 1 one reflection delayed by1 ms with attenuated of 0, 3, 6 and 12 dB relative tothe direct sound. ....................................................... 8

Figure 8. Comb filter destructive interference nullfrequencies for a single reflection delayed 1 ms fromthe direct sound. Constructive interference peaksoccur midway between adjacent nulls. ..................... 8

Figure 9. Comb filter due to equi-spaced flutter echos 1ms apart. ................................................................... 8

Figure 10. Time and frequency response of the directsound from a loudspeaker......................................... 8

Figure 11. Time and frequency response of the directsound combined with a side wall reflection. Thecomb filtering is apparent......................................... 9

Figure 12. Acoustic tools improve imaging, spaciousnessand bass response. .................................................. 10

Figure 13. Speaker-Bondary Interference The standarddeviations are 4.67 and 8.13 dB for the best solutionand worst case respectively. ................................... 12

Figure 14. Modal Response- The standard deviations are3.81 and 6.28 dB for the best solution and worstcase, respectively.................................................... 12

Figure 15. Low frequency membrane absorber response13Figure 16. The Acoustical Palette ................................. 14Figure 17. Increased low frequency absorption from a

variable depth air cavity ......................................... 15Figure 18. Relative attenuation of a specular reflection

with a 2D diffusor................................................... 15Figure 19. Diffusive attenuation of specular reflection

and accompanying comb filtering. ......................... 16Figure 20. Measurement Goniometer to map the

backscattered hemisphere....................................... 17Figure 21. Diffusion coefficient for a 2D diffusor......... 17Figure 22. Scattering coefficient for a quadratic residue

diffusor ................................................................... 17Figure 23. Hemidisc scattering from a 1D diffusor ....... 18Figure 24. Scattering hemi-shpere from a 2D diffusor .. 18Figure 25. Time response comparison of an untreated and

acoustically treated room........................................ 19

minimizing acoustic distortion in project...

Documents