Acoustics Treatment for a Small Space

8/4/2019 Acoustics Treatment for a Small Space

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Contents

Introduction................................................................................................................................................. 2

TheoryandBackground............................................................................................................................... 2

ReverberationTime ................................................................................................................................. 2

RoomModes............................................................................................................................................ 3

Method ........................................................................................................................................................ 3

InitialCondition ....................................................................................................................................... 3

ReverberationTime ............................................................................................................................. 3

RoomModesDistribution.................................................................................................................... 5

TheTreatment ......................................................................................................................................... 6

TreatmentforReverberationtime ...................................................................................................... 6

TunedPanelAbsorberBassTrap .................................................................................................... 11

Conclusion ................................................................................................................................................. 11

Reference................................................................................................................................................... 12


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Introduction

Inthispaper,amethodofconvertingaspaceintoacreativeaudioenvironmentisinvestigated.This

includes calculation of reverberation time and room modes of the initial space. On the treatment

section,theproposedlocationofthetreatmentispresentedinthelayoutoftheroomaccompanied

withtheexpectedacousticsresultsafterthetreatment.Thedesignisbasedonascenariowithseveral

requirementstosimplifytheprocessandalsoasaguidanceofthedesign.

TheoryandBackground

ReverberationTime

SabineReverberationTime

Reverberationtimeisthetimeneededforsoundenergytodecay60dBinaparticularspace.Itwasfirst

formulatedbyWallaceClementSabineinthelate1980s.Sabineempiricalformulais:

Equation1

Where

=Reverberationtimemeasuredinsecondormillisecond

V =Volumeoftheroom(

A =Totalareaofabsorptionintheroom(sabins)

=

NorrisEyringReverberationTime

Anotherformula forcalculation reverberation time iscalledNorrisEyring Reverberation formula, itis

formulatedas:

Equation2

NorrisEyringReverberation formulais more accurate then theSabinesformula fora very absorptive

room.Sabineformulaisaccurateforaroomwithsmallerabsorption,asaruleofthumb,Sabineformula

is accurate for .For thesakeof simplicity of calculation, on this paperall of thecalculation

involvingthereverberationtimewillbecompletedusingSabineReverberationtimeformula.


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RoomModes

One of the most common problems in employing small room for critical listening of music is the

irregularitiesoflowfrequencyresponse.Thisismainlycausedbythefactthatatlowfrequency,the

wavelengthoftheacousticswavesiscomparabletothedimensionoftheroom.

Roommodescanbecalculatedwiththeequation:

Equation3

Where

L,W,H=roomLength,Width,andHeight.

x,y,z = set of positive integer (including 0) corresponds to the number of half wavelength

betweenthesurfaces.

c =thespeedofsound(

Whentwointegersarezero,the mode iscalledaxialmodeandit isa onedimensionalstandingwave

between two parallel surfaces. When oneinteger is zero, the mode is called tangential modeand it

involvesreflectionfrom4surfacesparalleltotheremainingone.Whennointegershaveazerovalue,

themodeiscalledobliquemodeanditinvolvesreflectionfromallthesurfaces.Practicallythemost

importantmodeistheaxialmode.

Method

InitialCondition

In this section, the initial room acoustics properties of the room are calculated. This involves the

calculationofreverberationtimeforeachfrequencybandsandtheaverageRT60fortheroom.Firstfew

modeswillbecalculatedandalsothecriticalfrequencyoftheroom.

ReverberationTime

Theabsorptioncoefficientsforthesurfaceofthematerialintheinitialroomsare

FrequenciesMaterials

125Hz 250Hz 500Hz 1kHz 2kHz 4kHz

Plasterboard12mmGypsum 0.29 0.1 0.05 0.04 0.07 0.09

Plasterboard12mminsuspendedceilinggrid 0.15 0.11 0.04 0.04 0.07 0.08

Windows(FloatGlass) 0.35 0.25 0.18 0.12 0.07 0.04

woodflooringonjoist 0.15 0.11 0.1 0.07 0.06 0.07Table1(datafromHowardandAngus2006:290and

http://www.saecollege.de/reference_material/pages/Coefficient%20Chart.htm)


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Andthecalculationsoftheopenwindowareasforeachfrequencybandsare

frequencyMaterials

Area

(m2) 125 250 500 1k 2k 4k

Plasterboard12mmpanelingonstuds 53.18 15.42 5.32 2.66 2.13 3.72 4.79

Plasterboard12mminsuspendedceilinggrid 25.86 3.88 2.84 1.03 1.03 1.81 2.07

Windows(FloatGlass) 6.00 2.10 1.50 1.08 0.72 0.42 0.24

woodflooringonjoist 25.86 3.88 2.84 2.59 1.81 1.55 1.81

TotalopenWindowArea(m2) 25.28 12.51 7.36 5.69 7.50 8.91Table2

Andtheresultsare

Figure1

TheresultfromFigure1showsthatthereisarelativelybigdifferencebetweenthereverberationtime

foreachfrequencyband.Fierstein(inlong,2006:753)showsagraphicofsuggestedreverberationtime

as a function of room volume. For this particular imaginary space ( ) the suggested

reverberationtimeisaround200-300ms.Fromtheinitialreverberationtimecalculation,itisnecessary

toreducetheroomreverberationtimeacrossallthefrequencybandsespeciallyaroundthe1kHzarea.HowardandAngus(2006:297)suggestedthattheidealreverberationtimecharacteristicforacontrol

roomisflatacrossthespectrum.Thusthetreatmentdesignonthenextsectionwillrefertothisdata.


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ThecriticalfrequencycanbecalculatedwithEquation4 .

Equation4

Where,

Withthedimensionofourroomandspeedofsounds(c=344m/s),thecriticalfrequencyoftheroomis,

. below this frequency, the room cannot betreated asdiffuse field anymore and the

modalfrequencywillbedominant.Thiswillcausetheirregularitiesinthelowfrequencyresponsethatis

alsopositiondependant.

RoomModesDistribution

Figure2

Frequency

hz

Spacing

% p q r Mode

28.7 1 0 0 Axial

40 28.2 0 1 0 Axial

49.2 18.6 1 1 0 Tangential

57.4 14.2 2 0 0 Axial

60 4.3 0 0 1 Axial

66.5 9.7 1 0 1 Tangential

69.9 4.8 2 1 0 Tangential

72.1 3 0 1 1 Tangential

77.6 7 1 1 1 Oblique

79.9 2.8 0 2 0 AxialTable3


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ThefirstfewmodesislistedinTable3asthefrequencyincreasesthemodesbecamemoredenseandat

somepointtherewillbenoisolatedmodalfrequency.Abovethecriticalfrequencytheroomcanbe

considered as diffuse field and so the behavior could be predicted with the RT60 calculation. Data

presentedinFigure2isinlogfrequencyscaletogiveabetterrepresentationonthemodesdistribution

inrelationwithamusicalscale.The1st

modeisneartheA#(29.1),2nd

modeisneartheD#(38.09),3rd

modeisneartheF#(46.2)andthe4thmodeisneartheA#(58.3)onthenextoctave.Thereareonly4

modesinthefirstoctavewhichcanbequiteproblematic.

TheTreatment

This imaginary space will be converted into an audio related creative environment. To simplify the

design process and provide more focused discussion paper, this space will be designed under the

followingcondition:

Thespaceisusedforelectronicmusicproductionwhichinvolvesmidicomposing,synthesizerprogramming,mixingandmastering.

Acousticsinstrumentsandvocalrecordinginthisspaceisnotaprioritybutstillcouldbedonewithfairperformance.

Asitisgoingtobeusedformixingandmastering,areasonablyflatreverberationtimecurveisexpected.

Agoodlowfrequencyresponseisveryimportant,forthereasonthatthemusiccreatedinthisspacerequiresadetailattentiontobassandkickdrum.Alsoasubwooferortwowillbepresent

inthisroom

Aminimumacousticstreatmentisexpectedfortworeason,oneisbudgetconsiderationandsecondistoprovidemorespaceforequipment(e.g.midicontroller,rackeffectprocessor,

synthesizers,drummachines,sampler,turntable,etc)

TreatmentforReverberationtime

After calculating the initial reverberation time for every frequency band, next step is to propose an

acoustic treatment to reduce the reverberation time. The method of calculating the budget open

windowareaisusedinthispaperandthetarget [email protected]

windowareaiscalculatedasfollowing:

First,calculatethetargetOpenWindowareawithSabineequation,

Equation5

ForthisroomVolumeandtarget ,


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Therequiredadditionalopenwindowareathencalculatedbysimplysubtractingthevalueofthetarget

openwindowareawiththeinitialopenwindowarea,showninTable4


TargetOpenWindowArea

(m2) 39.83 39.83 39.83 39.83 39.83 39.83TotalopenWindowArea

(m2) 25.28 12.51 7.36 5.69 7.50 8.91

AdditionalOpenWindow

Area(m2) 14.55 27.32 32.47 34.14 32.33 30.92Table4

NoticethattheTargetOpenWindowAreaissameforallfrequencybands.Thereasonforthatisto

obtain thesame valuefor each frequencyband. Thehighest required Additional Open Window

Area isatthe 1kHzfrequencyband, this isasexpectedbecause fromFigure1it appearthatthe1kHz

areahasthehighestinitialreverberationtime.Withthisconditionitseemsthatalargeareaofporous

absorberwillbeneeded.Itshouldhaveenoughareatoabsorballtheexcessivereverberationandalsothickenoughtoabsorbthelowfrequencyenergy.

After doing a simulation with different types of absorber (porous, resonant and perforated) and

consideringthelayoutofthespace,theproposedtreatmentforthisspaceisbyaddingthreedifferent

materialstotheroom,whichconsistof:

1. Kestrel High density curtain type Coloured wool serge (data taken from the manufacturerwebsiteatwww.kestrel-acoustics.com)

2. OwensCorningFiberglass701,Plain,density= ,2(51mm)thick(datafromthemanufacturerwebsiteat

http://www.owenscorningcommercial.com/docs/specification/Fiberglas700Series.pdf)

3. Owens Corning Fiberglass 703,Plain, density = , 2(102mm) thick (data fromhttp://www.bobgolds.com/AbsorptionCoefficients.htm)

FrequenciesMaterials


ColouredWoolSergeHighdensityCurtain 0.07 0.31 0.49 0.75 0.7 0.6

OCPlainFiberGlass701,2"thick 0.22 0.67 0.98 1.02 0.98 1

OCPlainFiberGlass703,4"thick 0.84 1.24 1.24 1.08 1 0.97Table5(allthedataisfromthemanufacturerwebsiteorothersourcementioned)

The curtain is positioned on the front part of the room covering the window area. The fiberglass

materialisputintoacustommadetimberframewithwiremeshandacousticallytransparentfabricon

bothsidestopreventtheparticlesfromfallingoutintotheroom.Theabsorbermoduleisplaceddirectly

onthewallsorceilingwithoutairspace.Figure3showstheroomlayoutandpositionofthetreatment.


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Figure3RoomFloorPlan

ThecalculationonTable6showingtheAdditionalOpenWindowAreacomesfromtheaddedmaterials

aspartofaroomtreatment.

Table6

ThepositionoftheacoustictreatmentcanbeseenonFigure3,Figure4,Figure5,andFigure6,

Thecurtaincoversthewindowareawiththedimensionof TheOC703absorberispositionedontheceilingscoveringaspaceof

Figure4

TheOC701absorberisdividedintosideabsorber: andrearabsorber:Figure5


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Figure4CeilingPlan

Figure5RearElevation


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Figure6SideElevation

Nextstepis tocalculatethenewreverberationtimeoftheroomafterthetreatmenthas takenplace.

Table7showstheresults

Frequencies


InitialOpenWindowArea(m2) 25.28 12.51 7.36 5.69 7.50 8.91

AdditionalOpenWindowArea(m2

) 15.53 28.52 33.50 34.20 32.08 30.79

NewOpenWindowArea(m2) 40.81 41.03 40.86 39.89 39.58 39.70

newRT60(V=74.22m2) 0.29 0.29 0.29 0.30 0.30 0.30

Table7

The design proposed has successfully achieved the target reverberation time of 300ms and it is

consistentacrossthespectrum.Noticethatthebasstrapisnottakenintoaccountforthereverberation

timecalculation.Thisisbecausetheplacementofthebasstrapisoptionalandwillonlybedoneifthere

isanexcessivelowfrequencyresponseintheroom.Withoutthebasstrap,thelowfrequencyenergyin

theroomisalreadyreducedbytheplasterboardconstructionontheceilingandwalls,woodfloorand

alsothethickfiberglassconstructionontheceiling.

Atthispoint(beforedecidingwhetherornottoputthebasstrap),itisrecommendedtodonesometest

intheroom,includingimpulseresponsemeasurement,sweepsinetestforthefrequencyresponseand

alsolisteningtest.Ifthereisstillanirregularityinthelowfrequencyresponseoriftheclientfeelsthat

the room is sill muddy or boomy then a panel absorber tuned to the lowest mode or to the

problematiclowfrequencycanbeinstalled.


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TunedPanelAbsorberBassTrap

Oneofthesolutionwalkers(1996:8)suggesttoovercometheproblemcausedbytheirregularitiesof

low frequency response as a result ofthe first few modesis toincrease the modal damping factor.

Quoting from Long (2006:747) a few common practices to control the low frequency energy in the

roomsare:

1. Overallcontrolthroughlow-frequencypanelabsorbersprincipallyontherearandsidewalls2. Applicationofdeeplayersofabsorptivematerialsometimesusedinconjunctionwithpanel

absorbers

3. ConstructionofHelmholtzresonatorcavities4. Locatingthebassloudspeakerssothattheydonotexcitetheprincipalmodes5. Locatingthemainlistenerpositionsothatitdoesnotcoincidewithamajorlowfrequencynode

Inthisparticularimaginaryroom,atunedpanelabsorberlocatedinthecorneroftheroomasinthe

Figure 3 is proposed. The frequency for tuned panel absorber can be predicted using (from Long,

2006:273):

Equation6

Wheremisthepanelmassperunitareain anddisthethicknessofairspacebehindthepanelin

cm.whentheairspaceisfilledwithinsulationmaterial,theresonancefrequencyisreducedto

Equation7

Theairspace provided in ourfloor layout is about 50cm, using plywood with a density of about 600

and1cmthick,thepanelabsorber/basstrapwillbetunedtotheroomfirstmodewhichis28.7

Hz.

Conclusion

There are several steps in converting a space into creative audio environment. The first and most

importantisthedesignstagewhichinvolvescalculationoftheinitialacousticspropertiesoftheroom.

Thesecondstepistoproposeatreatmentforthegivencondition,therequiredacousticstreatmentis

verydependsonthefunctionoftheroomthereforethereisnoonesolutionthatfitsforallsituation.To

achievetherequired value,asimulationwithdifferenttypesofmaterialsandpositionhavetobe


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done,thistaskismadeeasierusingtheconceptofopenwindowarea.Intherealsituation,convertinga

roomintocreativeaudioenvironmentislotmorecomplexthanjusttheacousticsconsideration.The

designer has to consider other factor such as visual appearance, budget consideration and other

requirementfromtheclient.

Reference

1. Howard,D.M.andAngus,J.(2006)AcousticsandPsychoacoustics,3 rdedition,Oxford:FocalPress.

2. Long,M.(2006)ArchitecturalAcoustics,Elsevier3. Walker,R.(1996)RoomModesandLowFrequencyResponsesinSmallEnclosures,Tadworth:

BBCResearchandDevelopmentDepartment .

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Acoustics Treatment for a Small Space