5 Absorption. ELEC-E Noise Control P. Valtteri Hongisto

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5 Absorption ELEC-E5640 - Noise Control P Vltteri Hongisto vltteri.hongisto@turkumk.

1 5 Absorption ELEC-E Noise Control P Vltteri Hongisto vltteri.hongisto@turkumk.fi Docent in Noise Control, Alto University Reserch group leder, Turku University of Applied Sciences Espoo, Finlnd, 3 Nov

2 Sound bsorption Absorption coefficient I I i I i r I r I i I t Reduction of sound intensity level, D [db], in the boundry: D=L Ii - L Ir [db] D 10lg 1 2

3 Absorption versus trnsmission Absorption coefficient: I I i I i r I r I i I t Sound reduction index [db] R 1 10lg 10lg I I i t Airborne sound reduction index R (db). 1/3-octve bnds ISO /1-octve bnds Centre frequency of the third-octve bnd f (Hz) 3

4 Comprison of bsorption nd trnsmission losses Usul vlues: : D R [db] [db]

5 Mesurement of sound bsorption Impednce tube Reverbertion room 5

Mesurement of sound bsorption Impednce method ISO 10534-2 Norml sound incidence Loudspeker produces plne wve

125-4000 Hz: 63 mm; 500-8000 Hz: 29 mm Wter cutting of specimens Fst method for reserch nd development

6 Mesurement of sound bsorption Impednce method ISO Norml sound incidence Loudspeker produces plne wve inside the tube when dimeter > wvelength Dimeters of the tube & specimen for B&K tube: Hz: 100 mm, Hz: 63 mm; Hz: 29 mm Wter cutting of specimens Fst method for reserch nd development especilly becuse most prediction models re vlid for norml incidence The vlues re lower thn with reverbertion room method 6

7 Dependence of bsorption coefficient on sound incidence ngle Yuzw (1975) glss wool The vlues smller t 0 incidence thn t 60 incidence. The vlues re zero t grzing incidence (90). 7

Mesurement of sound bsorption Reverbertion room method ISO 354 Officil method" for bsorbers used in rooms Considers ll incidence ngles eqully Room is highly reverbernt nd 150-250 m 3

8 Mesurement of sound bsorption Reverbertion room method ISO 354 Officil method" for bsorbers used in rooms Considers ll incidence ngles eqully Room is highly reverbernt nd m 3 producing diffuse field within Hz Reltive humidity is constnt nd > 60 % Specimen size m 2 Vlues cn exceed Why? Lrge inter-lbortory differences Prediction models re less ccurte. 8

9 Mesurement of sound bsorption Reproducibility of ISO 354 Round Robin test of 23 lbortories, including TUAS Three mterils were tested A: 15 mm hrd wool B: 50 mm soft wool C: perforted gypsum Inter-lbortory differences (reproducibility vlues) were significnt especilly below 250 Hz where the diffuse field conditions re not fulfilled too few modes per third octve bnd Andersson N Å, Forum Acusticum

10 Wve number nd impednce The rtio of pressure p nd prticle velocity u is denoted by Z x when one-dimensionl sound propgtion long x- xis is considered. Porous mterils re chrcterized by two chrcteristic vribles: Chrcteristic complex wve number [1/m] lso known s propgtion constnt Chrcteristic complex impednce Z [Ps/m]: Z Γ x Z p u x x, t x, t Z j jz 10

11 Chrcteristic impednce Z Z depends on the speed of sound in the mteril Highly sound bsorbing mterils: smll c nd smll impednce imginry component is smll rel component is smll nd close to tht of ir, Z 0 poor sound insultion: sound is esily propgting through the mteril nd very little is reflected bck. Highly sound insulting mterils: lrge c nd lrge impednce imginry component is lrge rel component cn be smll poor sound bsorption: reflection is strong due to strong impednce mismtch with Z 0 11

12 Chrcteristic wve number Complex wvenumber ppers in the onedimensionl hrmonic plne wve in the following wy. Wvenumber cn be determined by mesuring the mplitude s function of distnce: ': ttenution '': phse unit [1/m] Γ p x, t loss term pe ˆ pe ˆ j Γ x Γ x e e jt jγx e jt vibrtion term e i cos i sin 12

13 Wve number nd impednce in ir The losses in the medi re described by the rel prt of ; the imginry prt of Z ) The losses re negligible in ir Therefore, in ir jt k x x, t pe ˆ p 0 Z = c 0 =jk 0 0 [kg/m 3 ] is the density of ir c 0 [m/s] is the speed of sound in ir The chrcteristic impednce of ir is denoted by Z 0. The vlue in room temperture is Z 0 =413 kg/sm 2 Γ j k 0 2 c 0 jk 0 2f c 0 13

14 Specific flow resistivity Specific flow resistivity is used to predict the chrcteristic impednce of porous mterils. Flow resistnce R [Ps/m 3 ] pressure difference over the specimen p [P] flow rte through the specimen q v [m 3 /s]. Specific flow resistnce R s [Ps/m] A [m 2 ] is the specimen re Specific flow resistivity r, [Ps/m 2, Ryl/m] is the specific flow resistnce per one qubic meter specimen: Rs d [m] is the specimen thickness R p q v R s r RA d Pump flow meter pressure meter specimen. Specimen is inside verticl metl tube. 14

Porosity nd tortuosity High porosity leds to low impednce nd high sound bsorption if the pores re inter-connected nd sound cn propgte inside the mteril nd the sound energy esily turns into therml

15 Porosity nd tortuosity High porosity leds to low impednce nd high sound bsorption if the pores re inter-connected nd sound cn propgte inside the mteril nd the sound energy esily turns into therml energy due to friction Porosity h is defined s the rtio of ir volume V [m 3 ] to the totl volume of the mteril V [m 3 ]: ' Prticle velocity inside the mteril, u [m/s], is s is tortuosity [ ] u is the prticle velocity in ir [m/s] Tortuosity, or structure fctor, describes how the pores re interconnected. It is difficult to mesure. h u V V u' s h Different structure fctors: () fom rubber full grid structure (b) fom rubber prtil grid structure (c) glss wool mt (d) minerl wool 96 kg/m 3. Fhy

16 Empiricl reltionships between Z, nd r E 0 r f Delny & Bzley 1968 Appl Acoust: Flow resistivity, impednce nd wvenumber ws mesured for severl hundreds of porous mterils. Empiricl interreltions were determined to be used in prediction models. 16

17 Chrcteristic properties of porous mterils Bsed in Delny & Bzley 1968 ide, complex specific impednce Z nd wvenumber cn be predicted when r is known. Γ Γ' Γ'' E j c0 Z Z' jz'' The four constnts re lter determined by Cox nd D Antonio (2004). m is the wvelenght of longitudinl wve in mteril [m] nd is phse ngle. E 0 j0.189e Z e j c E j0. 087E r f Cox TJ, D'Antonio P, Acoustic bsorbers nd diffusers, Theory, Design nd Appliction, Spon Press, London,

18 Effect of wool density nd speficic flow resistivity on kg/m3 76 kg/m3 18 kg/m r [Ps/m 2 ] Oliv, Häggblom & Hongisto (2010) Finnish Inst. Occup. Helth 18

19 Chrcteristic impednce vs. surfce impednce Chrcteristic impednce Z expresses the reltionship between sound pressure nd prticle velocity for plne wve inside the mteril. Surfce impednce Z 1 expresses the impednce exctly on the surfce of the mteril. It depends on the chrcteristic impednce Z of the mteril; the surfce impednce behind the mteril lyer. Z p x, t u( x, t) 19

20 Reflection in the boundry of two mterils Perpendiculr incidence Consider two mterils 0 (ir) n 1 (bsorbent) Z 0, 0 hving infinite thickness Absorption coefficient Wve theory results in Ii I r 1 I 1 R Using normlized impednce z, where Z 0 is the chrcteristic impednce of ir, we get 1 z z i 1 Z Z I I 1 1 z r i Z Z Z Z p r p i Z 1 Reduced form without complex nottion becomes 1 R 2 2 Z' 1Z0 Z'' 1 where Z 1 (Z1=Z 1 +jz'' 1 ) is the surfce impednce on the boundry. 2 Z 1, 1 p t 4Z' 1 Z 0 x 20

21 Sound bsorption coefficient for porous bsorber Three cses ccording to the surrounding mterils ) thick bsorber surrounded by ir b) thin bsorber ginst rigid bcking c) thin bsorber ginst cvity + rigid bcking Z chrcteristic impednce Z 1 surfce impednce ir bsorber ir ir bsorber rigid bcking ir bsorber ir rigid bcking Z 0 Z 1 Z 2 Z 0 Z 1 Z= Z 0 Z 1 Z 23 Z= ) Z 1 Z 1 Z 1 Z 2 Z 0 =Z 2 =Z 0 b) Z 0 =Z 0 c) Z 0 =Z 2 =Z 0 21

22 ) Thick porous bsorber ir bsorber ir The bord is thick if the thickness is t ppr. 32% of the wvelength,, inside mteril: 2d ' d 2 Z 0 Z 1 Z 2 Such thickness gurntees tht the reflection from the bckside is ttenuted so much tht it does no longer contribute to Z 1, nd Z 1 =Z 1. Absorption coefficient is ) Z 1 Z 0 =Z 2 =Z 0 1 R 2 4Z' Z' 1Z0 Z'' 1 Z 22

23 Exmple 5.1 Clculte sound bsorption coefficient for bord of infinite thickness t 1 khz. r 8000 Ps/m2 f 1000 Hz 23

24 b) Thin bsorber ginst rigid bcking Consider n bsorber of thickness d [m]. Both reflection from rigid bcking nd chrcteristic impednce Z 1 contribute to surfce impednce Z 1 : ir Z 2 ir bsorber rigid bcking Z 0 Z 1 Z= Z1 jz cot Γ d Z cothjγ d Absorption coefficient 1 R 2 4Z' 1 Z Z' 1Z0 Z'' 1 b) Z 1 Z 0 =Z 0 e coth Γ e Γ Γ e e Γ Γ cos '' cos '' ' ' ' ' e e j sin '' e e ' ' sin '' ' e e j e e ' 24

25 Optimum thickness of bsorber ginst rigid bcking Due to rigid edge conditions, stnding wve is lwys formed when sound enters rigid wll. Absorption performnce is mximized when the mteril is locted t prticle velocity mximum of the stnding wve. This is chieved either by locting the mteril /4 from the bcking or by using mteril thickness of /4 25

26 Effect of glss wool thickness: ginst rigid bcking Three thicknesses of minerl wool of density 18 kg/m /3-octve bnd frequency [Hz] ) 50 mm glss wool b) 100 mm glss wool c) 150 mm glss wool d) 200 mm glss wool Rigid bcking Oliv, Häggblom & Hongisto (2010) 26

27 c) Thin bsorber ginst cvity + rigid bcking Surfce impednce of ir cvity hving thickness t [m] behind the bsorber (in front of cvity): Z2 jz0 cot k0t Reflection coefficient from the bcking of the bsorber: Z2 Z,1 R Z 2 Z,1 ir bsorber ir rigid bcking Z 0 Z 1 Z 23 Z= Surfce impednce of the porous bsorber hving thickness d [m]: Z Absorption coefficient: 1 Z Z Z 2 cosh Γ cosh Γ d d Z Z 2 sinh Γ sinh Γ d d Z 1 Z 2 1 R 2 4Z' 1 Z Z' 1Z0 Z'' 1 c) Z 0 =Z 2 =Z 0 27

28 Effect of cvity thickness 50 mm wool bsorption Wool thickness d=50 mm Wool density =18 kg/m 3 Specific flow resistivity r=9600 Ps/m ) 50 mm glss wool b) 50 mm glss wool + 50 mm ir c) 50 mm glss wool mm ir d) 50 mm glss wool mm ir 1/3-octve bnd frequency [Hz] Oliv, Häggblom & Hongisto (2010) 28

29 Pnel resontor Air (Z 0 ) Bord (Z 1 ) Z 1 Z 2 Cvity (Z 2 =Z 0 ) d Air-tight unperforted bord bcked by cvity of thickness d [m] cts s resontor Impednce is lrge nd rel prt is smll (low dissiption) Resontor hs sound bsorption mximum t the resonnce frequency, which occurs when the imginry prt of Z 1 =0 Pnel types: building pnels plstic foils ir-tight pintings Cvity cn be empty or filled with sound bsorber. Chrcteristic impednce: Surfce impednce of cvity: Surfce impednce of bord: Absorption coefficient: Rigid bcking Resonnce frequency hving the bsorption mximum: Z 1 jm' Z2 jz0 cot k0d Z 1 R Z Z f 0 4Z' 1 62 Z m' d Z' 1Z0 Z'' 1 29

30 Exmple 5.2 Clculte the resonnce frequency: ) Wool 50 mm covered by plstic foil 100 gr/m2. b) Wool 50 mm covered with hrd bord 3.2 mm, 2.5 kg/m2 30

31 Pnel resontor vs. porous bsorber Plstic foil hs lrge impednce compred to wool becuse it is impermeble tight Foils re used in fcdes to protect constructions from humid ir especilly during winter time Foil on top of minerl wool prevents sound propgtion to the wool t high frequencies ) 0.20 mm plstic foil + 50 mm ir b) 0.20 mm plstic foil + 50 mm glss wool c) 50 mm glss wool 1/3-octve bnd frequency [Hz] Oliv, Häggblom & Hongisto (2010) 31

32 Effect of plstic foil on top of minerl wool Structures b nd d ct s resontor since the foil is on top of the wool. Resonnce is voided by sinking the foil inside the wool. The moisture isoltion properties of the fcde my not suffer if the plstic foil is snk t mximum of 1/4th of the wool thickness /3-octve bnd frequency [Hz] ) steel plte 4.0 mm perfortions 24 % mm glss wool b) steel plte 4.0 mm perfortions 24 % + plstic foil mm glss wool c) steel plte 4.0 mm perfortions 24 % + 50 mm glss wool + plstic foil + 50 mm glss wool d) steel plte 4.0 mm perfortions 24 % + plstic foil + 50 mm glss wool + plstic foil + 50 mm ir Oliv, Häggblom & Hongisto (2010) 32

33 Single Helmholtz-resontor Mximum bsorption is chieved t very nrrow resonnce frequency (Tnttri, 2011) f c 2π S l, V S n cross-sectionl re of the neck [m 2 ], l n,eq equivlent length of the neck [m] = l n d n V c volume of the cvity [m 3 ] Single Helmholz resontors re seldom used in room coustics but they re pplied in exhust silencers to remove fixed tonl components. 33

34 Perforted pnels A grid of Helmholz resontors Bord thickness usully 5-20 mm gypsum, veneer, chipbord, etc. Hole dimeter > 1 mm Perfortion rtio between 0 nd 50% Thin felt behind the holes provides dditionl viscous losses 34

35 Perforted pnels A. Perforted MDF bord with thin felt. Additionl wool behind. B. Perforted gypsum bord with thin felt. C. Perforted brick. Bcked by minerl wool. D. Perforted steel with thin felt. Bcked by wool. A B C D 35

36 Perforted pnel: effect of cvity thickness d for 3 products Resonnce frequency reduces with incresing cvity thickness Stnding wves (first nd multiple order) within the cvity cuse vrition of bsorption t high frequencies d=400 mm: stnding wve t =2d/n n=1: 428 Hz n=2: 856 Hz Gyptone 13 % Belgrvi M1 13 % Belgrvi Q1 19 % d=50 mm 0.9 d=100 mm /3-oktvikistn keskitjuus [Hz] 250 d=200 mm /3-oktvikistn keskitjuus [Hz] 1/3-oktvikistn keskitjuus 1/3-oktvikistn keskitjuus Oliv, Häggblom & Hongisto (2010) 1/3-octve bnd [Hz] 1/3-octve bnd [Hz] d=400 mm

37 Perforted pnel: effect of cvity thickness d empty cvity Perforted bord 13 mm incolving felt behind the bord (r=1183 Ps/m). Cvity is empty ) 13 mm gypsum bord 12x12 mm perfortions 19 % b) 13 mm gypsum bord 12x12 mm perfortions 19 % + 50 mm ir c) 13 mm gypsum bord 12x12 mm perfortions 19 % mm ir /3-octve bnd frequency [Hz] d) 13 mm gypsum bord 12x12 mm perfortions 19 % mm ir Oliv, Häggblom & Hongisto (2010) 37

38 Perforted pnel: effect of cvity thickness d filled cvity Perforted bord 13 mm incolving felt behind the bord (r=1183 Ps/m). Cvity filled with wool (=18 kg/m3, r=9600 Ps/m2) ) 13 mm gypsum bord 12x12 mm perfortions 19 % + 50 mm glss wool b) 13 mm gypsum bord 12x12 mm perfortions 19 % mm glss wool c) 13 mm gypsum bord 12x12 mm perfortions 19 % mm glss wool /3-octve bnd frequency [Hz] Oliv, Häggblom & Hongisto (2010) 38

39 Thin perforted pnel: effect of perfortion rtio when bord is bcked by minerl wool Consider minerl wool instlled ginst rigid wll Wool is covered by perforted bord with different perfortion rtios Thin metl bord, thickness 0.9 mm nd cvity 50 mm Cvity filled with minerl wool (d=50 mm, =18 kg/m 3, r=ps/m 2 ). Perfortion rtio is the percentge of perforted re of the totl re /3-octve bnd frequency [Hz] ) perf. steel 4.0 mm perfortions 1 % + 50 mm wool b) perf. steel 4.0 mm perfortions 4 % + 50 mm wool c) perf. steel 4.0 mm perfortions 15 % + 50 mm wool d) perf. steel 4.0 mm perfortions 24 % + 50 mm wool e) perf. steel 4.0 mm perfortions 34 % + 50 mm wool f) 50 mm wool Oliv, Häggblom & Hongisto (2010) 39

40 Thin perforted pnel: effect of perfortion rtio when bord is bcked by empty cvity Thin metl bord, thickness 0.9 mm nd cvity 50 mm. Cvity is empty ) perf. steel 4.0 mm perfortions 1 % + 50 mm ir b) perf. steel 4.0 mm perfortions 4 % + 50 mm ir /3-octve bnd frequency [Hz] c) perf. steel 4.0 mm perfortions 15 % + 50 mm ir d) perf. steel 4.0 mm perfortions 24 % + 50 mm ir Oliv, Häggblom & Hongisto (2010) 40

41 Microperforted pnels Viscosity of perfortion contributes to the sound bsorption when the perfortion dimeter is under 1 mm. Microperfortion enbles e.g. trnsprent sound bsorbers. 41

42 Modeling of multilyer bsorber Bsic pproch Absorption coefficient: α 1 R 1 Z Z Z Z Surfce impednce: Z Z Z coth Γ d Z Z Z coth Γ d Lyer index, i: Chrcteristic impednce Z,i : 0 Z 0 1 Z 1 2 Z 2 N-1 Z N-1 N Z N Surfce impednce Z i+1 : Z 1 Z 2 Z 3 Z N-1 Z N Reflected sound Incident sound 1 Z Air Absorption lyers Bcking Oliv & Hongisto 2012 Applied Acoustics 42

43 Modeling of multilyer bsorber Chrcteristics of lyers 1 Porous bsorber Z Z 1c E jc E Γ k c E j 1c E Constnt c 1 c 2 c 3 c 4 c 5 c 6 c 7 c 8 Vlue Air lyer Z,i =Z 0 = 0 c 0 =413 [kg/m 2 s].,i =jk 0 [1/m]. 3 Unperforted pnel Z,i =0,i =jm p m p [kg/m 2 ] is the surfce mss of the pnel Cox nd D Antonio 2004 Spon Press 43

44 Modeling of perforted pnel (resonnt bsorber) 4 Perforted pnel Surfce impednce: Resistnce of the felt integrted to the bord: R Perfortion rtio: Z R j ωm Z cot k d ε S S Mss of ir in the holes: m ρ ε d 2δ 8θ ω 1d 2 End correction, circulr holes: δ ε 0.47ε End correction, squre holes: δ ε Perforted pnel: m [kg/m 2 ] is the surfce mss of the ir in the holes d c [m] is the depth of the cvity behind the pnel r [Ps/m 2 ] is the specific flow resistivity of the felt. d r [m] is the thickness of the resistive lyer S p [m 2 ] is the perforted re of the pnel nd S [m 2 ] is the totl re of the pnel. Cox nd D Antonio 2004 Spon Press 44

45 Predicted vs. mesured vlues - wools Absorption coefficient 0 Absorption coefficient 0 Predictions were mde with the model described in previous slides. Norml sound incidence. Mesured vlues with impednce tube. Frequency [Hz] 50 mm wool, 76 kg/m3, ryl/m + reflecting bcking Frequency [Hz] 50 mm wool, 18 kg/m3, 9600 ryl/m mm empty cvity + reflecting bcking Oliv & Hongisto 2009 Akustiikkpäivät 45

46 Predicted vs. mesured vlues - Perforted pnels Predictions were mde with the model described in previous slides. Norml sound incidence. Mesured vlues with impednce tube. Absorption coefficient 0 Absorption coefficient 0 Oliv & Hongisto 2009 Akustiikkpäivät Frequency [Hz] 0.9 mm thick perforted steel sheet perfortion dimeter 1.3 mm, perfortion rtio 1.3 % 50 mm wool, 18 kg/m3, 9600 ryl/m 3 Frequency [Hz] 13 mm thick perforted gypsum 12x12 mm, 19 %, huop ryl/m 200 mm thick empty cvity 46

47 Prediction of sttisticl sound bsorption coefficient For bulk recting bsorbents (e.g. minerl wools where sound continues propgtting in oblique incidence), the sttisticl bsorption coefficient cn be estimted from the ngle-dependent sound bsorption coefficient () by: / 2 2 cos sin Estimtion of () requires other models not presented here. For loclly recting bsorbents (e.g. perforted bords where sound wve is forced to perpendiculr direction), the clcultion is strightforwrd: st z' z' z'' 1 z is the normlized surfce impednce t norml sound incidence ngle z' st z' z'' 0 d NOTE: Comprison between predicted nd mesured vlues of st contins lrge uncertinties since the inter-lbortory differences of ISO 354 re lrge z' z'' z'' 2z' z' z'' rctn ln z'' z' z'' 1 z' 47

48 Some selected sttisticl sound bsorption coefficients 1.0 * Instlled ginst concrete wll mm minerl wool* mm minerl wool*' Sttisticl bsorption coefficient f [Hz] 20 mm minerl wool mm cvity* Perforted bord (13 mm 18 %), 200 mm cvity* Full re crpet, fibre thickness 8 mm* Sffice chir, pillow 30 mm* Cotton curtins, 330 gr/m2, folded by 75 %* Lightweight wll (Gypsum 13 mm + 66 mm cvity with studs & wool + gypsum 13 mm* Concrete surfce Book shelf full of books nd files* 48

The effect of sptil position ISO 354 Verticl "low four

2 1.0 Verticl "low", clss C Verticl high four screens both

4 Verticl "high", clss C Horizontl, clss A Horizontl four

49 The effect of sptil position ISO 354 Verticl "low four screens both sided re 12.8 m Verticl "low", clss C Verticl high four screens both sided re 12.8 m 2 S Verticl "high", clss C Horizontl, clss A Horizontl four screens one sided re 11.2 m f [Hz] ISO 354 tests. Clss by ISO

Effect of cvity thickness on 50 mm wool ISO 354 Figure corresponds to cvity 350 mm Verticl edges ir-tight nd reflecting The results re difficult to predict S 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.

50 Effect of cvity thickness on 50 mm wool ISO 354 Figure corresponds to cvity 350 mm Verticl edges ir-tight nd reflecting The results re difficult to predict S f [Hz] Wool 50 mm - no cvity Wool 50 mm - cvity 50 mm Wool 50 mm - cvity 150 mm Wool 50 mm - cvity 350 mm 50

51 References Finnish studies Oliv, D., Hongisto, V. (2013). Sound bsorption of porous mterils - Accurcy of existing prediction methods, Applied Acoustics Oliv D, Keränen J, Hongisto V, Absorption modelling of multilyer constructions, Proceedings of Bltic-Nordic Acousticl Meeting NAM 2010, Bergen, Norwy, My, Oliv D, Häggblom H, Hongisto V, Monikerroksisten bsorptiorkenteiden mllintminen, Akustiikkpäivät 2009, Vs , , Akustinen Seur ry, Espoo, Oliv D, Häggblom H, Keränen J, Virjonen P, Hongisto V, Absorptiosuhteen riippuvuus mteriliprmetreist, Akustiikkpäivät 2007, , Espoo, , Akustinen Seur r.y., Oliv D, Häggblom H, Hongisto V, Sound bsorption of multi-lyer structures - experimentl study, Indoor Environment Lbortory, Turku, Finnish Institute of Occuptionl Helth, Helsinki, Finlnd, Oliv D, Room coustics modelling using the ry-trcing method: implementtion nd evlution, Licentite Thesis (in english), University of Turku, Deprtment of Physics, 2005, Turku, Finlnd. Study books nd journl rticles: Andersson, N-Å, Sound bsorption Round Robin Test, Proceedings of Forum Acusticum 2011, 27 June 1 July, Alborg, Denmrk. Bies DA, Hnsen CH, Engineering Noise Control, 2nd Ed. E&FN Spon, London, Boden H et l., Ljud och Vibrtioner, Kungl Teknisk Högskoln, Mrcus Wllenberg Lbortoriet, Stockholm, Sweden, Cox TJ, D'Antonio P. (2004). Acoustic bsorbers nd diffusers, Theory, Design nd Appliction, Spon Press, London. Guy, R. W. (1989). A preliminry study model for the bsorption or trnsmission of sound in multi-lyer systems. Noise Con. Eng. J. 33(3) Delny ME, Bzley EN, Acousticl properties of fibrous bsorbent mterils. Appl. Acoust. 3 (1970) Fhy FJ, Foundtions of Engineering Acoustics, Acdemic Press, London, UK, 2000 Mechel F P, Vér I L, Sound-bsorbing mterils nd sound bsorbers, In book "Noise nd Vibrtion Control Engineering", Ch. 8, Ed. Bernek L L nd Vér I L, John Wiley & Sons Inc. New York, USA, Books in Finnish: RIL Rkennusten kustinen suunnittelu, Rkennusinsinöörien liitto ry., Helsinki, 207. RIL Ääneneristyksen toteuttminen, Rkennusinsinöörien liitto r.y., Helsinki, Hlme, A. & Seppänen, O Ilmstoinnin äänitekniikk. Jyväskylä, Suomen LVI-liitto ry. Stndrds: Google knows the ltest versions of the ISO stndrds referred bove. 51

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