Room Acoustics Solution Provider: Reverberation Time Based Computational Diagnostics

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Evaluating accurate values of reverberation time and hence arriving at solutions for rectification of flawed room acoustics, turns out to be an involved process, especially when the number of absorbers is large and the coefficients, diverse. A pair of algorithms for developing a set of twelve specific purpose functions in ‘C’, in order to arrive at complete solutions for rectification of defective acoustics, is offered. The algorithms can be employed independently or in conjunction, subject to availability of parameters pertaining to the enclosure under investigation. Functions generated can be applied depending on whether the solution sought is specific or wide-ranging and whether the approach to be adapted is Sabine’s, Eyring’s or Millington’s. The functions can also be interlinked in order to develop a need-based correction-software and to generate ready-reckoners for reference in industries that manufacture acoustic materials.

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Room Acoustics Solution Provider: Reverberation Time Based Computational Diagnostics

  1. 1. Abstract- Evaluating accurate values of reverberation time and room acoustics, is in itself, an involved and time-consuminghence arriving at solutions for rectification of flawed room process. The process turns out to be tedious especially when theacoustics, turns out to be an involved process, especially when the number of absorbers present is large and absorption coefficientsnumber of absorbers is large and the coefficients, diverse. A pair wide-ranging.8,12 A pair of algorithms (Figs.1(a) and (b)) thatof algorithms for developing a set of twelve specific purposefunctions in ‘C’, in order to arrive at complete solutions for can be used to code a set of twelve, specific purpose functionsrectification of defective acoustics, is offered. The algorithms can in ‘C, to address this involved process of rectification, isbe employed independently or in conjunction, subject to offered. A function may be used independently or combinedavailability of parameters pertaining to the enclosure under with another depending upon the knowledge of basic acousticinvestigation. Functions generated can be applied depending on parameters pertaining to the enclosure. The functions arewhether the solution sought is specific or wide-ranging and divided into four subsets of three each, in order to:whether the approach to be adapted is Sabine’s, Eyring’s or i. Aid the selection of an appropriate function or combinationMillington’s. The functions can also be interlinked in order to thereof, anddevelop a need-based correction-software, and to generate ready- ii. Rapidly arrive at accurate, reliable and complete solutionsreckoners for reference in industries that manufacture acousticmaterials. for correction. The solutions delivered provide both quality and quantity of acoustic material required, and also the manner in which theKeywords: computational acoustics, reverberation material should be incorporated within the enclosure. 9,10,13,14 Astime, room acoustics, Sabine, Norris-Eyring, Millington-Sette the cost involved is a direct function of the amount of material required, the quantity estimates are critical, and therefore I. INTRODUCTION function sets 2 and 4 are significant. Evaluation of reverberation time for ‘live’ and ‘dead’ rooms, II. FUNCTION CONFIGURATIONand subsequent assessment of acoustic quality leading torevelation of defects, involves parameters like dimensions of The function-sets are as follows:the room, surface areas of absorbing materials and their Set 1: Functions RT1.0, 1.1 and 1.2 - beginning withabsorption coefficients.1 Auxiliary parameters like number of dimensions and absorption, assists in seeking specific solutionsabsorbing surfaces, the average absorption coefficient, and (Listing RT1.1 illustrated at Fig 3)deviation of coefficients from the average, are critical to a Set 2: Functions RT1.3, 1.4 and 1.5 - beginning withcorrect reverberation time estimate. Nevertheless, the dimensions and absorption, assists in seeking a range ofassumptions involved in evaluation and the techniques solutions by generating relevant ready reckoners (Listing RTemployed for computation, differ with the approach 1.5 illustrated at Fig 4)adapted.2,3,4,5 There exist three different approaches to choose Set 3*: Functions RT2.0, 2.1 and 2.2 - beginning withfrom depending upon the auxiliary parameters: Sabine’s, reverberation time and dimensions, assists in seeking specificEyring’s and Millington’s. Sabine’s approach, wherein the solutions (Listing RT2.0 illustrated at Fig 5) 0.049V Set 4*: RT2.3, 2.4 and 2.5 - beginning with reverberation timereverberation time is given by T = , is applicable ∑αi S i and dimensions, assists in seeking a range of solutions by generating relevant ready reckoners (Listing RT2.4 illustratedwhen the average absorption coefficient is less than 0.2 (‘live’ at Fig.6)rooms). For a coefficient of 0.2 or higher (‘dead’ rooms), thereverberation time estimate employing Sabine’s approach is in Sets 3 and 4 are employed when the reverberation time iserror by about 10%.3 Eyring’s approach is appropriate when predetermined. Sets 1 and 2 are used when reverberation time isthe average absorption coefficient exceeds 0.2 and the unknown. Further, sets 1 and 3 are used when seeking specificdifference between coefficients of surfaces contributing to total solutions for correction, that is, when applying a material ofabsorption is small. Eyring’s approach gives known absorption coefficient. Sets 2 and 4 could be used when 0.049V seeking a range of solutions for correction, that is when needingT = . Millington’s approach is used in case of − S ln(1 −α ) inputs in choosing a particular material from a range of‘dead’ rooms wherein the number of absorbing surfaces is materials of known absorption coefficients.considerably large and diverse. The reverberation time is then The 2x6 array (Fig.2) helps in selecting function(s) to be 0.049V employed, independently or as combinations depending upongiven by T = 3,6,7 whether: ∑− S i ln(1 −αi ) a) Reverberation time is known or unknown, Arriving at accurate values of reverberation time, and hence ___________________________________________________working out a complete solution for rectification of defective * Milington’s approach requires absorption in addition
  2. 2. b) Solution required is specific or a range thereof, and 2.4 and 2.5 can be combined to obtain yet another function thatc) Approach used is Sabine’s, Eyring’s or Millington’s lets us choose an approach leading to a range of solutions, or The functions are user friendly and the user simply has to another set of ready reckoners.#key in: i) Dimensions of the enclosure, and A column-wise combination is also possible: for instanceii) Either surface areas and corresponding absorptivities, or the RT1.0 and 2.0 can be combined in order to employ Sabine’spredetermined value of reverberation time approach to seek solutions either in the light or ignorance ofThe function(s) gives the value of total absorption and reverberation time (or absorption). The listing illustrated in Fig.reverberation time (if unknown initially) indicating 8(b) FUNRT9.0 elucidates the corresponding code in ‘C’.simultaneously whether the enclosure needs treatment and its Similarly we may combine RT1.1 and 2.1 (Eyring’s approachextent for a specific solution) or RT1.3 and 2.3 (Sabine’s to selectin ‘sabin’. Further, if the enclosure needs correction, the from a range of materials), and so on.functions eitheri) Prompts the user to select a material, and recommend the IV. CONCLUDING REMARKSquantity and manner in which the chosen material could beapplied11, or The functions and their combinations are so configured asii) Recommend a range of materials, their quantities and the to facilitate a perfect solution for the rectification of flawedmanner in which they could be incorporated. room acoustics. They incorporate checks and balances, not onlyFigs. 7(a) and (b) illustrate solutions in their simplest form, on the number of absorbers, but also on whether the absorptiongenerated by employing functions RT1.1 and 2.4 pertaining to coefficient of the material chosen for treatment, is appropriate.cases (i) and (ii) above for an enclosure in question. If an error or violation relating to any of these parameters is detected, the function demands a correction before it proceeds The functions can also be applied to generate ready any further. For instance, if absorption coefficient of thereckoners for a set of notional absorption coefficients, for material selected is lesser than the average of ones alreadyreference in industries that manufacture acoustic materials. Fig. existing, the function detects the breach and suggests the need7(b) which is a solution in case (i) above, doubles up as, one for a better selection. The same holds true for inappropriatelysuch ready reckoner. Solutions can be simulated for large dimensions and absorber-numbers.hypothetical parameters and a variety of approaches could becompared.11,12,13 REFERENCES III. FUNCTION COMBINATIONS 1. Nascimento R., Zindeluk M. and Feiteira J.F., Sound absorption in scale and model reverberation chamber, Journal of Acoustical The 2x6 array of functions, comprising RT1.0 to RT1.5 and Society of America, 2002, 112(5),2397RT2.0 to RT2.5, is so configured that they could be suitably 2. Fausti P., Farina A., Acoustic measurements in opera houses:combined either row-wise or column-wise in order to develop a Comparison between different techniques and equipment, Journal of‘Need based correction software’, or an all-encompassing Sound and Vibration, 2002, 232(1), 213-229 3. Kinsler L.E. and Frey A. R., Fundamentals in Acoustics, 2nd edn.,function. A row-wise combination of RT1.0, 1.1 and 1.2 results Wiely Eastern Limited, 415 - 458into a new function that offers a choice between the three 4. Moretessagne F,Legrand O, Sornette D, Role of the absorptionapproaches - Sabine’s, Eyring’s or Millington’s, leading to distribution and generalization of exponential reverberation lawspecific solutions even in the absence of any information in chaotic rooms, Journal of Acoustical Society of America, 1993, 94, (1), 154-161.regarding reverberation time. The listing FUNRT1.9 illustrated 5. Beranek L L, Concert hall acoustics, Journal of Acoustical Societyin Fig 8(a) elucidates the corresponding code in ‘C’. Similarly of America, 1992, 92(1), 1-39the functions RT2.0, 2.1 and 2.2 can be combined to obtain yet 6. Rettinger M., Acoustic Design and Noise Control, Vol. 1, Chemicalanother function that offers a choice between approaches and Publishing Company, New York, 17 - 25. 7. Legrand O, Sornette D, Test of Sabine’s reverberation time inleads to a specific solution #(in light of reverberation time yet in ergodic auditoriums within geometrical acoustics, Journal ofthe absence of any knowledge about absorption). Acoustical Society of America, 1990, 88(2), 865-870 8. Hodgson M., Rating, ranking and understanding acoustical quality in A combination of RT1.3, 1.4 and 1.5 results into a function university classrooms, Journal of Acoustical Society of America, 2002, 112(2), 568-575that allows selection of a suitable approach leading to a range 9. Camilo T. S., Medrado L. O. and Tenenbaum R. A., New softwareof solutions or ready-reckoners. Similarly, the functions RT2.3, for acoustic room simulation: A study of its performance and___________________________________________________ validation by international comparison, Journal of Acoustical# Millington’s approach being an exception, as it requires the Society of America, 2002, 112(5), 2396value of αi beforehand.
  3. 3. 10. Kahle E. and Essert R., Toward an open room acoustics 19. Evaluate: QTY OF MATERIAL REQUIRED IF PANELLED / measurement system. II. Software, Journal of Acoustical Society of SUSPENDED: America, 1996, 100(4), 2837-2838 FOR SPECIFIC: ABNEW / ABMAT 11. Casteaneda E. M., Computer based system for reverberation room FOR RANGE: INCREASE ABMAT IN SUITABLE STEPS AND design, Journal of Acoustical Society of America , 1994, 96(5), REPEAT 3249 12. Begault D.R., Challenges and solutions for realistic room ALGORITHM b: BEGINNING WITH REVERBERATION simulations, Journal of Acoustical Society of America , 2002, TIME AND DIMENSIONS, ASSISTS IN MATERIAL SELECTION 111(5), 2440 AND MOUNTING 13. Tetsuya Sakuma, Approximate theory of reverberation in rectangular rooms with specular and diffuse reflections, Journal of Acoustical 1. Enter: T OF ENCLOSURE Society of America 2012, 132(4), 2325 2. Check if: T VERY LARGE / IMAGINARY (T>5.0); RECTIFY / REJECT 14. David Canning, Adrain James, Bridjet M. Sheilds, Essex 3. Enter: DIMENSIONS OF ENCLOSURE experimental study: The impact of reverberation time on working 4. Evaluate: VOLUME, SURFACE AREA classrooms, Journal of Acoustical Society of America, 2012, 132(3), 5. Check If: VOLUME VERY LARGE / IMAGINARY (V>600000.0 cu.ft.); 2045 RECTIFY / REJECT 6. Evaluate: TOTAL EXISTING ABSORPTION (SELECT APPROACH): SABINE: LIVE; 0.049*V/TFig.1. Algorithms for coding functions to arrive at EYRING: DEAD; [1.0-[EXP {(-0.049*V)/(T*S)}]]*Scorrections for enclosures with flawed acoustics MILLINGTON; DEAD, DIVERSE α; [Σ - Si ln (1 - αi )]ALGORITHM a: BEGINNING WITH DIMENSIONS AND 7. Hence Evaluate: AVERAGE ABSORPTION COEF ‘ABOLD’:ABSORPTION, ASSISTS IN MATERIAL SELECTION AND SABINE: [0.049*V/T] /AREA;MOUNTING EYRING: [[1.0-[EXP {(-0.049*V)/(T*S)}]]*S ]/AREA;1. Enter: DIMENSIONS OF ENCLOSURE MILLINGTON: [Σ - Si ln (1 - αi )]/AREA2. Evaluate: VOLUME 8. Evaluate: TOTAL ABSORPTION REQD FOR TREATMENT ‘ABNEW’:3. Check If: VOLUME TOO LARGE / IMAGINARY (V>600000.0 cu.ft.); ABNEW = OPTIMUM (0.049*VOLUME / 1.2)– EXISTING;RECTIFY / REJECT 9. Check If: HAVE MATERIAL OF ABSORPTION COEFF. ‘ABMAT’4. Enter: NUMBER/TYPE OF AREAS FOR WHICH ABSORPTION IS TO 10. Enter: ‘ABMAT’ OF MATERIAL SELECTED FOR TREATMENTBE CALCULATED 11. Check If: ‘ABMAT’ TOO LARGE / IMAGINARY (>.85); RECTIFY /5. Check If: NO. OF AREAS LARGE / IMAGINARY (>20); RECTIFY / REJECTREJECT 12. Check If: (‘ABMAT’ < ABOLD); RECTIFY / REJECT6. Enter: AREA TYPES AND THE CORRESPONDING ABSORPTIONS 13. Evaluate: QTY OF MATERIAL REQD IF MOUNTED DIRECTLY ONCOEFS EXISTING:7. Evaluate: TOTAL AREA FOR A SPECIFIC SOLUTION: ABNEW / [ABMAT- ABOLD]8. Evaluate: TOTAL EXISTING ABSORPTION (SELECT APPROACH): FOR A RANGE OF SOLUTIONS: INCREASE ABMAT IN SUITABLE SABINE: LIVE; [Σ αi Si ] STEPS AND REPEAT EYRING: DEAD; [-S ln (1- α)] 14. Evaluate: QTY OF MATERIAL REQUIRED IF PANELLED / SUSPENDED: MILLINGTON; DEAD, DIVERSE α; [Σ - Si ln (1 - αi )] FOR SPECIFIC: ABNEW / ABMAT9. Hence Evaluate: AVERAGE ABSORPTION COEF ‘ABOLD’: FOR RANGE: INCREASE ABMAT IN SUITABLE STEPS AND [Σ αi Si ] /AREA; [-S ln (1- α)] /AREA; OR [Σ - Si ln (1 - αi )]/AREA REPEAT10. Evaluate: REVERBERATION TIME: SABINE: 0.049*V/TOTAL ABS; EYRING: 0.049*V/[(TOTAL AREA)*(LOG(1.0-α))]; OR MILLINGTON: 0.049*V/TOTAL ABS11. Check If: T IS TOO LARGE / IMAGINARY (>5.0 SEC) RECTIFY /REJECT12. Check If: (1.2<T <5.0)13. Evaluate: TOTAL ABSORPTION REQD FOR TREATMENT ‘ABNEW’: ABNEW = OPTIMUM (0.049*VOLUME / 1.2)– EXISTING;14. Check If: HAVE MATERIAL OF ABSORPTION COEFF. ‘ABMAT’15. Enter: ‘ABMAT’ OF MATERIAL SELECTED FOR TREATMENT16. Check If: ‘ABMAT’ TOO LARGE / IMAGINARY (>.85); RECTIFY /REJECT17. Check If: (‘ABMAT’ < ABOLD); RECTIFY / REJECT18. Evaluate: QTY OF MATERIAL REQD IF MOUNTED DIRECTLY ONEXISTING: FOR A SPECIFIC SOLUTION: ABNEW / [ABMAT- ABOLD] FOR A RANGE OF SOLUTIONS: INCREASE ABMAT IN SUITABLESTEPS AND REPEAT
  4. 4. Fig.2. 2x6 function-array divided into four subsets to simplify selection of the right function or a combination thereof. Specific solutions Range of solutions Approach Sabine Eyring Millington Sabine Eyring Millington T unknown RT1.0 RT1.1 RT1.2 RT1.3 RT1.4 RT1.5 T known RT2.0 RT2.1 RT2.2 RT2.3 RT2.4 RT2.5 scanf("%f%f",ands[j],anda[j]);Fig. 3. RT1.1: Treatment for reverberant enclosures aa=aa+s[j]*a[j];(T>1.2 sec.)† using Eyring’s approach for dead rooms areatotl=areatotl+s[j];(beginning with dimensions and absorption) } abar=aa/areatotl;#include<stdio.h> t=-0.049*v/(areatotl*(log(1.0-abar)));#include<math.h>#include<conio.h> printf("nThe volume of the enclosure is %f cubic feetn",v);void main (void){ printf("The total absorption is %f sabin n",aa);int j=0,i=0; printf("The reverberation time is %f secondsn",t);float if(t>5)printf("T is too large/imaginary yet aceptablen");t,l,w,h,v,a[100],abar,s[100],areatotl=0.0,aa=0.0,abnew,abmat,s if(t>1.2)mat,smat1; {clrscr(); printf("The enclosure needs treatment !n");printf("TREATMENT OF REVERBERANT ENCLOSURES abnew=(0.049*v/1.2)+(areatotl*(log(1.0-(T>1.2 SEC.) - n"); abar)));printf(" Using Eyrings approach for printf("Must add atleast %f sabin absorptionDEAD ROOMSn"); to enclosuren",abnew);printf("Beginning simply with dimensions and absorption, the aerror:function asists in material selection and mountingnn"); printf("nEnter absorption coeff. of materialprintf("Enter the length, width and height of enclosure in selected for treatmentn");feetn"); scanf("%f",andabmat);scanf("%f%f%f",andl,andw,andh); if(abmat<=abar)printf("ERROR ! Coeff. mustv=l*w*h;if(v>600000.0)printf("Volume too large/imaginary be > %4.2fn",abar);yet acceptablen"); if(abmat<=abar)goto aerror;printf("Enter the number of areas for which absorption is to be if(abmat>.85)printf("coeff. too calculatedn"); large/imaginary yet aceptablen");scanf("%d",andi); smat=abnew/(abmat-abar);if(i>20)printf("No. of areas too large/imaginary yet smat1=abnew/abmat;acceptablen"); printf("n%e sq. feet of material is required if for(j=1;j<=i;j++) to be mounted directly on the { surfaces whose absorption coefficient lies around printf("Enter area no. %d in sq feet and the %4.2fn",smat,abar);corresponding absorption coeff.n",j);
  5. 5. printf("ORn%e sq. feet of material is }required if to be panelled / suspended t=0.049*v/aa;coef=aa/s1; freelyn",smat1); printf("nThe volume of the enclosure is %f cubic feetn",v); } printf("The total absorption is %f sabin n",aa);getch(); printf("The reverberation time is %f secondsn",t);} if(t>5)printf("T is too large/imaginary yet aceptablen"); if(t>1.2) { printf("The enclosure needs treatment !n");___________________________________________________ abnew=(0.049*v/1.2)-aa;† The condition is variable printf("Must add atleast %f sabin absorptionFig.4. RT1.5: Treatment for reverberant enclosures to enclosuren",abnew);(T>1.2 sec.)† using Millington’s approach for dead berror:rooms. Beginning with dimensions and absorption, the printf("Enter mean absorption coeff. of areasfunction creates a ready reckoner to be covered with new materialn"); scanf("%f",andabold);#include<stdio.h> if(abold>coef)printf("coeff. must be <=#include<math.h> %4.2f ERROR !n",coef);#include<conio.h> if(abold>coef)goto berror;void main (void) clrscr();{ printf("ttPOSSIBLE SOLUTIONSn");int j=0,i=0,k=0; printf("ttOld Coeff. = %4.2fn",abold);float printf("nQuantity_1tQuantity_2ttNewt,l,w,h,v,a[100],s[100],s1=0.0,coef=0.0,aa=0.0,abnew,abmat,ab Coeff.n");old,smat,smat1; printf("Over old tFreely suspendedn");clrscr(); printf("(sq. ft.)t(sq. ft.) nn");printf("TREATMENT OF REVERBERANT ENCLOSURES abmat=abold;(T>1.2 SEC.) - n"); for(k=1;k<=15;k++)printf(" Using Millington and Sette approach {for DEAD ROOMSn"); abmat=abmat+.01; smat=abnew/printf("Beginning simply with dimensions and absorption, the (abmat-abold); smat1=abnew/abmat;function creates anready reckoner"); printf("%et%ettprintf(" that assists in selecting the materialnn"); %4.2fn",smat,smat1,abmat);printf("Enter the length, width and height of enclosure in }feetn"); }scanf("%f%f%f",andl,andw,andh); elsev=l*w*h;if(v>600000.0)printf("Volume too large/imaginary printf("nT < 1.2 sec - Well within the limitsn NOyet acceptablen"); TREATMENT REQUIREDn"); cerror: getch();printf("Enter the number of areas for which absorption is to be } calculatedn"); Fig.5. RT2.0: Treatment of reverberant enclosures (T>1.2 sec.) †scanf("%d",andi); using Sabine’s approach for live rooms (beginning withif(i>100)printf("ERROR ! No. of areas too large and NOT reverberation time and dimensions)ACCEPTABLEn");if(i>100)goto cerror; #include<stdio.h>if(i>20)printf("No. of areas too large/imaginary yet #include<conio.h>acceptablen"); void main (void) for(j=1;j<=i;j++) { { float printf("Enter area no. %d in sq feet and the t=0.0,l,w,h,v=0.0,s,aa=0.0,amean,abnew=0.0,abmat,smat,smat1corresponding absorption coeff.n",j); ; scanf("%f%f",ands[j],anda[j]); aa=aa- clrscr();s[j]*(log(1.0-a[j])); s1=s1+s[j];
  6. 6. printf("TREATMENT OF REVERBERANT ENCLOSURES beginning with reverberation time and dimensions,(T>1.2 sec.) - n"); the function creates a ready reckonerprintf("Beginning with reverberation time and dimensions, thefunction assists innmaterial selection and mountingnn"); #include<stdio.h>printf("Enter the reverberation time of the defective enclosure #include<math.h>in sec.n"); #include<conio.h>scanf("%f",andt); void main (void)if(t>5)printf("T is too large/imaginary yet aceptablen"); {if(t<1.2)goto derror; float___________________________________________________ t=0.0,l,w,h,v=0.0,s,aa=0.0,amean,abnew=0.0,abmat,smat,smat1† The condition is variable ; int k;printf("Enter the length, width and height in feetn"); clrscr();scanf("%f%f%f",andl,andw,andh); printf("TREATMENT OF REVERBERANT ENCLOSURESv=l*w*h;if(v>600000.0)printf("Volume too large/imaginary (T>1.2 sec.) - n");yet acceptablen"); printf(" Using Eyrings approach fors=2*(l*w+l*h+w*h); DEAD ROOMSn");aa=0.049*v/t; printf("Beginning with reverberation time and dimensions, theamean=aa/s; function assists innmaterial selection and mountingnn");printf("nThe volume of the enclosure is %f cubic feetn",v); printf("Enter the reverberation time of the defective enclosureprintf("The total absorption is %f sabin n",aa); in sec.n");printf("The mean absorption coeff. is %fn",amean); scanf("%f",andt); if(t>1.2) if(t>5)printf("T is too large/imaginary yet aceptablen"); { if(t<1.2)goto derror; printf("The enclosure needs treatment !n"); printf("Enter the length, width and height in feetn"); abnew=0.049*v/1.2-aa; scanf("%f%f%f",andl,andw,andh); printf("Must add atleast %f sabin absorption v=l*w*h;if(v>600000.0)printf("Volume too large/imaginaryto enclosurenn",abnew); yet acceptablen"); aerror: s=2*(l*w+l*h+w*h); printf("nEnter absorption coeff. of material amean=1.0-(exp((-0.049*v)/(t*s)));selected for treatmentn"); aa=amean*s; scanf("%f",andabmat); printf("nThe volume of the enclosure is %f cubic feetn",v); if(abmat<=amean)printf("coeff. must be > printf("The total absorption is %f sabin n",aa);%4.2f ERROR !n",amean); printf("The average absorption coeff. is %fn",amean); if(abmat<=amean)goto aerror; if(t>1.2) if(abmat>.85)printf("coeff. too {large/imaginary yet aceptablen"); printf("The enclosure needs treatment !n"); smat=abnew/(abmat-amean); abnew=(0.049*v/1.2)-aa; smat1=abnew/abmat; printf("Must add atleast %f sabin absorption printf("n%e sq. feet of the material is to enclosurenn",abnew);required if to be mounted on the nsurface directlyn",smat); printf("Press ENTER to continuen"); printf("ORn%e sq. feet of the material is getch();required if to be panneled / suspended freelyn",smat1); clrscr(); } printf("ttPOSSIBLE SOLUTIONSn"); else printf("ttOld Coeff. = %4.2fn",amean); derror: printf("nQuantity_1tQuantity_2ttNew printf("nT < 1.2 sec - Well within the Coeff.n");limitsnNO TREATMENT REQUIREDn"); printf("Over old tFreely suspendedn");getch(); printf("(sq. ft.)t(sq. ft.) nn");} abmat=amean; for(k=1;k<=15;k++)Fig.6. RT2.4: Treatment of reverberant enclosures {(T>1.2 sec.) † using Eyring’s approach for dead rooms: abmat=abmat+.01;
  7. 7. smat=abnew/(abmat-amean); 140 50 30 smat1=abnew/abmat; The volume of the enclosure is 210000.000000 cubic feet printf("%et%ett The total absorption is 5199.019043 sabin%4.2fn",smat,smat1,abmat); The average absorption coeff. is 0.201536 } The enclosure needs treatment ! } Must add atleast 3455.980957 sabin absorption to enclosure else derror: printf("nT < 1.2 sec - Well within thelimitsnNO TREATMENT REQUIREDn"); ___________________________________________________ †getch(); The condition is variable} POSSIBLE SOLUTIONSFig.7 (a). Solution generated by RT1.1 Old Coeff. = 0.20TREATMENT OF REVERBERANT ENCLOSURES (T>1.2 Quantity_1 Quantity_2SEC.) - New Coeff.Using Eyring’s approach for DEAD ROOMS Over old Freely suspendedBeginning simply with dimensions and absorption, the function ( sq. ft. ) (sq. ft.)assists in material 3.45598e+05 1.63375e+04selection and mounting 0.21Enter the length, width and height of the enclosure in feet 1.72799e+05 1.56001+e04140 50 30 0.22Enter the number of areas for which absorption is to be 1.15199e+05 1.49263e+04calculated 0.232 8.63995e+04 1.43083e+04Enter area no. 1 in sq feet and corresponding absorption coeff. 0.2418400 .21 6.91196e+04 1.37395e+04Enter area no. 2 in sq feet and corresponding absorption coeff. 0.257000 .22 5.75997e+04 1.32142e+04The volume of the enclosure is 210000.000000 cubic feet 0.26The total absorption is 5404.000000 sabin 4.93712e+04 1.27275+e04The reverberation time is 1.693518 seconds 0.27The enclosure needs treatment ! 4.31998e+04 1.22754e+04Must add atleast 2498.890381 sabin absorption to enclosure 0.28Enter absorption coeff. of material selected for treatment 3.83998e+04 1.18544e+04.33 0.292.13136e+04 sq. feet material is required if to be mounted 3.45598e+04 1.14612e+04directly on the surfaces whose absorption coefficient lies 0.30around 0.21 3.14180e+04 1.10934e+04OR 0.317.57240e+03 sq. feet of material is required if to be panelled / 2.87999e+04 1.07483+e04suspended freely 0.32 2.65845e+04 1.04241e+04Fig.7(b). Solution generated by RT2.4 0.33 2.46856e+04 1.01189e+04TREATMENT OF REVERBERANT ENCLOSURES (T >1.2 0.34sec.) – 2.30399e+04 9.83108e+03Using Eyring’s approach for DEAD ROOMS 0.35Beginning with reverberation time and dimensions, the functionassists in Fig.8 (a). FUNRT1.9: Combination of RT1.0,1.1 and 1.2 intomaterial selection and mounting FUNRT1.9: offers a choice of approach leading to specificEnter reverberation time of the defective enclosure in sec. solutions in the absence of any information regarding1.8 reverberation time.Enter the length, width and height in feet
  8. 8. #include<stdio.h> Fig.8(b). FUNRT9.0: RT1.0 and RT2.0 combined to#include<math.h> employ Sabine’s approach for#include<stdlib.h> seeking solutions in the ignorance#include<conio.h> of reverberation time or absorptionint i=0,j=00; #include<stdio.h>char ch; #include<math.h>float #include<stdlib.h>t,l,w,h,v,a[100],abar=0.0,s1=0.0,s[100],areatotl=0.0,aa=0.0,coe #include<conio.h>f=0.0,abnew,abmat,abold,smat,smat1; /* intchar and float globally defined */ int i=0,j=0; char ch;rt10(void); floatrt11(void); t,l,w,h,v,a[100],s1=0.0,s[100],aa=0.0,coef=0.0,abnew,abmat,abrt12(void); old,amean,smat,smat1; /* int char and float globally defined */main (){ rt10(void);clrscr(); rt20(void);printf("SOLUTION FOR CORRECTION OF DEFECTIVEACOUSTICS IN ENCLOSURES (T>1.2 SEC.) - n"); main ()printf("nCHOOSE A METHOD:1. Using Sabines equation for {LIVE ROOMS n"); clrscr();printf(" 2. Using Eyring and Norris approach for printf("SOLUTION FOR CORRECTION OF DEFECTIVEDEAD ROOMS n"); ACOUSTICS IN ENCLOSURES (T>1.2 SEC.) - n");printf(" 3. Using Millington and Sette for DEAD printf("Employing Sabines equation for LIVE ROOMSn");ROOMS n"); printf("nCHOOSE A METHODnn");ch=getchar(); printf("1. Beginning simply with dimensions and absorption, switch(ch) the function assists innmaterial selection and mountingnn"); { printf("2. Beginning with reverberation time and dimensions, case 1: rt10(); break; the function assists innmaterial selection and mountingnn"); case 2: rt11(); break; ch=getchar(); case 3: rt12(); break; switch(ch) } { return; case 1: rt10(); break;} case 2: rt20(); break; }rt10(void) return;{ }Insert “RT1.0” here; return;} rt10(void) {rt11(void) Insert “RT1.0” here; return;{ }Insert “RT1.1” here; return;} rt20(void) {rt12() Insert “RT2.0” here; return;{ }Insert “RT1.2” here; return;}

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