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.

1. Abstract- Evaluating accurate values of reverberation time and room acoustics, is in itself, an involved and time-consuming
hence arriving at solutions for rectification of flawed room process. The process turns out to be tedious especially when the
acoustics, turns out to be an involved process, especially when the number of absorbers present is large and absorption coefficients
number of absorbers is large and the coefficients, diverse. A pair wide-ranging.8,12 A pair of algorithms (Figs.1(a) and (b)) that
of algorithms for developing a set of twelve specific purpose
functions in ‘C’, in order to arrive at complete solutions for
can be used to code a set of twelve, specific purpose functions
rectification of defective acoustics, is offered. The algorithms can in ‘C, to address this involved process of rectification, is
be employed independently or in conjunction, subject to offered. A function may be used independently or combined
availability of parameters pertaining to the enclosure under with another depending upon the knowledge of basic acoustic
investigation. Functions generated can be applied depending on parameters pertaining to the enclosure. The functions are
whether 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 combination
Millington’s. The functions can also be interlinked in order to thereof, and
develop a need-based correction-software, and to generate ready-
ii. Rapidly arrive at accurate, reliable and complete solutions
reckoners for reference in industries that manufacture acoustic
materials. for correction.
The solutions delivered provide both quality and quantity of
acoustic material required, and also the manner in which the
Keywords: computational acoustics, reverberation material should be incorporated within the enclosure. 9,10,13,14 As
time, 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 CONFIGURATION
and subsequent assessment of acoustic quality leading to
revelation 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 with
absorption coefficients.1 Auxiliary parameters like number of dimensions and absorption, assists in seeking specific solutions
absorbing 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 with
correct reverberation time estimate. Nevertheless, the dimensions and absorption, assists in seeking a range of
assumptions involved in evaluation and the techniques solutions by generating relevant ready reckoners (Listing RT
employed 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 with
from depending upon the auxiliary parameters: Sabine’s, reverberation time and dimensions, assists in seeking specific
Eyring’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 time
reverberation 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 illustrated
when the average absorption coefficient is less than 0.2 (‘live’
at Fig.6)
rooms). For a coefficient of 0.2 or higher (‘dead’ rooms), the
reverberation time estimate employing Sabine’s approach is in
Sets 3 and 4 are employed when the reverberation time is
error by about 10%.3 Eyring’s approach is appropriate when
predetermined. Sets 1 and 2 are used when reverberation time is
the average absorption coefficient exceeds 0.2 and the
unknown. Further, sets 1 and 3 are used when seeking specific
difference between coefficients of surfaces contributing to total
solutions for correction, that is, when applying a material of
absorption 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 needing
T = . 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 upon
given 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. b) Solution required is specific or a range thereof, and 2.4 and 2.5 can be combined to obtain yet another function that
c) 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 instance
ii) Either surface areas and corresponding absorptivities, or the RT1.0 and 2.0 can be combined in order to employ Sabine’s
predetermined value of reverberation time approach to seek solutions either in the light or ignorance of
The 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 approach
extent for a specific solution) or RT1.3 and 2.3 (Sabine’s to select
in ‘sabin’. Further, if the enclosure needs correction, the from a range of materials), and so on.
functions either
i) Prompts the user to select a material, and recommend the IV. CONCLUDING REMARKS
quantity and manner in which the chosen material could be
applied11, or The functions and their combinations are so configured as
ii) Recommend a range of materials, their quantities and the to facilitate a perfect solution for the rectification of flawed
manner in which they could be incorporated. room acoustics. They incorporate checks and balances, not only
Figs. 7(a) and (b) illustrate solutions in their simplest form, on the number of absorbers, but also on whether the absorption
generated 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 the
reckoners for a set of notional absorption coefficients, for material selected is lesser than the average of ones already
reference in industries that manufacture acoustic materials. Fig. existing, the function detects the breach and suggests the need
7(b) which is a solution in case (i) above, doubles up as, one for a better selection. The same holds true for inappropriately
such ready reckoner. Solutions can be simulated for large dimensions and absorber-numbers.
hypothetical parameters and a variety of approaches could be
compared.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),2397
RT2.0 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 - 458
into a new function that offers a choice between the three 4. Moretessagne F,Legrand O, Sornette D, Role of the absorption
approaches - Sabine’s, Eyring’s or Millington’s, leading to distribution and generalization of exponential reverberation law
specific 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 Society
in Fig 8(a) elucidates the corresponding code in ‘C’. Similarly of America, 1992, 92(1), 1-39
the functions RT2.0, 2.1 and 2.2 can be combined to obtain yet 6. Rettinger M., Acoustic Design and Noise Control, Vol. 1, Chemical
another 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 in
leads to a specific solution #(in light of reverberation time yet in ergodic auditoriums within geometrical acoustics, Journal of
the 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), 568-575
that allows selection of a suitable approach leading to a range 9. Camilo T. S., Medrado L. O. and Tenenbaum R. A., New software
of 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), 2396
value of αi beforehand.

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/T
Fig.1. Algorithms for coding functions to arrive at EYRING: DEAD; [1.0-[EXP {(-0.049*V)/(T*S)}]]*S
corrections 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 )]/AREA
2. 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 TREATMENT
BE CALCULATED 11. Check If: ‘ABMAT’ TOO LARGE / IMAGINARY (>.85); RECTIFY /
5. Check If: NO. OF AREAS LARGE / IMAGINARY (>20); RECTIFY / REJECT
REJECT 12. Check If: (‘ABMAT’ < ABOLD); RECTIFY / REJECT
6. Enter: AREA TYPES AND THE CORRESPONDING ABSORPTIONS 13. Evaluate: QTY OF MATERIAL REQD IF MOUNTED DIRECTLY ON
COEFS 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 / ABMAT
9. 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 REPEAT
10. 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 ABS
11. Check If: T IS TOO LARGE / IMAGINARY (>5.0 SEC) RECTIFY /
REJECT
12. 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 TREATMENT
16. Check If: ‘ABMAT’ TOO LARGE / IMAGINARY (>.85); RECTIFY /
REJECT
17. Check If: (‘ABMAT’ < ABOLD); RECTIFY / REJECT
18. Evaluate: QTY OF MATERIAL REQD IF MOUNTED DIRECTLY ON
EXISTING:
FOR A SPECIFIC SOLUTION: ABNEW / [ABMAT- ABOLD]
FOR A RANGE OF SOLUTIONS: INCREASE ABMAT IN SUITABLE
STEPS AND REPEAT

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 Eyring's approach for printf("Must add atleast %f sabin absorption
DEAD 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 material
printf("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. must
v=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. 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 absorption
Fig.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 areas
function 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_2ttNew
t,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%ett
printf(" 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); else
v=l*w*h;if(v>600000.0)printf("Volume too large/imaginary printf("nT < 1.2 sec - Well within the limitsn NO
yet 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 with
if(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,smat1
corresponding 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. printf("TREATMENT OF REVERBERANT ENCLOSURES beginning with reverberation time and dimensions,
(T>1.2 sec.) - n"); the function creates a ready reckoner
printf("Beginning with reverberation time and dimensions, the
function 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 ENCLOSURES
v=l*w*h;if(v>600000.0)printf("Volume too large/imaginary (T>1.2 sec.) - n");
yet acceptablen"); printf(" Using Eyring's approach for
s=2*(l*w+l*h+w*h); DEAD ROOMSn");
aa=0.049*v/t; printf("Beginning with reverberation time and dimensions, the
amean=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 enclosure
printf("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/imaginary
to 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. 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 the
limitsnNO TREATMENT REQUIREDn"); ___________________________________________________
†
getch(); The condition is variable
} POSSIBLE SOLUTIONS
Fig.7 (a). Solution generated by RT1.1 Old Coeff. = 0.20
TREATMENT OF REVERBERANT ENCLOSURES (T>1.2 Quantity_1 Quantity_2
SEC.) - New Coeff.
Using Eyring’s approach for DEAD ROOMS Over old Freely suspended
Beginning simply with dimensions and absorption, the function ( sq. ft. ) (sq. ft.)
assists in material 3.45598e+05 1.63375e+04
selection and mounting 0.21
Enter the length, width and height of the enclosure in feet 1.72799e+05 1.56001+e04
140 50 30 0.22
Enter the number of areas for which absorption is to be 1.15199e+05 1.49263e+04
calculated 0.23
2 8.63995e+04 1.43083e+04
Enter area no. 1 in sq feet and corresponding absorption coeff. 0.24
18400 .21 6.91196e+04 1.37395e+04
Enter area no. 2 in sq feet and corresponding absorption coeff. 0.25
7000 .22 5.75997e+04 1.32142e+04
The volume of the enclosure is 210000.000000 cubic feet 0.26
The total absorption is 5404.000000 sabin 4.93712e+04 1.27275+e04
The reverberation time is 1.693518 seconds 0.27
The enclosure needs treatment ! 4.31998e+04 1.22754e+04
Must add atleast 2498.890381 sabin absorption to enclosure 0.28
Enter absorption coeff. of material selected for treatment 3.83998e+04 1.18544e+04
.33 0.29
2.13136e+04 sq. feet material is required if to be mounted 3.45598e+04 1.14612e+04
directly on the surfaces whose absorption coefficient lies 0.30
around 0.21 3.14180e+04 1.10934e+04
OR 0.31
7.57240e+03 sq. feet of material is required if to be panelled / 2.87999e+04 1.07483+e04
suspended freely 0.32
2.65845e+04 1.04241e+04
Fig.7(b). Solution generated by RT2.4 0.33
2.46856e+04 1.01189e+04
TREATMENT OF REVERBERANT ENCLOSURES (T >1.2 0.34
sec.) – 2.30399e+04 9.83108e+03
Using Eyring’s approach for DEAD ROOMS 0.35
Beginning with reverberation time and dimensions, the function
assists in Fig.8 (a). FUNRT1.9: Combination of RT1.0,1.1 and 1.2 into
material selection and mounting FUNRT1.9: offers a choice of approach leading to specific
Enter reverberation time of the defective enclosure in sec. solutions in the absence of any information regarding
1.8 reverberation time.
Enter the length, width and height in feet

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 absorption
int 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; /* int
char and float globally defined */ int i=0,j=0;
char ch;
rt10(void); float
rt11(void); t,l,w,h,v,a[100],s1=0.0,s[100],aa=0.0,coef=0.0,abnew,abmat,ab
rt12(void); old,amean,smat,smat1;
/* int char and float globally defined */
main ()
{ rt10(void);
clrscr(); rt20(void);
printf("SOLUTION FOR CORRECTION OF DEFECTIVE
ACOUSTICS IN ENCLOSURES (T>1.2 SEC.) - n"); main ()
printf("nCHOOSE A METHOD:1. Using Sabine's equation for {
LIVE ROOMS n"); clrscr();
printf(" 2. Using Eyring and Norris approach for printf("SOLUTION FOR CORRECTION OF DEFECTIVE
DEAD ROOMS n"); ACOUSTICS IN ENCLOSURES (T>1.2 SEC.) - n");
printf(" 3. Using Millington and Sette for DEAD printf("Employing Sabine's 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;
}