A Study on the Computer Aided Acoustic Analysis of an Auditorium

(Ms) S Pancharatnam, Non-member

A Ramachandraiah, Non-member

This paper discusses the architecture and acoustics of the IMAGE auditorium at Chennai, India. The hall has been

modelled using CATT-acoustic software and the objective room-acoustic parameters such as reverberation time (RT),

early decay time (EDT), clarity factor (C

80

), strength (G) and lateral energy fraction (LEF) are determined. The quality

of the hall in relation to these parameters and the spatial variation in the hall are analysed.

Keywords: Acoustics; Architecture; Concert halls; Computer aided theatre technique (CATT)

NOTATIONS
CATT

: Computer Aided Theatre Technique

C

80

: Clarity Factor, dB

EDT

: Early Decay Time, s

G

: Strength, dB

LEF

: Lateral Energy Fraction, %

RT

: Reverberation Time, s

INTRODUCTION
The auditorium, which forms a part of the Indian Bank

Management Academy for growth and excellence at Chennai,

is known as ‘IMAGE’ Auditorium. It was constructed in 1996

and serves as a venue for many conferences and music

concerts.
In a subjective study, the hall obtained a high ranking for its

acoustics. This was determined by conducting a questionnaire

survey among regular concertgoers in December 2001, where

the hall was rated as one of the best for South Indian classical

music performances. The authors subsequently conducted an

acoustical diagnosis of the hall, ie, determination of the

objective room-acoustic parameters through computer

modelling using computer aided theatre technique (CATT) —

Acoustic Software. In this paper a detailed study of the

architectural features and acoustical parameters of the hall are

presented.

ARCHITECTURAL DETAILS
The IMAGE auditorium is rectangular in shape, measuring 27.0

m × 24.3 m with a seating capacity of 885, as shown in Figure

1. The hall has a non-enveloping proscenium stage, which is

also rectangular and measures 18.25 m × 9.15 m with a

2.3 m apron. The size of the proscenium opening is 18.25 m ×

5.5 m. Other geometrical details of the concert hall are shown

(Ms) S Pancharatnam and Shri A Ramachandraiah are with the Department

of Civil Engineering, Indian Institute of Technology, Madras, 600 036.
This paper was received on December 3, 2002. Written discussion on the paper

will be entertained till June 30, 2003.

Figure 1

Plan of the IMAGE auditorium showing seating arrangement

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IE (I) Journal—AR

Table 1

Basic geometrical details of the concert halls

Geometrical Parameter

IMAGE Auditorium

Average length L, m

27.20

Average width W, m

20.70

Average height H, m

7.40

Depth of the hall D, m

28.55

Volume V, m

3

4612.50

Seating capacity N, number

885.00

Seating area Sa, m

2

432.00

Acoustical seating area SA, m

2

553.78

Total area ST, m

2

680.78

Mean rake angle MRA, (‘)

6.70

Note : Terminology from [1]

MODEL STUDIES USING CATT-ACOUSTIC SOFTWARE
Modelling of the auditorium has been done using CATT

acoustic software for the computation of objective room-

acoustic parameters

2

. Computer modelling using this software

envisages the following three steps:

(1) Preparation: This serves as a preface to the modelling

stage. It involves complete and detailed architectural

documentation of the concert hall in the form of

AutoCAD drawings.

(2) Modelling: The geometry input of the hall is made by

a program written using the CATT text editor and a

wire-framed model of the concert hall is developed as

shown in Figure 3(a) to Figure 3(d). In the model, the

source and receiver positions are identical to those

placed in the experiment. The measured background

noise level is also incorporated in the model.

(3) Prediction: Based on the shape of the space, positions

of the source and receiver, the software predicts the

objective room acoustic parameters over a time

domain of 1 ms to 200 ms. In order to validate the

CATT model, values of reverberation time, RT for

unoccupied conditions are compared with the

measured values. From Table 2, it is seen that the

predictions through the software are in good

agreement with experimental values.

RESULTS AND DISCUSSIONS
Room-acoustic Parameters
In the CATT model, the sound source is placed on the stage, 1 m

from the edge of the proscenium and twelve receiver

locations are identified in the model as shown in Figure 3(c).

The room acoustic parameters obtained for unoccupied

conditions are shown in Table 2. They are the mean values of

early decay time (EDT ), clarity factor (C

80

), strength (G) and

lateral energy fraction (LEF ) and mid-audience reverberation

time (RT ).

(a) Reverberation time (RT) is the time required for

sound to decay 60 dB, whereas early decay time

(EDT) refers to the early part or the first 10 dB of the

sound decay. RT and EDT values generally range

Vol 84, April 2003

11

Figure 2

Longitudinal section through IMAGE auditorium

Table 2

Objective room-acoustic parameters evaluated through CATT

acoustic software

No Parameter Frequency, Hz

125

250

500

1000 2000 4000

1 Reverberation time —

Measured, s

1.60

1.50

1.30

1.40

1.30

1.20

Reverberation time —

CATT, s

1.93

1.57

1.19

1.42

1.29

1.16

2 Early Decay time, s

1.84

1.47

1.14

1.45

1.29

1.16

3 Strength, dB

8.00

7.00

5.80

6.90

6.50

6.00

4 Clarity Factor, dB

0.60

2.00

4.50

2.60

3.30

4.10

5 Lateral Energy

Fraction, %

37.60

37.00 35.70

36.80 36.40 36.70

in Table 1. The lower reaches of the sidewalls and rear wall are

treated with un-perforated veneer mounted on hardboard

panels while the upper reaches are treated with perforated

panels backed by absorptive foam. The front portions of the

sidewalls are made irregular with lower recessed press boxes

and upper triangular protrusions in plan as control boxes as

shown in Figure 2. The ceiling has a curvilinear profile and is

untreated. The flooring has a linoleum finish with carpeted

aisles and the seating in the hall is rexin-backed.
ACOUSTICAL MEASUREMENTS
Reverberation time decay measurements were made in the

hall (unoccupied), using the following instruments:

(1) Standard sound sources (B and K Type 4224) capable

of generating pink noise signals placed on the stage

along its centreline 1 m from the edge of the

proscenium;

(2) Precision integrating sound level meter (B and K

Type 2230) along with filter (B and K Type 1625)

placed at mid-audience position; and

(3) Level recorder (B and K Type 2317).

The measurement procedure satisfies the ISO 3382

1

. The

measured RT for unoccupied conditions varies from 1.3 s-1.4 s

in the mid-frequency range (500 Hz-1000 Hz) as shown in

Table 2.

from 1 s to 3 s in good concert and recital halls

3,4

. In

the IMAGE auditorium, mid frequency RT

mid

ranges

from 1.16 s to 1.45 s. It is seen that the hall is more

reverberant at low frequency (125 Hz-250 Hz) and

moderately reverberant at higher and mid

frequencies. The hall average EDT is similar to RT at

all frequencies and mid frequency EDT

mid

values

range from 1.14 s to 1.45 s. The two quantities are

identical indicating that the decay is completely linear

and that the hall has a diffuse sound field.

(b) Strength or the total sound level as it is called is a

measure of the loudness in a hall

5,6

and is expressed

as

where, p(t), is the impulse response at the receiver
position in the auditorium and

p t

A

( )

, is the response

at 10 m from an identical source in an anechoic

environment.

G values in a concert hall generally range from 1 dB to

+10 dB and the recommended value for optimum

loudness in a concert hall for symphony music at mid

frequency lies in the range of 4 dB to 5.5 dB. In the
IMAGE auditorium, hall average low frequency

G

low

values are high and average mid frequency

G

mid

values range from 5.8 dB to 6.9 dB indicating that

music in the hall can be quite large and
overpowering. The difference

G

G

low

mid

−

value is

about 1.15 dB indicating that the hall has considerably

high bass gain. G is proportional to RT, which is

evident from Table 2.

(c) Clarity factor indicates the early and late arrivals of

sound energy and can be expressed as

For symphony music, concert halls with low clarity

are judged the best. In the IMAGE auditorium, mid

(a) longitudinal section; (b) transverse section; (c) plan; and (d) view
Figure 3

CATT model of IMAGE auditorium

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IE (I) Journal—AR

G

p t dt

p t dt

dB

A

=

L

N

MM

MM

MM

O

Q

PP

PP

PP

∞

∞

z

z

10

2

0

2

0

log

( )

( )

,

C

p t dt

p t dt

dB

80

2

0

0 08

2

0

10

=

L

N

MM

MM

MM

O

Q

PP

PP

PP

z

z

∞

log

( )

( )

,

.

frequency

C

80

is high with positive values of 2.6 dB

to 4.5 dB indicating that the music heard in the hall
will be very clear.

C

80

3

that is the average of values in

the 500 Hz, 1000 Hz and 2000 Hz bands is 3.5 dB

whereas for symphony music the preferred range
is –1 dB to –4 dB.

C

80

is inversely related to RT

values of a concert hall, which is seen in the present

study. At higher and mid-frequencies, the relatively
less reverberant hall has greater

C

80

values.

(d) Lateral energy fraction is the ratio of the lateral energy

received by a figure-of-eight cardiod microphone to

the lateral energy measured by an omni directional

microphone over the first 10 ms of the pulse

response. It is expressed as

where,

P t

L

( )

is the response from the figure-of-eight

microphone.

LEF is related to the subjective sense of spatial

impression or envelopment and is inversely related to

the width of the hall. In some of the best concert halls

for symphony music, where the width varies from 25 m

to 40 m, LEF ranges from 10% to 23%. LEF values are

higher and constant over a wide frequency range of

35.7% to 37.6% in the IMAGE auditorium where the

average width is 20.7 m. Narrower halls exhibiting

greater LEF are considered in this study, as the IMAGE

auditorium is rectangular and narrower.

Spatial Variations
The spatial variation of acoustical parameters is studied by

estimating the standard deviation. The three listening

positions considered are grouped column-wise-left, centre

and right.
The average EDT values are shown in Figure 4(a). The values

range between 1 s to 2 s and Figure 4(b) shows the standard

deviation. These results show that the reverberance quality is

uniform. A medium sized hall like the IMAGE auditorium has

these attributes whereas EDT would vary spectacularly in a

large hall

7

.

Figure 5(a) shows the G values determined for listening

positions grouped column-wise. It is seen that the variation of

(a) hall average; and (b) spatial standard deviation of CATT-EDT values

against octave band frequency
Figure 4

Early decay time

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13

(a) hall average; and (b) spatial standard deviation of CATT-G values

against determined column-wise against octave band frequency
Figure 5

Strength

L F

p

t d t

p

t d t

L

=

L

N

MM

MM

MM

O

Q

PP

PP

PP

z

z

2

0

0 0 8

2

0

0 0 8

( )

( )

.

.

G is minimal but centre locations possess slightly greater

values since they experience greater amount of direct sound.

The standard deviation is minimal along the centre column as

shown in Figure 5(b).

Figure 6(a) compares

C

80

values at all frequencies and it is

seen that all the three groups of listening positions have uni-

form clarity factor but, the standard deviation is higher for left

and right side receivers than those placed in the centre as

shown in Figure 6(b) and Figure 7(a) shows the comparison of

LEF values. The receivers in the centre are found to have

lower LEF values than those near the auditorium sidewalls but

as seen in Figure 7(b), the standard deviation is found to be

higher.

Variations between the Front, Centre and Rear Seats
The variation in parameters is also studied by grouping the

listening positions row-wise as front, centre and rear locations.
From Figure 8(a), it can be seen that the first and second rows

of receivers experience lesser G compared to the third and

fourth rows. This could be due to the decreased height of the

ceiling and that of the lesser room width at the rear end of the

hall. The standard deviation of G is high in the first rows as

seen from Figure 8(b). However, overall standard deviations

are within 1.5 dB at all receiver positions and the sound field in

the auditorium can be considered as uniformly loud.

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IE (I) Journal—AR

(a) hall average; and (b) spatial standard deviation of CATT-C

80

values

determined column-wise against octave band frequency
Figure 6

Clarity factor

(a) hall average; and (b) spatial standard deviation of CATT-LEF1 values

determined column-wise against octave band frequency

Figure 7

Lateral energy fraction

(a) hall average; and (b) spatial standard deviation of CATT-G values

against determined row-wise against octave band frequency
Figure 8

Strength

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15

(a) hall average; and (b) spatial standard deviation of CATT-C

80

values

determined row-wise against octave band frequency
Figure 9

Clarity factor

(a) hall average; and (b) spatial standard deviation of CATT-LEF1 values

determined row-wise against octave band frequency

Figure 10 Lateral energy fraction

The hall average

C

80

values are presented in Figure 9(a). The

first and second rows have lower

C

80

values than the rear

rows. This is due to reflections from the sidewall projections

and the concave ceiling profile at that point reducing clarity.

The spatial standard deviation is seen to be higher in the first

and last rows compared to the second and third rows as shown

in Figure 9(b) but the overall hall indicates little deviation of

about 2 dB to 3 dB from the mean.

Figure 10(a) presents the hall average LEF values. The

receivers in the first row have lower LEF than the second and

third rows and as seen in Figure 10(b), the standard deviation

is high in the first row.

CONCLUSIONS

1. The usefulness of computer modelling for prediction

of parameters has been demonstrated in the paper.

The CATT — acoustic software has proved to be a

useful tool for studying the acoustical characteristics

of the IMAGE auditorium in detail.

2. The source and receiver distance in the IMAGE

auditorium is minimal which might have influenced

the rating of the IMAGE auditorium as a good concert

hall. A medium size of the hall results in minimum

variation of RT, EDT, G, LEF and

C

80

values within the

hall ensuring uniform acoustic conditions in the hall.

3. In comparison with acoustical conditions in concert

halls for other types of music

8

, reverberation time for

the six octave frequencies shows an acceptable curve

for Italian opera, but very low values for symphony

music. The strength (G), clarity factor (

C

80

) and

lateral energy fraction (LEF ) values are high

compared to concert halls intended for symphony

musical performances.

A more detailed investigation on concert halls for South Indian

classical music and a study of the acoustical conditions for

good concert halls is in progress.

ACKNOWLEDGEMENTS
The authors wish to acknowledge their thanks to Dr B I

Dalenback (Sweden) of CATT for supplying the software for

research purposes and are grateful to Mr and Ms Pancharatnam

for providing necessary financial aid and support.

REFERENCES

1. ISO 3382: 1997(E). ‘Acoustics-Measurement of the Reverberation
Time of Rooms with Reference to other Acoustical Parameters.’ 1997.

2. S Pancharatnam and A Ramachandraiah. ‘Computational Architectural
Acoustics: Evaluation of Acoustical Parameters in Concert Halls.’
Proceedings of the Eighth National Annual Convention — MIRC of ASA,
Kavaraipettai, India, 2002, pp 51-54.

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IE (I) Journal—AR

3. L L Beranek. ‘Concert and Opera Halls: How They Sound.’ American
Institute of Physics, Woodbury, USA, 1996.

4. M Barron. ‘Auditorium Acoustics and Auditorium Design.’ E and FN
Spon, London, 1993.

5. J S Bradley. ‘Comparison of Three Classical Concert Halls.’ Journal of
the Acoustical Society of America, vol 89, no 3, 1999, pp 1176-1192.

6. M Barron and L J Lee. ‘Energy Relations in Concert Auditoriums I.’
Journal of the Acoustical Society of America, vol 84, 1988, pp 289-618.

7. D Templeton. ‘Acoustics in the Built Environment.’ Butterworth-
Heinemann, Oxford, UK, 1993.

8. F W Winckel. ‘Optimum Acoustic Criteria of Concert Halls for the
Performance of Classical Music.’ Journal of the Acoustical Society of
America, vol 34, 1962, pp 81-86.