Abstract Acoustic study of spaces deals with

Abstract

Acoustic
study of spaces deals with the assessment of the distribution and dissipation
of sound energy within a certain space. This is accomplished by assessing a set
of acoustic parameters defined with respect to their objective and subjective characters.
The former correspond to measureable physical parameters which strongly relate
to enclosure’s architectural characteristics, while the latter correspond to
acoustic aspects subjectively acknowledged by a listener. The objective
characteristics of a space are in a way interrelated to their subjective ones. The
impulse response of spaces may be obtained by computational techniques, which are
eventually used to retrieve the most relevant acoustic parameters in order to
characterize conveniently the acoustical quality of the space. For temples,
there are no pre-defined values of the parameters since architecture of each
temple is different. Also, apart from music and speech, temples are meant for
mass prayers and worship purposes, for which acoustic characteristics are entirely
different, though significant. This work intends to study the acoustical
characterization parameters which include reverberation time, early decay time
and clarity (of bell sound) in few temples. An analysis of these measurements
is done which would further support for characterization of temples.

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!


order now

Key-words: acoustic
characterization, acoustic quality, impulse response, acoustic parameters.

 

1)  
Introduction

Temples
are usually meant for individual prayer, mass prayer, meditation, religious speech
(like the Keertana / Pravachana) and
musical performances. The acoustical characteristics for all such activities
would have divergent standards keeping in mind the varied expected end effects
of acoustical response which should benefit the priests/artists and the
devotees alike. The quality of sounds as perceived by a listener essentially
depends on four factors:

1.      Physical
characteristic of sound source (the source here may be a human being, a group
of priests and/or devotees, a temple bell, a conch shell or a gong, or all of
these sounded simultaneously);

2.      The
relative position of the sound source and listener;

3.      Architecture
of the space (temple);

4.      Impact/sensation
by the sound stimuli perceived by devotees.

It
is possible to quantify the first three parameters objectively, while the
fourth factor remains on the boundary of measurements between Physics and Psychology.
This is because every individual would have his or her own opinion about the
acoustical quality of the space. This depends, to a very high extent, on the
sensation of quality of perceived sounds and also on the kind of training an
individual has been exposed to in understanding the nature of sound. However,
psychologically, it is imperative to measure this factor in order to understand
how contented devotees are following a temple visit. Psychoacoustics may prove
to be a helping hand here which deals with various characteristics of sound that
are related to subjective characteristics of spaces 12. These
characteristics may further be related to measureable physical quantities which
are considered as objective indicators of acoustic quality of spaces 34.

The
work done here is aimed at measuring values of reverberation time (RT), Early
Decay Time (EDT) and Clarity of sound (C80 and C50) for
bell sounds at few temples namely Siddheswar, Kashivishweshwar, Belbag,
Omkareshwar and Pataleshwar in Pune district, Maharashtra State in India
(Figure 1(a) to 1(d) shows four of these temples with bell photos). All these
temples are heritage temples dedicated to Lord Shiva and material used for
construction was mainly stone cut-outs. All the temples have different
architectural styles.  The acoustical
parameters studied herein would allow characterization of the temple spaces and
also give a brief idea about the subjective impression about acoustic quality
of these places. These parameters are basically based on how sound energy is
propagated through space in time. These parameters are calculated by using
computer software Wavanal and VizIR. The purpose of the bell waveform analysis
program (Wavanal.exe) is the analysis of bell sounds using a personal computer.
It provides facilities for graphical display of recorded bell sounds,
identification of partial frequencies, and synthesis of bell sounds from a list
of partials. It allows complete determination of the harmonic character of a
bell using the facilities available on any multi-media home PC. It also allows
exploration of the way that changing the tuning of a bell changes its resulting
sound 5. VizIR does automatic calculation of acoustics criteria from a .wav
impulse response without manual selection of the response time frame 6.

Figure
1 : Temples undertaken for the acoustical study (with photos of bells)

 

2)  
An
illustration of the Impulse Response and Decay Curve for bell sound in temples

Decay
curves are obtained by the impulse response method as given by Schroeder 7
which demonstrated that the spectrum of sound energy associated with the
average of the infinite decay curves is identical to the energy spectrum
associated with the impulse response obtained with a single measurement. In
general, a linear fit is performed over the points of the decay curve obtained
and the reverberation time, defined as the time necessary for the sound level
to decrease by 60 dB. It is given graphically by

Where,
m is the rate of sound energy decay given by the slope of the line in dB/s. According
to the standard document 8, the linear fit should be performed by using 30 dB
decay (in the range of 5 to 35 dB below the stationary state level). That slope
is used in the computation of reverberation time, T30. The same can
be done for a dynamic range of 20 dB (-5 to -25 dB) called T20 and
for 10 dB (-5 to -15 dB) called T10.

Figure
2 : Impulse Response of bell Sound from Omkareshwar Temple (for 1000 Hz)

 

E – Integrated

E – Corrected

E – Measured

Figure
3 : Decay Curve of bell Sound from Omkareshwar Temple (for 1000 Hz)

 

3)
Objective measurements

3.1)
Reverberation, Reverberation time (RT) and Early Decay Time (EDT)

Reverberation
refers to persistence of sound in an enclosure after the sound source has been
disconnected. The human perception to this phenomenon is quantified by the
objective parameter reverberation time (RT). RT serves as one of the most
crucial parameters for the designing of an acoustic space based on absorption
coefficient of building material been put to use, volume of the enclosure,
surface area of walls and purpose of the construction. The RT is defined by a
60-dB decay of sound based on a 30-dB decay from -5 to -35 dB or even a 20-dB
decay in some cases.  A reverberant enclosure
is said to be a ‘live’ enclosure and an enclosure with low reverberation is
called a ‘dead’ or ‘dry’ enclosure. The sensation of ‘liveliness’ is associated
with the reverberation time at mid-frequencies (average of octaves 500 Hz, 1000
Hz and 2000 Hz), although in some enclosures it may be related to the parameter
early decay time (EDT). The EDT is an expression of reverberation time but
based on the decay from 0 to -10 dB. A 60-dB or even 30-dB decay is rarely
encountered in temples if bells are struck continuously or devotees and priests
enchant prayers uninterrupted. This is because new notes emerge before the
previous notes are decayed. Thus, EDT is considered to be a good descriptor of
reverberance which is the term used to describe the subjective experience of
reverberation. In cases where the EDT is much lower than the RT, such places
are less ‘lively’. The reverberation of sound influences directly the
intelligibility of the sound content perceived by a listener and hence it also governs
the aspect of measurement of clarity of sound. The term ‘running reverberation’
is used for EDT and describes the liveliness of the enclosure. The EDT,
theoretically, is calculated from the initial slope of the decay trace curve and
the decay trace is derived by integration in reverse time of the squared
impulse response 9. If, for example, there is an unusual group of strong
early reflections (or particularly prominent direct sound) the decay trace will
have a form similar to Fig. 6 (a); the early-to-late index will be raised and
the slope of the decay trace over the first 10 dB, as used for the EDT, becomes
steeper, implying a shorter EDT. With weak early reflections, the decay trace
has a form like Fig.6 (b) and an EDT longer than the RT can result. If the
deviation from average behaviour is caused by the late sound, it is, as already
mentioned, generally weak not strong late sound conditions that are found in practice.
With weak late sound, the early sound will be relatively stronger and a decay
trace of the form of Fig. 6 (a) is appropriate.

Figure
4 : Types of early decay curves; the arrow indicates the arrival time of the
direct sound.

(a)
cliff-type decay, (b) plateau-type decay and (c) sagging decay

 

3.2)
Clarity of Sound

Clarity
is a subjective parameter to evaluate the degree of separation of successive
sounds and the ability to distinguish between overlapping tones 4. The usual
physical measurement of clarity is the ratio of the energy in the early sound
to that in reverberant sound, designated by C80 for music and C50
for speech. Clarity is a parameter to measure how correctly and definitely the
sounds are perceived in an enclosure. It is defined as the ratio between the
initial sound energy (early sound) received between the instants 0 and t
seconds, and the received reverberated energy after t. It is given by

Where,
t is the initial time of sound arrival (early sound) and function p(t)
corresponds to the measured impulse response.

The
clarity parameter influences the intelligibility of the perceived sounds inside
enclosures. In the case of speech enclosure, the early sound must be higher
than the reverberated energy and C50 will be positive. A higher
value of C50 indicates better intelligibility of speech. In an
enclosure meant for music, negative values of C80 are acceptable.
The value of t is greater for music than that for speech, which means that the
part of initial energy, received later (between 50 ms and 80 ms) is still
useful for the definition mixture of musical sounds.

Clarity,
to a large extent, demands a low reverberation time while sustained loudness
calls for a higher reverberation time. According to Barron, the ear’s response
to low tones in the 125 Hz and 250 Hz octave bands is slow, therefore the
objective clarity is usually calculated as an average of values corresponding
to 500 Hz, 1 kHz and 2 kHz bands. Clarity is inversely proportional to
reverberation.

 

3.3) Early Decay Time (EDT)
compared with Reverberation Time (RT)

To
design an enclosure meant for speech and/or music, like a temple, the
reverberation time is usually specified based upon the intended sense of
reverberation in the enclosure. Using Sabine’s formula, then, the appropriate
volume of the enclosure may be predicted. However, in case of temples, it is
not clear if acoustical characteristics were taken into consideration prior, during
or after designing of the temple structure. Also, from a subjective point of
view it is necessary to specify the early decay times within a specified range.
In temples, therefore, the differences between EDTs and RTs may be quite large,
and this paper aims at those temples where these two values are significantly
different. In the present time, for design purposes we need to know the causes
of significant differences between them.

There are two options to specify the
difference between EDT and RT; either to find the difference between the two,
or to find the ratio between them 9. Here we consider the ratio between EDT
and RT and name it as EDT-RT ratio, since this appears more appropriate from
the point of view of comparison. The mean EDT’s for temples divided by their
respective reverberation times are plotted in Fig. 1. The ratios in Fig. 1 are
the average for the octaves 500, 1000 and 2000 Hz. The enclosure mean EDT-RT
ratios are seen to vary from 0.59 to 1.89; with two of the values below 1 and
three values above 1 reaching as high as 1.89.  If the full decay in an
enclosure is perfectly linear, the EDT and RT are the same. EDT is dependent on
enclosure position whereas RT is more stable.

 

 

Figure
5: Ratio of mean EDT to RT for all temples taken over frequency octaves 500 Hz,
1kHz and 2kHz.

It
should be noted here that EDT is a parameter similar to RT, but being only
retrieved via the slope of a line fitted to 10 dB decay below the maximum sound
level 10. EDT, however, seems to be particularly sensitive to changes in the
geometry of the enclosure.

 

3.4)
Variation in EDT values within temples

 

For
each temple, the standard deviation of EDT values measured has been calculated
at each of the five octaves. One expects however a larger spread of EDT values
when the mean EDT is larger. For this reason, results are presented here in
terms of the standard deviation divided by the mean EDT for each temple. This dimensionless
ratio of standard deviation to mean EDT is the coefficient of variation of the
EDT is in a way the outcome of the process of normalization done in several
other fields like communication; it will however be called here the ‘relative
standard deviation’. Values of the relative standard deviation at
mid-frequencies (that is averaged between 500 and 2000 Hz) are plotted in Fig.
2. Typical values for the relative standard deviation are between 0.49 and
twice of this value in one of the temples. One would observe that although
there is an excessive variation of EDT and standard deviation of EDT in all
temples but the variation in relative standard deviation is small and all the
values for relative standard deviation fall below 1.

 

 

Figure
6: Relative Standard Deviation of EDT for all temples over frequency octaves
500 Hz, 1kHz and 2kHz.

 

3.5)
Relative Standard Deviation of EDT as a function of frequency

 

The
relative standard deviations of EDT for all temples as a function of frequency
(500 Hz, 1 kHz and 2 kHz) are plotted in Fig. 3. It is observed that for three
temples, the relative standard deviation value increases at high frequency
while for two temples it reduces with frequency. Also, the spread in the
relative standard deviation values is more at lower frequency octaves while the
spread reduces considerably at high frequencies.

 

Figure
7 : Relative standard deviation by octave frequency for all temples for 500 Hz,
1 kHz, 2 kHz

 

3.6)
Differences between EDT and RT values

To
establish reasons for differences between EDT and RT values, here we use the
parameters C80 and C50 the early to late sound index,
commonly referred to as the ‘clarity’ of sound. In Fig. 4(a) (all five graphs),
C80 values are plotted against EDT for the mid frequency octaves 500
Hz to 2 kHz, while fig. 4(b) (all five graphs) shows the variation of C50
values with EDT for the mid frequency octaves. A common observation for all
temples is that with increase in early decay time, the early to late sound
index goes on decreasing.

C50
values are positive when early sound is higher than the reverberated energy,
while C80 values are generally negative and are defined for
enclosures meant for music.

Figure 8 (a) : Early-to-late sound
index (C80) with EDT for mid-frequency octaves 500 Hz, 1 kHz and 2
kHz

 

Figure 8 (b) : Early-to-late sound
index (C50) with EDT for mid-frequency octaves 500 Hz, 1 kHz and 2
kHz

 

Fig.
5 shows the relation between early-to-late index and EDT-RT ratio for all
temples in the mid-frequency octaves 500 Hz, 1 kHz and 2 kHz. The curves are
also fitted as shown in the figure. It is seen that there is a negative
correlation between the early-to-late index and EDT-RT ratio.

Figure
9 : Early to late sound index vs EDT-RT ratio for all temples for 500 Hz, 1 kHz
and 2 kHz

 

4)
Conclusion

In
this study, rather than focusing on early decay time values, the emphasis has
been placed on looking at deviations between the EDT and RT values, as measured
by EDT-RT ratio. An EDT-RT ratio other that 1 can be considered as a change
from the average situation. It is apparent that the decay curves in such cases
are non-linear.

It
is observed that in Siddheshwar Dhom and Kashivishweshwar temples, mean EDT
values are shorter than RT. This means that the strongest reflections are
coming from large surfaces which do not form the actual temple enclosure. These
surfaces may be nearby pillars which extend from the floor to the ceilings.
Further, in such places, the decay curve must be steep in its first stage and
thereafter flatten out and attain a value in accordance with the reverberation
time of the enclosures. The entire space inside temples shows a “coupled enclosures
effect”. This also shows that the early energy is directed more towards the
rear side of the temples than on the front side. However, in none of the
temples, mean EDT is much smaller than RT and hence, there is always some
amount of ‘liveliness’ in every temple. For Omkareshwar temple, the EDT-RT
ratio is close to 1. Thus, the decay curve in this case must be more linear.
This shows that this temple space is more diffused, because a diffuse enclosure
is characterized by a linear decay. Higher RT values may be accepted for
musical performances if the enclosure is well diffused. Fig. 1 also shows that
in Siddheshwar Dhom and Kashivishweshwar, large part of first reflections are
directed towards the devotees in the hall and only a small part reaches the
people ringing the bell while in other temples, the sound field is more
diffused.

It
is observed that Kashivishweshwar temple shows positive C50 for most
of the frequency octaves whereas Siddheshwar Dhom temple shows negative C80
values for most of the frequency octaves. This
implies that Kashivishweshwar temple is more suited to speech, like prayers or
religious preaching whereas Siddheshwar Dhom temple is best suited for
activities like musical performances or prayers with musical accompaniments.

A
high value of the early to late index (C80) may be due to either a high
level of early sound or a low level of late sound, and either of these may also
result in low values for the early decay time. The corresponding causes of high
values for the EDT relative to the RT may be due to weak early sound or a high level
of late sound.

 

 

References

1               The Psychoacoustics of Sound Quality
Evaluation – Fastl, H.,
Acta Acustica         united with Acustica, Volume
83, Number 5, September/October 1997, pp. 754-           764(11)

2               Psychoacoustic basis of sound
quality evaluation and sound engineering – Hugo    Fastl,   The Thirteenth
International Conference on Sound and Vibration, ICSV –        13, Vienna,      Austria,
July 2-6, 2006

3               BERANEK, L.L. – Music, Acoustics and
Architecture, USA, John Wiley & Sons,

            Inc., 1962.

4               BERANEK, L.L. – Concert and Opera
Enclosures : How they sound, New York,             Acoust.
Soc.     Amer., 1996

5               http://www.hibberts.co.uk

6                   https://www.sonium.fr/acoustique-architecturale

7               M. R. Shroeder – New Method of
Measuring Reverberation Time, J. Acoust. Soc.             Amer.,
Vol 71, 619-629, 1982

8               ISO 3382-1:2009, Acoustics –
Measurement of Enclosure Acoustic Parameters – 

Part      1 :
Performance Spaces

9               M. BARRON – Interpretation of Early
Decay Times in Concert Auditoria,            Acustica,
Vol 81, 1995

10                      
V. L. Jordan – Acoustical Criteria for
Auditoriums and Their Relation to Model    Techniques,
J. Acoust. Soc. Amer., Vol 47, 408-412, 1970