Neubauer - Prediction of Reverberation Time with Non-Uniformly Distributed Sound Absorption.pdf - Akustyka(1) - dzidzia2603

Prediction of the Reverberation Time in Rectangular Rooms with Non-

Uniformly Distributed Sound Absorption

R. Neubauer 1 , B. Kostek 2

1 Consulting Bureau, Ingolstadt, Germany

2 Sound & Vision Engineering Department,

Faculty of Electronics, Telecommunications and Informatics,

Technical University of Gdansk, PL

SUMMARY

The aim of this paper is first to review the best known reverberation time formulae and then to

show that the reverberation time cannot be thereby predicted accurately in cases mostly

encountered in practice, where the sound field is not diffuse. Introducing a correction to

Fitzroy’s formula allows better prediction of the reverberation time in the case of non-

uniformly distributed sound absorption. Comparison of calculation results obtained on both

the basis of classical equations and the new time reverberation formula introduced is shown.

In addition, the results obtained by measuring reverberation conditions in situ and those

predicted for the same enclosure are compared and conclusions drawn.

1. Introduction

There exist many parameters that describe acoustic quality of an enclosure. The importance of

some has been already established in the pioneering study of Beranek [4] and later by other

researchers [3][32][33][38], but there is still no consensus on a set of parameters that should

be taken into account while describing the acoustical quality of a room [22]. This is due to

differences in functionality of a given room, volume of rooms, distribution of absorption, etc.

[2][27][32][33]. A so-called optimum reverberation time can serve as an example of such

problems. Optimum values of this acoustical quantity that can be found in many literature

sources differ to a large extent, which was pointed out by Straszewicz in his paper [40]. In his

opinion a pronounced divergence of opinions makes doubtful whether it is possible to assign

the optimum reverberation time related to the given volume of a room or to the kind of sound

produced only [40]. Numerous research studies show that rather than trying to achieve the

optimum reverberation time for a given room, it is better to govern other acoustical

parameters that influence acoustical quality. This is especially true in the case of the

multifunction interiors. Niemas, Sadowski and Engel formulated some requirements as to

designing and estimating acoustical properties of sacral enclosures [27]. They pointed out the

importance of other quantities than the reverberation time in the evaluation of the acoustical

quality of such interiors [27]. Problems related to designing and estimating acoustical

properties of interiors were also reviewed by other researchers [39][42][43], among others by

Rakowski [30] and Sadowski [32][33]. In addition the relationship between acoustical

parameters measured in a room and the acoustic quality assessed subjectively is still

researched [17][22]. However as was pointed out by Vorländer, one of the most relevant

sensations of the sound field in rooms is still the cognition of reverberation [42].

Reverberation appears to be responsible for the impression of being in a room as well as

providing an awareness of distance from the source, whereas for example spatial impression

due to lateral reflections appears to be more a source-specific effect involving the feeling to

be close to the listener [3]. As Budzynski [8] pointed out, early reflections from sidewalls are

also responsible for the effect of increasing auditory distance localization.

During the past century several formulae for predicting reverberation time were

developed empirically and theoretically, based on the assumption of homogeneous repartition

of sound energy within the room, and consequently uniformly distributed sound absorption.

The problem of the reverberation time prediction for non-uniform distribution, however,

remains so far, open for discussion and for finding solutions fitted better to practical

application.

The first and most remarkable approach to describe the reverberation characteristics of

an enclosure was found by W.C. Sabine [31] around 1900. Sabine established his theory on

the basis of practical results. To find a theoretical basis for calculating reverberation time,

many researchers contributed new theories. Since Sabine published his results, several

different approaches have been adopted to obtain equations that describe the reverberation

characteristics. Among others, the best known researchers, who developed theories of

reverberation include: Franklin (1903) [14], Jaeger (1911) [15], Fokker (1924) [13],

Buckingham (1925) [7], Schuster and Waetzmann (1929) [36]. Then, Eyring (1930) [11]

presented his remarkable paper, followed shortly after by Millington (1932) [24] and Sette

(1933) [37]. After a further 25 years Fitzroy (1959) [12] published an empirical solution for

reverberation time prediction in non-uniform rooms, his paper, however, went almost

unrecognized at that time and was rather negatively perceived. In the last 30 years, Schroeder

(1965) [34], Kosten (1965) [19], Cremer and Müller (1978) [9] Kuttruff (1975) [20], Nilsson

(1992) [28], Tohyama et al. (1995) [41] added some new issues to the theory of reverberation.

In 1988 Arau [1] presented an improved reverberation formula taking into account the non-

uniform distribution of sound absorption. Lately, papers by Kutruff [21] and Bistafa and

Bradley [6], which dealt with the similar problems, appeared. Recently, within the framework

of the standardization process an improvement of the estimation of the reverberation time in

rooms with irregular absorption distribution based on Nilsson’s model was proposed and

discussed [23][28].

A general description of the reverberation time based on Sabine’s reverberation theory is

still in common use. However, in the case of a room in which sound absorption is not

uniformly distributed, the reverberation time frequency characteristics cannot be predicted

accurately using Sabine’s or other classical reverberation theories. These theories are based on

the assumption that the sound field considered is completely diffuse. This will, in general, be

sufficiently diffuse if there are no large differences in the basic dimensions of the room, walls

are not parallel, sound absorbing material is uniformly distributed, and most interior surfaces

are divided into parts. In practice, almost none of these requirements is fulfilled. In 1959,

Fitzroy introduced an empirically derived equation that considers non-uniform distribution of

absorption. However, a thorough investigation of Fitzroy’s equation revealed that in most

cases the predicted reverberation time was generally too long. It is worth noting that

acousticians are not altogether satisfied with existing formulae on reverberation time, thus the

European standard concerning this issue is still an open question [10]. Furthermore, the

reverberation time is an important parameter in calculating other objective descriptions of

room acoustics. Since such parameters are well related to subjective assessment descriptors of

room acoustics, it is most important for the acoustical design process to provide a general

design tool which enables prediction of relevant sensations in the stage of planning a certain

type of room [5][17].

In the following paragraphs a review on best known formulae for predicting

reverberation time is presented, along with corresponding calculations results. This is shown

for the case of rectangular enclosures, because in such cases it is possible to systematically

study the reverberation time related to the room volume.

2. Time Reverberation Formulae

Most of parameters that describe characteristics of an acoustic hall are calculated basing

on the assumption that it is usually sufficient to consider the propagation of sound energy and

not sound pressure or particle velocity, therefore all phase effects can be neglected. The basis

of this assumption is that the dimensions of a hall should be large enough in comparison with

the acoustic wavelengths. The so-called Schroeder cut-off frequency [35]:

f S

2000

[Hz]

(1)

limits the frequency under which this assumption is not justified. That is, f s can be considered

as the lower limit of frequencies at which a statistical treatment of superimposed normal

modes in a room is permissible. In contrast, below the Schroeder cut-off frequency, the

resonance peaks of the sound field are insufficiently dense to be analyzed statistically.

One of the most important parameters describing the quality of the room is the

reverberation time. According to the classical formula reverberation time is defined as time

needed to decrease energy by 60 dB from its original level after instantaneous termination of

the excitation signal. This parameter, originally introduced by Sabine, is given by equation

(2):

Neubauer - Prediction of Reverberation Time with Non-Uniformly Distributed Sound Absorption.pdf

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