A PAPER

ON

THE BEHAVIOUR OF SOUND IN NON-

RECTANGULAR HALLS

COMPILED BY

ALOBA TOWOJU E. ARC/09/7363

ASA’AH YVONNE O. ARC/09/7365

SUBMITTED TO:

THE DEPARTMENT OF ARCHITECTURE,

THE FEDERAL UNIVERSITY OF TECHNOLOGY, AKURE.

IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE

AWARD OF

BACHELOR IN TECHNOLOGY (B.TECH) IN ARCHITECTURE.

COURSE LECTURER:

PROFESSOR O.O OGUNSOTE.

JULY 2014.

INTRODUCTION

Over the years, spaces such as

swiftly shifted from just being regular

interesting architectural forms, leavi

such as circles and ellipses, horseshoe

advancement in the form of this spaces coupled with the aesthetics

men but even elites, it is a turn off for acousticians because little or nothing is known about the

acoustic qualities of such shapes.

Conspicuously, not many experts have attempted to research into this aspect, this paper therefore

intends to ride on the research works of a few

behavior of sound in non-rectangular halls and relating them with sound behavior in rectangular

halls. The peculiar acoustics challenges will also be highlighted and possible recommendatio

will be suggested afterwards, therefore the design of hall spaces can be eventually ma

1.0 NATURE OF SOUND WAVES

Sound is the human ear’s response to pressure

Sound travels in space by a phen

travelling layers of compression and rarefaction of

fluctuations. The characteristics

characteristics of its surfaces and

level. It’s important to review the behavior of sound in

decay of sound in a room and its eff

Propagation of Sound Indoors:

Sound from an omnidirectiona

Inverse Square Law, and its intensity reduces a

Over the years, spaces such as community halls, religious auditoria, lecture the

from just being regular shapes such as square or rectangle into more fanciful, and

esting architectural forms, leaving architects with the option of using curvilinear shapes

such as circles and ellipses, horseshoe shapes, fan-shapes and polygons. Despite this notable

advancement in the form of this spaces coupled with the aesthetics they present not only to lay

, it is a turn off for acousticians because little or nothing is known about the

ic qualities of such shapes.

ot many experts have attempted to research into this aspect, this paper therefore

intends to ride on the research works of a few painstaking acousticians or architect, stating the

rectangular halls and relating them with sound behavior in rectangular

The peculiar acoustics challenges will also be highlighted and possible recommendatio

will be suggested afterwards, therefore the design of hall spaces can be eventually ma

RE OF SOUND WAVES

s response to pressure fluctuations in the air caused by vibrating

travels in space by a phenomenon called wave motion. This motion is created by outward

ssion and rarefaction of the air particles, that is, by pressure

fluctuations. The characteristics of room (room geometry, volume, and the absorption

acteristics of its surfaces and contents) greatly influence both the sound quality as well as its

review the behavior of sound in rooms as well as the phenomenon of the

room and its effect on speech communication and perception.

f Sound Indoors:

Sound from an omnidirectional source in a free space Fig (a) radiates in accordance wi

and its intensity reduces at a rate of 6dB per doubling of distance.

Fig. 1. Sound reflection

halls, religious auditoria, lecture theatres, e.t.c, have

shapes such as square or rectangle into more fanciful, and

ng architects with the option of using curvilinear shapes

and polygons. Despite this notable

they present not only to lay

, it is a turn off for acousticians because little or nothing is known about the

ot many experts have attempted to research into this aspect, this paper therefore

painstaking acousticians or architect, stating the

rectangular halls and relating them with sound behavior in rectangular

The peculiar acoustics challenges will also be highlighted and possible recommendations

will be suggested afterwards, therefore the design of hall spaces can be eventually made better.

in the air caused by vibrating objects.

omenon called wave motion. This motion is created by outward

the air particles, that is, by pressure

of room (room geometry, volume, and the absorption

th the sound quality as well as its

ms as well as the phenomenon of the

perception.

a) radiates in accordance with the

t a rate of 6dB per doubling of distance.

Elevating the audience Fig (b) provides both better

in intensity at listening position is limited to 3dB

radiation.

Adding reflecting surfaces will provide further strength to the

reinforcement can be obtained by more

in sound transitioning to indoor acoustics is,

extended Fig (e). At this point, t

continuously reflected by the enclosing

Fig. 2.Sound reflection from surrounding surfaces

2.0 ACOUSTICAL PHENOMENA IN ENCLOSURES

When a sound wave meets an obstacle, its behavior will

on its size relative to the wavele

be simply replaced by imaginary sound rays

traveling in straight lines in every direction

b) provides both better sight lines and hearing lines. The reduct

position is limited to 3dB as the result of the change to

Adding reflecting surfaces will provide further strength to the direct signal. Further

rcement can be obtained by more fully enclosing the sound source. Fig (

tioning to indoor acoustics is, when the enclosure on around

e). At this point, the radiated sound is completely contained and will be

enclosing boundaries until it dies away

Sound reflection from surrounding surfaces

ACOUSTICAL PHENOMENA IN ENCLOSURES

an obstacle, its behavior will depend on the nature of the obstacle and

relative to the wavelength of the sound. Studying the behavior of sound

imaginary sound rays perpendicular to the advancing

very direction within the space.

nd hearing lines. The reduction

as the result of the change to hemispherical

direct signal. Further

e sound source. Fig (c, d)The final step

when the enclosure on around the listening area is

he radiated sound is completely contained and will be

Sound reflection from surrounding surfaces

epend on the nature of the obstacle and

of sound in a room can

perpendicular to the advancing wave front,

2.1 Reflection:

Similar to the effect of light ray reflected from a mirror

produced by a new source when in a positio

behind the surface. This illustrates

angle of reflection in all cases equals the angle of incidence.

Fig. 3.Reflection of convex, plane and concave surfaces

Convex reflecting surfaces tend to

sound waves in the room.

2.2 Diffusion

If the sound pressure is equal in all parts of an

are traveling in all directions, the sound

diffusion or sound dispersion

promotes a uniform distribution of sound, accentuates

prevents the occurrence of undesirable acoustical defec

achieved, listeners will have the sensation of sound

Similar to the effect of light ray reflected from a mirror, the reflected sound to be as it was

source when in a position corresponding to the original source but situated

This illustrates the familiar law of reflection from which is seen that the

angle of reflection in all cases equals the angle of incidence.

Reflection of convex, plane and concave surfaces

Convex reflecting surfaces tend to disperse and concavesurfaces tend to concentrate the

ure is equal in all parts of an auditorium and it is probable that sound waves

in all directions, the sound field is said to be homogeneous, in other words,

sion prevails in the room. Adequate sound diffusion is necessary

tribution of sound, accentuates the natural qualities of speech, and

undesirable acoustical defects. When satisfactory diffusion

ill have the sensation of sound coming from all directions at equal levels.

Fig. 4.Diffusion of sounds

reflected sound to be as it was

n corresponding to the original source but situated

ion from which is seen that the

Reflection of convex, plane and concave surfaces

urfaces tend to concentrate the reflected

it is probable that sound waves

, in other words, sound

te sound diffusion is necessary as it

atural qualities of speech, and

ts. When satisfactory diffusion has been

directions at equal levels.

2.3 Diffraction

Diffraction involves a change in direction of waves as

barrier in their path which causes soun

corners, columns, walls and

Experience gives evidence that deep galleries cast

underneath, causinga noticeable loss in high frequency sound which doesn’t

protruding balcony edge. This condition

2.4 The Growth and Decay

As sound waves travel at about 344 meters/second, the

within an auditorium will generally reach a listene

seconds. Shortly after the arrival of the

surrounding surfaces will reach the lis

about 50 milliseconds. If the sound source is a

point will not suddenly disappear, but will

to die off and reflections get weaker

total and final sound level, the sligh

The rate of buildup of sound is much steeper t

is perceived by the ear as being instantaneo

sounds, and because sound decay is far

sound, not its buildup, that affects the acoustics of lecture halls

This gradual decay of sound energy is known

relationship between absorption and

sound pressure level (in dB) of a decaying rever

change in direction of waves as they pass through an opening or around a

path which causes sound waves to be bent or scattered around such obstacles as

corners, columns, walls and beams. This is more common for low frequency than for high.

that deep galleries cast an acoustical shadows on the audience

underneath, causinga noticeable loss in high frequency sound which doesn’t

ng balcony edge. This condition creates poor hearing conditions und

Decay of Sound

at about 344 meters/second, the sound coming direc

will generally reach a listener after a time of anywhere from

hortly after the arrival of the direct sound, a series of semi distinct reflections from

surrounding surfaces will reach the listener. These early reflections typically will occu

If the sound source is abruptly switched off, the sound

ot suddenly disappear, but will fade away gradually as the indirect sound field begi

off and reflections get weaker. As the direct sound level is often only a little less

the slight and slower stages of build-up is often passed unnoticed.

The rate of buildup of sound is much steeper than its decay. Because of its steepne

the ear as being instantaneous. Due to the transient nature

and because sound decay is far more perceptible than build-up[5], it’

not its buildup, that affects the acoustics of lecture halls

Fig. 5.Decaying of sound vs. time

This gradual decay of sound energy is known asreverberation and, as a result of this proportional

relationship between absorption and sound intensity, it is exponential as a function of ti

(in dB) of a decaying reverberant field is graphed against

through an opening or around a

d waves to be bent or scattered around such obstacles as

mmon for low frequency than for high.

hadows on the audience

underneath, causinga noticeable loss in high frequency sound which doesn’t bend around the

creates poor hearing conditions under the balcony.

sound coming directly from a source

r after a time of anywhere from 0.01 to 0.2

es of semi distinct reflections from

reflections typically will occur within

the sound intensity at any

fade away gradually as the indirect sound field begins

only a little less than the

up is often passed unnoticed.

decay. Because of its steepness, the buildup

us. Due to the transient nature of most practical

up[5], it’s the decay of

s a result of this proportional

exponential as a function of time. If the

berant field is graphed against time, the

reverberation curve renders as fairly straight,

factorsincluding the frequency spectrum of the sound and the

2.5 Reverberation

As a listener the first thing one hears is the direct sound

source. This is followed by a series of early reflections fro

sound has to travel further, so will

(unless some focusing of the reflection occurs).

conditions [1] because sound within this ti

listener’s brain.

Reverberation is a smooth decrease in the energycontent of successive reflections, so that the

reflections are not individually perceptible.

off is related to the amount of

in space in various directions and hits room surfaces,

By extensive and ingenious measurements in h

considerable amount of research in this area

volume of an auditorium, the amount o

called the Reverberation Time (RT).

Other phenomena of sound in enclosures include refraction, absorption, transmission,

and echo. These will not necessarily be explained

3.0 FACTORS AFFECTI

Sound intensity dies out over distance

Sound travels at constant speed and so delay

rve renders as fairly straight, although the exact form depends[15]

y spectrum of the sound and the shape of the room.

g one hears is the direct sound which travels in a straigh

followed by a series of early reflections from side walls, ceiling etc. Reflected

has to travel further, so will arrive later. It will not be as loud as the direct component [9]

sing of the reflection occurs). It should be less than 30ms for good listening

because sound within this time interval is perceived as one

Fig. 6.Sound level against time

decrease in the energycontent of successive reflections, so that the

not individually perceptible. The persistence of sound in a

off is related to the amount of absorption in the room. As soon as a sound is produced i

ections and hits room surfaces, from which it’s reflected and

ingenious measurements in halls of different types, Sabine

amount of research in this area and arrived at an empirical relationship between the

of an auditorium, the amount of absorptive material within it and a quantity which he

called the Reverberation Time (RT).

Other phenomena of sound in enclosures include refraction, absorption, transmission,

and echo. These will not necessarily be explained due to the scope of this paper.

FACTORS AFFECTING SOUND BEHAVIOR IN ENCLOSURES

Sound intensity dies out over distance

at constant speed and so delay depending on distance

ough the exact form depends[15] upon many

shape of the room.

ch travels in a straight line from the

m side walls, ceiling etc. Reflected

oud as the direct component [9]

ss than 30ms for good listening

me interval is perceived as one impression in a

decrease in the energycontent of successive reflections, so that the

The persistence of sound in a room after it’s turned

soon as a sound is produced it travels

s reflected and re-reflected.

alls of different types, Sabine carried out a

at an empirical relationship between the

and a quantity which he

Other phenomena of sound in enclosures include refraction, absorption, transmission, diffraction

due to the scope of this paper.

NG SOUND BEHAVIOR IN ENCLOSURES

depending on distance to perceiver.

The perceiver in a room will also hear the echo resulting from the walls, ceiling, and

floors, low frequency sounds tend to have lower efficiencies due to their harmonics of a

single sound travel differently.

Part of the sound wave curves around the edge of a barrier which is known as edge

diffraction.

Barriers that obstruct or prevent sound transmission cause sound shadow to occur.

Surface absorption of direct and reflected sound.

The angle of incidence is equal to the angle of reflection.

4.0 GEOMETRICAL ANALYSIS OF SOUND RAY

In analyzing the behavior of sound in any enclosed space, the concept of a sound ray and the

geometrical study ofsound ray paths play an important role, more so in the design of large rooms

and auditoria.

In tracing sound ray, the wave nature of sound is neglected, and the propagationof sound is

studied like the propagation of light rays. This assumption is valid when the wavelength of

sound is small compared to the area of the surfaces of the room, and large compared with their

roughness. All phenomena due to the wave nature, such as diffraction and interference, are

ignored, since propagation in straight lines is its main postulate.

Three major techniques will be discussed in the geometrical analysis of sound ray. They include;

1. Ray Diagram Graphical Techniques

2. Image Source Technique

3. Hybrid Techniques

4.1 Ray Diagram Graphical Techniques

Ray diagram analysis is used to study the effect of roomshape on the distribution of sound and to

identify surfaceswhich may produce echoes. It’s based on simulating a point source emitting a

large number of rays. The rays are followed on their way through the room either through a

sufficiently long time span or until they hit a surface.[19] Therefore the sound is believed to be

like a particle where certain particles are emanating from the speaker and then they are bouncing

back and forth following the specular reflection rule[20](angle of incidence equals angle of

reflection).

Fig. 7.

4.2 Image Source Technique

Image source or mirror source method is commonly usedf

properties of enclosures. It’s

sound contributions from images of the real

all transmission paths betwee

possible sound reflection paths should be discovere

method. It can determine to a high degree of

direction, the early reflections

feeling of listeners.

4.3 Hybrid Techniques

Computerized prediction techniques continue to be anactive research area. Also,

prediction of room acoustical responses still rely

As an example, the two leading c

CATT Acoustic and Odeon; both

computer programs for room acoustic

being hybrid, they comprise

Fig. 7.Sound ray tracing Technique

Image Source Technique

Image source or mirror source method is commonly usedfor the analysis of the acoustic

s based on regarding all reflections from the boundary surfaces as

butions from images of the real source. The strength of this method is that it covers

transmission paths between source and receiver. To model an ideal impulse response al

paths should be discovered and this is guaranteed

n determine to a high degree of accuracy in terms of level, arrival time and

early reflections, which are the most important in the subjective hearing and

Fig 8.Image Method Technique

Computerized prediction techniques continue to be anactive research area. Also,

acoustical responses still rely on the ray tracing technique to a large extent.

ading commercial software that are used by practitioners today, i.e.

Acoustic and Odeon; both use variants of the ray tracing technique

uter programs for room acoustic predictions are based on models that we characterize as

e elements from ray tracing method as well as from im

or the analysis of the acoustic

l reflections from the boundary surfaces as

is method is that it covers

an ideal impulse response all the

d and this is guaranteed by the image

erms of level, arrival time and

subjective hearing and

Computerized prediction techniques continue to be anactive research area. Also, computerized

on the ray tracing technique to a large extent.

ed by practitioners today, i.e.

use variants of the ray tracing technique A number of

models that we characterize as

method as well as from image source

method. An important aspect when developing such programs is to reduce computing time. A

common practice is based on initially finding available image sources by following ray

trajectories, and thereby one is testing whether these reflection sequence will contribute to the

energy in a given receiver position in the same manner as when using image source method.

However, application of such technique is limited by time and lack of availability. This research

investigating the most common simple shapes in lecture halls, so I’ve used both Ray tracing and

Image source method which are reliable techniques in such case.

5.0 RESEARCH INTO SOUND BEHAVIOUR IN DIFFERENT SHAPES OF SPACES

A thesis report was done by Nada Mohamed Ibrahim Yousif, in The Sudan University of science

and technology. It was his final Master’s degree thesis presentation, July 2011. The following

information were gathered from the thesis as he researched into the acoustics in various shapes

of halls that could possibly be designed.

The primary purpose of the research was to investigatethe relationship between speech

intelligibility and architectural features in lecture halls. Therefore different possible lecture hall

shapes: square, rectangle, rhombus, fan-shaped, horseshoe and polygons were examined, in

addition to evaluating quantitatively their differences acoustically. The architectural features of

these shapes were also simplified for the computational analysis. The hall seating capacity was

adjusted in order to provide the same condition in each shape, because seating capacity has a

major effect on the absorption area which in turn influences the RT, and so there will be

adequate sound level throughout the hall without sound reinforcement systems. Generally the

hall capacity less than 500 seats, speech will be well heard in the rear part of the hall [5].

Therefore, seating capacity about 400 seats was considered in this study.

5.1 Measurement Method:

Measurements were taken for various acoustical parameters along a pre-arranged grid

comprising nine spaced points in each shape to uniformly represent the entire lecture hall. Each

shape was composed of three position rows: front, middle, and rear, and each row were divided

by three parts: right, center and left side. ArchiCADv12 was used to design all of the shapes. In

this research, the sound source was placed 1.20m set back from the edge of the stage, and raised

1.10m above the stage floor. Level of normal speech from the speaker is taken as equal to 65dB.

Acoustical analysis was applied at horizontal and cross sections of typical listening positions

using both Ray diagram and Image source method as clearly seen in the appendices. Each shape

is examined for diffusion, loudness and associated acoustic defects, through the calculation of

possible reflection paths to typical listener positions, giving a predictable data that will stand up

to testing and verification.

5.2 Shapes Configuration:

The following abbreviations are used for each model:

FNL : Fan shape with linear background wall

FNC : Fan shape with curved background wall

HS : Horse shoe shape

FR : Flat rectangle shape

DR : Deep rectangle shape

SQ : Square shape

RH : Rhombus shape

PN : Pentagon shape

HX : Hexagon shape

OC : Octagon shape

The acoustic parameters used were:

1. Path length

2. Total internal surface

3. Absorption area

4. Volume

Fig. 9. values of volume per seat for each shape (m³). Source: Madan Mehta- Architectural Acoustics, page 238

5.3 Regular shapes, fan-shape and horseshoe shape

For the sake of the scope of this paper, little or no emphasis will be given to the rectangular

shaped halls observed in this experiment; nevertheless it will be referred to in comparisms to be

made.

Sound pressure level mean values in four shapes werecompared in Figure (10). The mean values

in each shape ranged from 47.9 to 50.5dB. The flat rectangle and rhombus had the highest mean

value of 50.5 dB & 49.3dB respectively, probably due to the short path length of the direct

sound. However, the SPL values at different positions varied in deep rectangle and square

shapes.

Fig. 10.Mean values of sound pressure level for flat rectangle, square, deep

rectangle and rhombus

Fig. 11 Sound pressure levels at front, middle and back seats for Flat rectangle, square, deep rectangle and rhombus

Table 1 Descriptions of Fan shapes & Horsethe average of

Fig 12 Mean values of sound pressure level for FNL, FNC and HS

When the sound pressure level values were compared

value of 52.9dB was found at front pos

shaped with linear back wall and fanshaped

51.8 dB respectively. Fan-shaped ge

according to the small amount of

Fig 13 comparison of normalized values of

Descriptions of Fan shapes & Horse-shoe shape [RT mid givesthe average of reverberation time at 500Hz and 200Hz]

Mean values of sound pressure level for FNL, FNC and HS

When the sound pressure level values were compared at front, middle and back, the highest

52.9dB was found at front position of the horse shoe shaped, at this position,

linear back wall and fanshapedwith curved back wall had the values of 52.2 and

shaped geometrical features provide more

l amount of absorption provided and the small amount of volume/seat.

comparison of normalized values of the mean free path in FNL, FNC

shoe shape [RT mid gives reverberation time at 500Hz and 200Hz]

Mean values of sound pressure level for FNL, FNC and HS

at front, middle and back, the highest

ition of the horse shoe shaped, at this position, the fan-

ack wall had the values of 52.2 and

ometrical features provide more reverberant energy

and the small amount of volume/seat.

the mean free path in FNL, FNC and HS.

Fig 14.Comparison of the absorption area needed in FNL, FNC and HS

First reflections of sound come to the audience fromdifferent dir

source, due to the short mean free paths

and reflected sound leads to differen

sensation” or spatial impression.

shoe, acoustical defects are more likely to occur, which suggest

used and less reverberant energ

back wall were 4.4, 3.6 respectively,

wall, again it suggests more reverberant energy in fan

5.4 Polygon shapes

Table 2.Descriptions of Polygon shapes [RT mid gives the average ofreverberation time at 500Hz and 200Hz]

Sound pressure level mean values in three shapes were

from 48.7 to 49.9dB. However the three shapes have similar SPL values

Comparison of the absorption area needed in FNL, FNC and HS

reflections of sound come to the audience fromdifferent directions, also directly from the

short mean free paths in such a way the perception at the sa

sound leads to different stimulations to the two ears, creating the so

or spatial impression. While in the fan-shaped hall with curved back wall and horse

more likely to occur, which suggest more absorptio

energy. The volume/seat in horseshoe and fan

back wall were 4.4, 3.6 respectively, while it was only 2.5 in the fan-shaped with linear back

everberant energy in fan-shaped [with linear back wall].

Descriptions of Polygon shapes [RT mid gives the average ofreverberation time at 500Hz and 200Hz]

Sound pressure level mean values in three shapes were. The mean values in each shape

9.9dB. However the three shapes have similar SPL values

Comparison of the absorption area needed in FNL, FNC and HS

ections, also directly from the

the same time of direct

creating the so-called “spatial

shaped hall with curved back wall and horse

more absorption materials to be

seat in horseshoe and fan-shaped with curved

shaped with linear back

[with linear back wall].

Descriptions of Polygon shapes [RT mid gives the average of

The mean values in each shape ranged

9.9dB. However the three shapes have similar SPL values with slightly higher

level in hexagonwith a value of 49.9dB due to the less attenuation of the direct sound. This

suggests high sound level in hexagon.

Fig. 15.Comparison of sound pressure level in Pentagon, Hexagon and Octagon

Sound pressure level mean values in three shapes werecompared. The mean values in each shape

ranged from 48.7 to 49.9dB. However the three shapes have similar SPL values with slightly

higher level in hexagonwith a value of 49.9dB due to the less attenuation of the direct sound

Fig 15.Comparism in sound pressure level Fig 16 sound pressure level at different positions.

CONCLUSION

It is an undeniable truth that the best types of space shapes for auditoriums are rectangles, however with

the findings that this paper has been able to present, it is possible to have other shapes, yet with good

acoustic values.

REFERENCES

Evaluations of geometric configurations on the acoustic quality of auditoria, Nada Mohamed Ibrahim Yousif, 2011. W.C. Sabine, Collected Papers on Acoustics, New York: Dover Publications, 1921.

O.O. Ogunsote, Lecture Notes, Arc 507: Environmental Control III (Acoustics and Noise Control), Federal University of Technology, Akure, 2007