Room acoustics modeling using the ray- tracing method

116 Pages·2006·9.98 MB·English

Room acoustics modeling using the ray-
tracing method: implementation and
evaluation

Licentiate Thesis
University of Turku
Department of Physics
2005
David Oliva Elorza
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A mi abuelo
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Abstract
This thesis discusses room acoustics modeling and the basics and drawbacks of different
methods. Then it concentrates on the ray-tracing algorithm, and offers the author's
implementation of the method and an evaluation of its accuracy when comparing
modeled sound decays and predicted acoustical parameters with the corresponding
measured data in three different enclosures.

First, a general introduction of the sound propagation principles and a discussion of the
state of the art in room acoustics modeling are given. How to implement the ray-tracing
algorithm is explained, not only the way adopted by the author but also other
possibilities which could improve accuracy. That is followed by a geometrical and an
acoustical description of the three studied enclosures, and the comparison of the
modeled and measured data. Sound pressure level is predicted with very good accuracy,
while reverberation time is more contradictory due to the negation of the wave nature of
sound which is inherent in the model. The paper ends with a discussion of the results’
accuracy and the reasons for similarities and/or differences.
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Preface
In August 2004 I started to write this thesis. In principle, it had to include the form of
the ray-tracing method that I had implemented during my time in the Finnish Institute of
Occupational Health (Työterveyslaitos), together with the evaluation of its accuracy in
some indoor enclosures, but it turned out to include more than that. The referred method
is good, although it is not perfect and it has several drawbacks. Hence, I finally ended
up writing down many things which in principle were outside the scope of the thesis,
but that constituted a part of the whole. That is, I discussed diffraction at great length
although I had not yet implemented it, but just because I thought I might do so some
day. Therefore, it became a very long paper, which could be hard to read for some
readers, useless until page 56 or 70 for others, and for the rest of them utterly pointless.
I do not know yet into which category my thesis reviewers belong, but maybe to one of
them. Their opinion made me work a little harder on the paper, delete about twenty
pages, and reorganize most of it. However, that was very positive, not only because this
thesis now looks better than it did before, but also because I have improved my
knowledge. A lot of time has passed since I typed the first lines of this paper, but on the
other hand, I have been doing some other things since then. For instance, the form of the
algorithm which is currently on my hard disk differs considerably from the one
described in this work, and my expected future work, and even more has already been
done. However, that is definitely another story about which I will perhaps still write
some day. Just one more thing: if you decide to go on with the reading of this thesis,
please, enjoy it!
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Table of contents
ABSTRACT....................................................................................................................................4
PREFACE.......................................................................................................................................5
TABLE OF CONTENTS..............................................................................................................6
List of symbols and abbreviations.............................................................................................................8
INTRODUCTION..........................................................................................................................9
1. OVERVIEW OF SOUND.......................................................................................................13
1.1. Sound: Wave propagation.................................................................................................................13
1.2. Sound: Reflection...............................................................................................................................16
1.3. Sound: wave effects............................................................................................................................18
1.3.1. Diffraction.................................................................................................................................18
1.3.2. Interference...............................................................................................................................19
1.4. Temporal distributions of reflections; the impulse response..........................................................22
1.5. Diffuse sound field..............................................................................................................................23
1.6. Acoustic levels.....................................................................................................................................24
1.7. Sound absorption...............................................................................................................................25
1.7.1. Air absorption...........................................................................................................................26
1.7.2. Wall absorption........................................................................................................................26
2. MODELING METHODS IN ROOM ACOUSTICS...........................................................28
2.1. Modeling methods..............................................................................................................................28
2.1.1. Empirical and statistical methods...........................................................................................28
2.1.2. Wave-based methods................................................................................................................29
2.1.3. Geometrical acoustics methods...............................................................................................30
2.1.3.1. Ray-tracing method.....................................................................................................31
2.1.3.2. Image method..............................................................................................................33
2.1.3.3. Particles........................................................................................................................35
2.1.3.4. Fitting-zone method....................................................................................................35
2.1.3.5. Cone or pyramids tracing method.............................................................................36
2.1.3.6. Hybrids.........................................................................................................................37
2.2. Diffusion and diffraction in the ray-tracing algorithm...................................................................38
2.2.1. Modeling diffusion in the ray-tracing method.......................................................................38
2.2.1.1. Statistical treatment of diffuse reflections. The scattering coefficient....................38
2.2.1.2. Reflection models with secondary diffuse sources....................................................43
2.2.2. Modeling diffraction in the ray-tracing method....................................................................46
2.3. Considerations about the ray-tracing algorithm.............................................................................49
2.3.1. Frequency range.......................................................................................................................49
2.3.2. Negation of wave nature, interference and diffraction.........................................................49
2.3.3. Angular distribution of reflected sound.................................................................................50
2.3.4. Geometrical description...........................................................................................................51
2.3.5. Frequency dependent factors. The absorption and the scattering coefficients...................51
2.3.6. Number of rays.........................................................................................................................52
2.3.7. The detection problem.............................................................................................................52
2.3.8. Other problems.........................................................................................................................54
2.4. Round Robin.......................................................................................................................................54
3. IMPLEMENTATION OF THE RAY-TRACING ALGORITHM...................................57
3.1. Flowchart of the implemented ray-tracing algorithm....................................................................58
3.2. Geometrical calculations...................................................................................................................59
3.2.1. Geometrical description of the enclosure...............................................................................59
3.2.2. Shooting rays............................................................................................................................60
3.2.3. Detection of collisions...............................................................................................................61
3.2.3.1. Point-in-polygon test...................................................................................................61
3.2.3.2. Visibility test................................................................................................................63
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3.2.4. Modeling reflections.................................................................................................................64
3.2.4.1. Specular reflection.......................................................................................................65
3.2.4.2. Diffuse reflection.........................................................................................................65
3.2.5. The image method...........................................................................................................................66
3.3. Energy calculations............................................................................................................................66
3.3.1 The instant power of every ray.................................................................................................66
3.3.2. Reception of sound rays...........................................................................................................67
3.3.3. Calculation of acoustic indices................................................................................................68
3.3.3.1. Sound pressure level....................................................................................................69
3.3.3.2. Reverberation time......................................................................................................69
4. MATERIALS AND METHODS............................................................................................71
4.1. Description of the enclosures.............................................................................................................71
4.1.1. Reverberant room, Room 1......................................................................................................71
4.1.2. Industrial hall, Room 2a and Room 2b....................................................................................71
4.1.3. Auditorium................................................................................................................................72
4.2. Measuring methods............................................................................................................................73
4.2.1. SWL of the sound source.........................................................................................................73
4.2.2. Measurement of SPL and RT..................................................................................................73
4.2.3. Measurement and estimation of the absorption properties of materials.............................74
4.3. Modeling of the enclosures................................................................................................................74
4.3.1. Reverberant room, Room 1......................................................................................................74
4.3.2. Industrial hall, Room 2a and Room 2b...................................................................................75
4.3.3. Auditorium, Room 3.................................................................................................................77
4.4. Validation methods............................................................................................................................79
5. RESULTS.................................................................................................................................81
5.1. Reverberant room, Room 1...............................................................................................................81
5.2. Industrial hall, Room 2a....................................................................................................................82
5.3. Industrial hall, Room 2b....................................................................................................................85
5.4. Auditorium, Room 3...........................................................................................................................88
6. DISCUSSION...........................................................................................................................92
6.1. Reverberant room, Room 1...............................................................................................................92
6.2. Industrial hall, Room 2a....................................................................................................................93
6.3. Industrial hall, Room 2b....................................................................................................................95
6.4. Auditorium, Room 3...........................................................................................................................97
6.5. General discussion..............................................................................................................................99
7. CONCLUSIONS AND FUTURE WORK..........................................................................101
8. ACKNOWLEDGMENTS.....................................................................................................103
9. BIBLIOGRAPHY..................................................................................................................104
Appendix 1.
Measurement of sound absorption in a reverberation room, ISO 354............................................A1-1
Measurement of the random-incidence scattering coefficient of surfaces, ISO/DIS 17497-1........A1-3

Appendix 2.
Survey of existing commercial software.............................................................................................A2-1
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List of symbols and abbreviations

α absorption coefficient 2D two dimensional space
δ scattering coefficient 3D three dimensional space
∆ path difference BEM Boundary Element Method
ϑ incidence angle EDT early decay time
i
FEM Finite Element Method
ϑ reflection angle
r FDTD Finite Difference Time Domain
Θ temperature
Method
λ wavelength
FIOH Finnish Institute of
Σ wave front
Occupational Health
ϕ azimuth angle
GTD geometrical theory of diffraction
ψ phase shift ISO International Organization for
i
ω angular frequency Standardization
A area RT reverberation time
A amplitude SPL sound pressure level
i
c speed of sound SWL sound power level
d distance TO transition order
dB decibel
D diffuse
f frequency
F false
h height
I intensity
IL insertion loss
k wavenumber
l height
L length
L acoustic intensity level
I
L acoustic pressure level
p
L acoustic power level
w
m air absorption coefficient
M Maekawa function
N Fresnel number, number of rays
P source strength
P pressure, point
Q directivity factor
r distance, radius
rr vector direction
R receiver
S specular
S sound source
S' virtual sound source
t time
T period
T true
V volume
W sound power
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Introduction
There are many reasons for the development and improvement of computer-aided
acoustical modeling of rooms. There are also many reasons to think that no existing
method is exact or 100 % accurate 1. This thesis is about the second of these topics, and
it presents the author's implementation of the ray-tracing algorithm and an evaluation of
its accuracy in the prediction of two acoustical parameters when comparing the
measured data of three different studied enclosures.

Acoustics is important in many different spaces, especially where noise exposure is high
and causes hearing loss or disturbance in the workers, and in places where music and
speech performance is very important, i.e. concert halls and auditoria. In the first case
we could refer to noise and in the second to sound, but the laws that govern both are the
same, and we define it as the problem of room acoustics.

The adverse effects of sound on human beings are numerous. For instance, high levels
of noise and long exposure to it cause hearing loss in industry workers 2. Noise also
affects the workers’ concentration, i.e. in hospitals, schools and in open-plan offices 3.
On the other hand, good acoustics are very important in concert halls, theatres and
auditoria, but also in public buildings. Probably we have all had the experience of being
in an airport or bus station where the announcements coming from loudspeakers are
difficult, if not impossible, to understand.

All these problems have a technical solution. Noise machines can be timbered and the
industrial hall can be acoustically treated 4. The ceiling of open-plan offices can be
made more absorptive, and the same solution can be applied in schools and hospitals. In
concert halls the solutions are normally more complicated, depending on the subjective
opinion of musicians and audience, but normally they consist of achieving relatively
long reverberation time and improving diffusion 5. Almost the opposite is normally
required in public buildings for message announcements. In general, correct acoustic
treatment makes a space more comfortable and desirable.

However, the problem in all of them is basically economic, although it is also a matter
of common sense. If an acoustic treatment costs money, to do it when the construction
is already finished will cost much more. And it is senseless to spend one year designing
a building and another building it, to finally obtain a bad environment. Not only
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acoustics but also lighting, humidity, ventilation, temperature, etc. are key elements that
affect occupant satisfaction 6. Acoustic modeling can give information before
construction about the acoustical problems or lucks that a building may have. However,
it seems that communication between architects and acousticians has not been very
good 7. In this thesis, I hope to shed some light on and bring some sense to the acoustic
phenomena involved in room acoustics. Not only for architects or acousticians, but also
for the general public who may find it interesting to know a bit more about it and about
the methods that are normally applied in room acoustics modeling.

Sound is wave motion within matter 8, and the physical phenomena involved in sound
wave propagation in enclosures are both numerous and complex, making overall
analytical modeling difficult, if not impossible, to perform 9. Because of the large
number of parameters to be taken into account for the description of a real situation,
only an approximation of it is possible. That is needed because the equation that
describes the propagation of sound, the wave equation, is not solvable in real enclosures
10. So the problem is how to find a good approximation, which simplifies the problem
but not too much, as it seems, from the existing literature, that the greater the
simplification is, the less accurate the results become. The use of a digital computer in
room acoustics has opened possibilities for the prediction of acoustical behavior of
enclosures 11, so computer modeling of acoustic enclosures has developed in various
forms, although none of them has yet been demonstrated to have 100 % accuracy 1, 12.

The thesis is organized in four parts. In the first part, an introduction to the general
principles of acoustics is given. It is difficult to set the limits of this part, and some
readers may find no need to read it, as it might not tell them anything new. However, it
has been considered a fundamental part in this work, because many approaches and
their failure or success could not be understood without the knowledge of the wave
propagation principles in enclosures. How sound propagates and distributes, what kind
of movement it is, and the main effects due to the wave nature of sound, i.e. diffusion,
diffraction and interference, are explained. Moreover, the concept of frequency and
wavelength, and the description of the impulse response are given space in this chapter.

The second part of this work deals with existing modeling methods. Their principles,
limitations and accuracy will be the main topics. Existing methods can be separated into
three groups or categories: empirical, wave-based, and geometrical acoustics methods.