I created a grid using excel and a simple random number generator that gives each cell a value of 0 or 1, then assigned conditional formatting to color any cells with a value of 1. Seems like a simple method to achieve the same result. Are you sure about that? If you examine the complex mathematical equations used to create the optimum number sequence for the EXPO panel and the BAD panel array, you will learn that these number sequences are anything BUT simple random 1's and 0's.
I doubt that 'Antonio just simply used a basic random number generator to come up with such a complex design. There are many factors which MUST be determined when these numbers are folded to take in consideration important factors such as "Auto-Correlation", Modulation, and that of a very bad thing called "lobing" which must be reduced to a minimum!
You have the valuable and proven array shown to you here which is very easy to duplicate. If I may, I would like to suggest a very comprehensive source of information for educating someone interested in acoustic science.
Acoustic Absorbers and DiffusersAcoustic Absorbers and Diffusers
Theory, design and application
Trevor J. Cox
University of Salford, UK
and
Peter D’Antonio
RPG Diffusor Systems Inc., USAContents
Preface xiv
Acknowledgements xviii
Glossary of frequently used symbols xix
Introduction 1
1 Applications and basic principles of absorbers 6
1.1 Reverberation control 6
1.1.1 A statistical model of reverberation 7
1.2 Noise control in factories and large rooms with
diffuse fields 11
1.3 Modal control in critical listening spaces 12
1.4 Echo control in auditoria and lecture theatres – basic
sound propagation models 13
1.4.1 Sound propagation – a wave approach 15
1.4.2 Impedance, admittance, reflection factor and
absorption 16
1.5 Absorption in sound insulation – transfer matrix
modelling 18
1.5.1 Transfer matrix modelling 19
1.6 Absorption for pipes and ducts – porous absorber
characteristics 20
1.6.1 Characterizing porous absorbers 21
1.7 Summary 22
1.8 References 22
2 Applications and basic principles of diffusers 23
2.1 Echo control in auditoria 23
2.1.1 Example applications 23
2.1.2 Wavefronts and diffuse reflections 26
2.1.3 Coherence and terminology 30
2.2 Reducing colouration in small rooms 32
2.2.1 Sound reproduction 32
2.2.2 Music practice rooms 39
2.3 Controlling modes in reverberation chambers 43
2.4 Improving speech intelligibility in underground
or subway stations 44
2.5 Promoting spaciousness in auditoria 44
2.6 Reducing effects of early arriving reflections
in large spaces 45
2.7 Diffusers for uniform coverage with overhead
stage canopies 46
2.8 Diffusers for rear and side of stage enclosures 48
2.9 Diffusers to reduce focussing effects of concave surfaces 52
2.10 Diffusion and road side barriers 53
2.11 Diffusion and street canyons 55
2.12 Conclusions 55
2.13 References 56
3 Measurementof absorber properties 58
3.1 Impedance tube or standing wave tube measurement 58
3.1.1 Standing wave method 61
3.1.2 Transfer function method 62
3.2 Two microphone free field measurement64
3.3 Multi-microphone techniques for non-isotropic,
non-planar surfaces 65
3.3.1 Multi-microphone free field measurement
for periodic surfaces 66
3.4 Reverberation chamber method 68
3.4.1 Measurement of seating absorption 71
3.5 In situ measurement of absorptive properties 74
3.6 Internal properties of absorbents 78
3.6.1 Measurement of flow resistivity 78
3.6.2 Measurementof flow impedance 81
3.6.3 Directmeasurementof wavenumber 82
3.6.4 Indirectmeasurementof wavenumber and
characteristic impedance 82
3.6.5 Measurementof porosity 83
3.7 Summary 85
3.8 References 85
4 Measurement and characterization of diffuse reflections
or scattering 87
4.1 Measurement of scattered polar responses 88
4.1.1 Near and far fields 95
viii Contents
4.1.2 Sample considerations 102
4.1.3 The total field and comb filtering 103
4.2 Diffusion and scattering coefficients, a general discussion 104
4.3 The need for coefficients 105
4.3.1 Diffuser manufacturer and application 105
4.3.2 Geometric room acoustic models 106
4.4 The diffusion coefficient107
4.4.1 Principle 107
4.4.2 Obtaining polar responses 109
4.4.3 Discussion 110
4.4.4 Diffusion coefficienttable 111
4.5 The scattering coefficient 112
4.5.1 Principle 112
4.5.2 Rationale and procedure 113
4.5.3 Sample considerations 116
4.5.4 Anisotropic surfaces 116
4.5.5 Predicting the scattering coefficient 118
4.6 From polar responses to scattering coefficients,
the correlation scattering coefficient 120
4.6.1 Scattering coefficient table 123
4.7 Contrasting diffusion and scattering coefficient:
a summary 124
4.8 Other methods for characterizing diffuse reflections 124
4.8.1 Measuring scattering coefficients by solving
the inverse problem 124
4.8.2 Room diffuseness 125
4.9 Summary 126
4.10 References 127
5 Porous absorption 129
5.1 Absorption mechanisms and characteristics 129
5.1.1 Covers 131
5.2 Material types 132
5.2.1 Mineral wool and foam 132
5.2.2 Recycled materials 133
5.2.3 Curtains (drapes) 134
5.2.4 Carpets 135
5.2.5 Absorbentplaster 135
5.2.6 Coustone or quietstone 137
5.3 Basic material properties 137
5.3.1 Flow resistivity 138
5.3.2 Porosity 140
5.4 Modelling propagation within porous absorbents 141
5.4.1 Macroscopic empirical models such as
Delany and Bazley 141
Contents ix
5.4.2 Further material properties 144
5.4.3 Theoretical models 145
5.5 Predicting the impedance and absorption
of porous absorbers 148
5.5.1 Single layer porous absorber with
rigid backing 149
5.6 Local and extended reaction 150
5.7 Oblique incidence 151
5.8 Biot theory for elastic-framed materials 153
5.9 Summary 155
5.10 References 155
6 Resonantabsorbers 157
6.1 Mechanisms 158
6.2 Example constructions 159
6.2.1 Bass trap membrane absorber 159
6.2.2 Helmholtz absorption 160
6.2.3 Absorption and diffusion 162
6.2.4 Clear absorption 163
6.2.5 Masonry devices 164
6.3 Design equations: resonant frequency 166
6.3.1 Helmholtz resonator 166
6.3.2 Losses 172
6.4 Example calculations 178
6.4.1 Slotted Helmholtz absorber 178
6.4.2 Porous absorbent filling the cavity 179
6.5 More complicated constructions 180
6.5.1 Double resonators 180
6.5.2 Microperforation 180
6.5.3 Lateral orifices 183
6.6 Summary 184
6.7 References 184
7 Miscellaneous absorbers 186
7.1 Seating and audience 186
7.2 Absorbers from Schroeder diffusers 188
7.2.1 Energy flow mechanism 189
7.2.2 Boundary layer absorption 191
7.2.3 Absorption or diffusion 191
7.2.4 Depth sequence 193
7.2.5 Use of mass elements 194
7.2.6 Number of wells 196
7.2.7 Theoretical model 196
x Contents
7.3 Summary 200
7.4 References 200
8 Prediction of scattering 202
8.1 Boundary elementmethods 202
8.1.1 The Helmholtz–Kirchhoff integral equation 204
8.1.2 General solution method 205
8.1.3 Thin panel solution 209
8.1.4 Periodic formulation 212
8.1.5 Accuracy of BEM modelling: thin rigid
reflectors 215
8.1.6 Accuracy of BEM modelling: Schroeder
diffusers 216
8.2 Kirchhoff 219
8.3 Fresnel 224
8.4 Fraunhofer or Fourier solution 225
8.4.1 Near and far field 226
8.4.2 Fraunhofer theory accuracy 227
8.5 Other methods 228
8.5.1 Transientmodel 228
8.5.2 FEA 229
8.5.3 Edge diffraction models 229
8.5.4 Wave decomposition and mode-matching
approaches 230
8.5.5 Random roughness 230
8.5.6 Boss models 231
8.6 Summary 231
8.7 References 231
9 Schroeder diffusers 233
9.1 Basic principles 233
9.2 Design equations 234
9.3 Some limitations and other considerations 236
9.4 Sequences 239
9.4.1 Maximum length sequence diffuser 239
9.4.2 Quadratic residue sequence 242
9.4.3 Primitive root sequence 242
9.4.4 Index sequences 245
9.4.5 Huffman and beyond 245
9.5 The curse of periodicity 248
9.6 Improving base response 257
9.7 Multi-dimensional devices 260
9.8 Absorption 263
Contents xi
9.9 But. . . 266
9.10 Optimization 268
9.10.1 Process 268
9.10.2 Results 271
9.11 Summary 273
9.12 References 274
10 Geometric reflectors and diffusers 276
10.1 Plane surfaces 276
10.1.1 Single panel response 276
10.1.2 Panel array response: far field arc 281
10.1.3 Panel array response: near field 282
10.2 Triangles and pyramids 284
10.2.1 Arrays of triangles 287
10.3 Concave arcs 288
10.4 Convex arcs 290
10.4.1 Geometric scattering theory and cut-off
frequencies 291
10.4.2 Performance of simple curved diffusers 293
10.5 Optimized curved surfaces 297
10.5.1 Example application 297
10.5.2 Design process 298
10.5.3 Performance for unbaffled single
optimized diffusers 301
10.5.4 Periodicity and modulation 303
10.5.5 Stage canopies 305
10.6 Fractals 307
10.6.1 Fourier synthesis 308
10.6.2 Step function addition 309
10.7 Summary 311
10.8 References 311
11 Hybrid surfaces 313
11.1 Planar hybrid surface 313
11.2 Curved hybrid surface 314
11.3 Simple theory 316
11.4 Number sequences 318
11.4.1 One-dimensional sequences 318
11.4.2 Two-dimensional sequences 324
11.5 Designing curved hybrid surfaces 324
11.6 Absorption 324
11.7 Accuracy of simple theories 327
11.8 Diffuse reflections 330
xii Contents
11.9 Boundary element modelling 332
11.10 Summary 333
11.11 References 334
12 Absorbers and diffusers in rooms and geometric models 335
12.1 Absorption coefficients: from free field to random
incidence 335
12.2 From the reverberation chamber absorption
coefficients to room predictions 338
12.3 Absorption in geometric room acoustic models 339
12.4 Diffuse reflections in geometric room acoustic
models 343
12.4.1 Ray re-direction 345
12.4.2 Transition order using particle tracing 345
12.4.3 Diffuse energy decays with the reverberation
time of the hall 346
12.4.4 Radiosity and radiant exchange 346
12.4.5 Early sound field wave model 346
12.4.6 Distributing the diffuse energy 346
12.4.7 Scattering coefficients 349
12.5 Summary 352
12.6 References 352
13 Active absorption and diffusion 355
13.1 Some principles of active control 356
13.2 An example active impedance system and
a general overview 359
13.3 Active absorption in ducts 361
13.4 Active absorption in three dimensions 362
13.4.1 Low frequency modal control – example
results 364
13.4.2 Low frequency modal control – alternative
control regime 365
13.5 Hybrid active–passive absorption 368
13.6 Active diffusers 371
Here is one excerpt from this book.
8 Prediction of scatteringTo enable the design and characterization of a diffusing surface, it is necessary to be
able to predict the reflected pressure from the surface. Currently, this is usually done
by considering the scattering from the surface in isolation of other objects and
boundaries. The prediction techniques could also be used as part of a whole space
prediction algorithm, where all surfaces in a room are simultaneously modelled. At
the moment, however, long computation times and storage limitations mean that
whole space prediction algorithms are forced to use relatively crude representations of
the actual scattering processes. Consequently, when predicting the responses in rooms
and semi-enclosed spaces such as street canyons or pavilions, it is more common to
use geometric models. The issue of modelling scattering in geometric models is
discussed in Chapter 12.
Therefore, the issue for this chapter is predicting the scattering from isolated
surfaces. There is a range of choices of models, from the numerically exact but
computationally slow, to the approximate but fast models. The prediction methods
can also be differentiated as either time or frequency domain models. In diffuser
design, frequency domain methods have dominated the development of the modern
diffuser. For this reason, this chapter will concentrate on these methods. Table 8.1
summarizes the prediction models which will be considered in this chapter, along with
their key characteristics.
The next section will start with the
most accurate model, a boundary element
method (BEM) based on the Helmholtz–Kirchhoff integral equation. It will then be
demonstrated how the more approximate models can be derived from this integral
equation, and the relative merits and limitations of the techniques will be discussed.
To round off the chapter, an overview of less commonly used techniques will be given.
8.1 Boundary element methodsWhen BEMs are applied to diffusers, remarkable accuracy is achieved. The accuracy
is much better than most acousticians are used to achieving from an acoustics theory.Acousticians are used to using empirical fixes to make measurement match predic-
tion, but that is not often needed when BEMs are used to predict diffuser scattering.
The only real disadvantages of BEMs are that the method is prone to human error in
meshing the surface, and most importantly, it is slow for high frequencies and large
surfaces. Some have attempted to apply the prediction methods to whole rooms for
low frequencies, but this is
very computationally intense, requiring super computing
facilities or a considerable amount of patience while waiting for results.
Here is another excerpt from this book.11.1 Planar hybrid surface
The binary amplitude diffsorber, also known as a BAD panel, is a flat hybrid
surface having both absorbing and diffusing abilities.
The panel simultaneously provides
sound diffusion at high and mid-band frequencies, and crosses over to absorption below
some cut-off frequency. Figure 11.1 shows a typical construction. Mineral wool is faced
with a complex perforated mask, and the panel is fabric wrapped for appearance. The
white patches on the mask are holes, and the black patches hard reflecting surfaces.
Figure 11.2 shows the random incidence absorption coefficient for a hybrid surface
compared to the mineral wool alone,
the effect of changing the backing depth is also
shown.
The additional vibrating mass within the holes of the mask causes the absorption
curve to shift down in frequency generating additional low to mid-frequency absorp-
tion. At high frequency, the hard parts of the mask reflect some of the sound, preventing
absorption happening in some parts of the mineral wool, and so causing the absorption
coefficient to reduce.
It is at these high frequencies, where the absorption is reduced, that
the surface should start to generate significant amounts of diffuse reflections.To accomplish mid- to high frequency dispersion, a 31 by 33 2D array of absorptive and reflective areas is used.
The reflective areas map to the 1 bit and the absorptive areas map to the 0 bit in a binary pseudorandom number sequence.
The distribution of these binary elements is based on an optimal binary sequence with a flat power spectrum as this maximizes dispersion.
For example, this could be based on an maximum length sequences.