First Pan-American/Iberian Meeting on Acoustics Cancun, Mexico 2 – 6 December 2002 Neil A. Shaw Menlo Scientific Acoustics, Inc. Topanga, California © 2002 Menlo Scientific Acoustics, Inc.
First Pan-American/Iberian Meeting on AcousticsCancun, Mexico
2 – 6 December 2002
Neil A. ShawMenlo Scientific Acoustics, Inc.
Topanga, California
© 2002 Menlo Scientific Acoustics, Inc.
Acoustics• Acoustics is the science of sound, including its
production, transmission and effects - Allan D.Pierce, Acoustics An Introduction to Its PhysicalPrinciples and Applications, McGraw-Hill BookCompany, New York, 1981 (ASA reprint 1989).
Architectural Acoustics• Sound in an Enclosure.
(We all know what it is, but it's difficult to define.)
Menlo Scientific Acoustics2
© 2002 Menlo Scientific Acoustics, Inc.
Density: ρo(Po,T)
Pressure: Po ≈ 100 kPa
p(t) = instantaneous
p = effective =
Frequency/ Wavelength:Speed of Sound: c= λ f
c= 331.4
c= γ Po ρ o
√_____<p2(t)>
√_____ T 273___
__Menlo Scientific Acoustics
3© 2002 Menlo Scientific Acoustics, Inc.
Log Notation
Figure 1
Menlo Scientific Acoustics4
© 2002 Menlo Scientific Acoustics, Inc.
SPL (sound pressure level)
Lp= SPL = 20 log p/ pref
pref = 0.00002 Pa
Pa = [N/m²] = [Kg⋅m/s²⋅m²] = [kg/s²- m]
Menlo Scientific Acoustics5
© 2002 Menlo Scientific Acoustics, Inc.
SWL (sound power level)
SWL = 10 log W / Wref
Wref = 1 x 10-¹² W = 1 pW
W = [kg - m2 / s3 ]
Menlo Scientific Acoustics6
© 2002 Menlo Scientific Acoustics, Inc.
I (intensity)
L I = IL = 10 log I / Iref
Iref = 10-¹² W/m² = 1x10-¹² kg/s³
Menlo Scientific Acoustics7
© 2002 Menlo Scientific Acoustics, Inc.
Waves
PLANE:
∂ ²p = 1 ∂ ²p∂ x² c² ∂ t²
COMPLEXFORM OF THEHARMONICSOLUTION
P = Ae + Bej(wt-kx) j(wt+kx)
Menlo Scientific Acoustics8
© 2002 Menlo Scientific Acoustics, Inc.
WavesCYLINDRICAL: ∇ ²p + k²p = 0 (k=Τ /c)
∇2 = 1 ∂ ( ∂ ) 1 ∂2 ∂2
w ∂w ∂w w2 ∂φ2 ∂z2
One solution:
p = A J0 (2πνw) + iN0 (2πνw) e-2πiνt
c c
W → ∞ A 2 eik(w-ct) - i(π/4) k = 2πν = 2π πkw c λ
W → 0 2A ln(w)e-2πiνt
π
+ +w
][
√ ___
i
→→
Menlo Scientific Acoustics9
© 2002 Menlo Scientific Acoustics, Inc.
WavesSPHERICAL:
1 ∂ ∂p 1 ∂²p r2 ∂r ∂r c² ∂t²
if a<<λ then p/r >> ∂p/∂r @ r = a
P ≅ ρ dS at r = a 4π dt
p ≅ ρ r where S’(z) = (d/dz)S(z) 4πr c
S = Total Flow
r2
S’ ( t – )
( ) =
Menlo Scientific Acoustics10
© 2002 Menlo Scientific Acoustics, Inc.
Human FactorsRANGEOFAUDIBILITY:
Figure 2
Menlo Scientific Acoustics11
© 2002 Menlo Scientific Acoustics, Inc.
Human Factors20Hz 10kHz60Hz 250Hz 500Hz 1kHz 2.5kHz 5kHz
kick drum
bass guitar
snare drum
cymbals
acoustic guitar
acoustic piano
electric guitar
toms
voice
horns
Figure 3Menlo Scientific Acoustics
12© 2002 Menlo Scientific Acoustics, Inc.
Human Factors
Soun
d Le
vel (
dB)
Frequency (Hz)
Symphonic MusicSpeech
RangeThreshold of Feeling
Threshold of Audibility
Dynamic RangeFor SymphonicMusic
η
ι
------------
------------
4k
Figure 4Menlo Scientific Acoustics
13© 2002 Menlo Scientific Acoustics, Inc.
Human Factors
Critical BandsFigure 5Menlo Scientific Acoustics
14© 2002 Menlo Scientific Acoustics, Inc.
3020
40
60
80
100
120
140 dB
10
130
50
70
90
110
0
Common SoundsJet Plane (100 feet)
Amplified Rock and Roll (6 feet)Threshold of Pain
Diesel Truck (30 feet)
Food Blender (3 feet)Motorcycle (30 feet)Automobile (25 feet)Loud Singing (3 feet)
Inside CarNormal Conversation
Quiet Street
Quiet Home
Quiet Whisper (3 feet)
Rustling Leaves
Human Breathing
Threshold of Hearing
117 dB Chainsaw (3 feet)115 dB Pneumatic Riveter (3 feet)107 dB Power Mower (3 feet)
94 dB Subway (inside)
Figure 6
Menlo Scientific Acoustics15
© 2002 Menlo Scientific Acoustics Inc
85617 to 11234
5621 to 70827077 to 89168909 to 11225
6300-- 8000 --
10000
383940
72815 to 5630
2817 to 35493547 to 44694465 to 5625
3150-- 4000 --
5000
353637
61411 to 2822
1412 to 17791778 to 22402238 to 2819
1600-- 2000 --
2500
323334
5707 to 1414
708 to 892891 to 1123
1122 to 1413
800-- 1000 --
1250
293031
4354 to 709
355 to 447447 to 563562 to 708
400-- 500 --
630
262728
3178 to 355
178 to 224224 to 282282 to 355
200-- 250 --
315
232425
289 to 178
89 to 112112 to 141141 to 178
100-- 125 --
160
202122
145 to 89
45 to 5656 to 7171 to 89
50-- 63 --
80
171819
Sub-Octave22 to 45
22 to 2828 to 3635 to 45
25-- 31.5 --
40
141516
CORRESPONDING OCTAVEBAND
FREQUENCY RANGE (Hz)CENTER FREQUENCY (Hz.)THIRD OCTAVEBAND NO.
Measurement
Figure 7© 2002 Menlo Scientific Acoustics, Inc.
Exodus XXVI
History
Menlo Scientific Acoustics17
© 2002 Menlo Scientific Acoustics, Inc.
History
Menlo Scientific Acoustics18
© 2002 Menlo Scientific Acoustics, Inc.
History
Menlo Scientific Acoustics19
© 2002 Menlo Scientific Acoustics, Inc.
History
Menlo Scientific Acoustics20
© 2002 Menlo Scientific Acoustics, Inc.
History
Menlo Scientific Acoustics21
© 2002 Menlo Scientific Acoustics, Inc.
Reflectionx > 4 λ
Menlo Scientific Acoustics22
Figure 8
© 2002 Menlo Scientific Acoustics, Inc.
Diffusion
x ≈ λ
Menlo Scientific Acoustics23
Figure 9
© 2002 Menlo Scientific Acoustics, Inc.
Diffraction
Menlo Scientific Acoustics24
Figure 10
© 2002 Menlo Scientific Acoustics, Inc.
Concave Reflector
Menlo Scientific Acoustics25
Figure 11
© 2002 Menlo Scientific Acoustics, Inc.
Flat Reflector
Menlo Scientific Acoustics26
Figure 12
© 2002 Menlo Scientific Acoustics, Inc.
Convex Reflector
Menlo Scientific Acoustics27
Figure 13
© 2002 Menlo Scientific Acoustics, Inc.
Room Modes
Menlo Scientific Acoustics28
Figure 14 Figure 16
Figure 15
© 2002 Menlo Scientific Acoustics, Inc.
Reverberant Decaylarge room
Menlo Scientific Acoustics29
Figure 17
© 2002 Menlo Scientific Acoustics, Inc.
Reverberant Decaysmall room
Menlo Scientific Acoustics30
Figure 18
© 2002 Menlo Scientific Acoustics, Inc.
Materials
Menlo Scientific Acoustics31
Figure 19
© 2002 Menlo Scientific Acoustics, Inc.
Small Rooms
Modes
Shape
Reflection management
Menlo Scientific Acoustics32
© 2002 Menlo Scientific Acoustics, Inc.
TIME METRICS
Reverberation Time (RT60)
Bass Ratio (BR)
Large Rooms
Menlo Scientific Acoustics33
© 2002 Menlo Scientific Acoustics, Inc.
Large Rooms
Strength (G) Sound Pressure Distribution (∆L)
Center Time (ts) Energy Definition Measure (C50)
Register Balance Measure (BR)
Speech Time Index (STI) Articulation Loss (ALcons)
Subjective Intelligibility Tests Clarity (C80)
Sound Coloration (Kt and Kh)
ENERGY METRICS
Menlo Scientific Acoustics34
© 2002 Menlo Scientific Acoustics, Inc.
Spacial Impression Measurefor Music (R)
Lateral Efficiency(LE for Music, LF and LFC) Interaural Cross Correlation
Coefficient (IACC) Interaural Time-Delay Gap
(ITDG, t1)Reverberance Measure (H)
Diffusion Stage Support (ST1) Texture
Early Decay Time (EDT) Intimacy Spaciousness
Large Rooms
Menlo Scientific Acoustics35
© 2002 Menlo Scientific Acoustics, Inc.
ReferencesAcoustics, Leo L. Beranek, McGraw-Hill Book Company, New
York, 1954 (available from the ASA) Acoustics An Introduction to Its Physical Principles and
Applications, Allan D. Pierce, McGraw-Hill Book Company,New York, 1981 (available from the ASA)
Architectural Acoustics, Vern O. Knudsen, John Wiley & Sons,
New York, 1932 Architectural Acoustics, M. David Egan, McGraw-Hill, Inc., New
York, 1988 Collected Papers on Acoustics, Wallace Clement Sabine,
Harvard University Press, Cambridge, Massachusetts, 1922(available from the ASA)
Menlo Scientific Acoustics36
© 2002 Menlo Scientific Acoustics, Inc.
Fundamentals of Acoustics, Lawrence E. Kinsler, Austin R. Frey,Alan B. Coppens and James V. Sanders, John Wiley & Sons,New York, 1982
Handbook for Sound Engineers, Glen M. Ballou (editor), FocalPress, Boston, 2002
The Pentateuch and Haftorahs, J. H. Hertz (editor), SoncinoPress, London, 1960
Theoretical Acoustics, Philip M. Morse and K. Uno Ingard,McGraw-Hill Book Company, New York, 1968
Books and Acoustics, Especially Wallace Clement Sabine'sCollected Papers on Acoustics, Neil A. Shaw, Jesse Klapholzand Mark R. Gander, paper 1aAAb2, Proceedings WallaceClement Sabine Centennial Symposium, Acoustical Society ofAmerica, Woodbury, New York, 1994
References
Menlo Scientific Acoustics37
© 2002 Menlo Scientific Acoustics, Inc.
List of FiguresWaves equations (slides 9-10): Morse and Ingard
Figure 2: “Transition to Digital - Elements ofPsychoacoustics,” Michael Robin, Broadcast Engineeringmagazine, March 2002, p 34
Figure 3: “Panning for Gold,” Randy Neiman, ElectronicMusician magazine, March 2002, p 48
Figure 4: derived from Egan, p 9
Figure 5: “Transition to Digital - Elements ofPsychoacoustics,” Michael Robin, Broadcast Engineeringmagazine, March 2002, p 32
Figure 6: Egan, p 13
Figure 8: Egan, p 89Menlo Scientific Acoustics
38© 2002 Menlo Scientific Acoustics, Inc.
Figure 9: Egan, p 89
Figure 10: Egan, p 90
Figure 11: Egan, p 93
Figure 12: Egan, p 93
Figure 13: Egan, p 94
Figure 14: Ballou, p 91
Figure 15: Ballou, p 92
Figure 16: Ballou, p 92
Figure 17: Egan, p 108
Figure 18: Egan, p 109
Figure 19: Egan, p 109
List of Figures
Menlo Scientific Acoustics39
© 2002 Menlo Scientific Acoustics, Inc.
Menlo Scientific Acoustics, Inc.Los Angeles Office: San Francisco Office:Post Office Box 1610 5161 Raincloud DriveTopanga, California 90290 Richmond, California 94803fon +310-455-2221 fon: +510-758-9014fax +310-455-0923 fax: +510-758-9016
China Office: Taiwan Office:c/o Sea Galleon c/o Kou Ryou EnterprisesJinhaihua Xincun, Chiling, 2/F, 92 Neihu Road,Houjie, Dongguan, Guangdong Section 1, TaipeiChina Taiwanfon: +86-769-5887752, 5817646 fon: +886-2-2657 1100
© 2002 Menlo Scientific Acoustics, Inc. 40