neil a. shaw - noise pollution clearinghouse · fundamentals of acoustics, lawrence e. kinsler,...

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


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



SPL (sound pressure level)

Lp= SPL = 20 log p/ pref

pref = 0.00002 Pa

Pa = [N/m²] = [Kg⋅m/s²⋅m²] = [kg/s²- m]



SWL (sound power level)

SWL = 10 log W / Wref

Wref = 1 x 10-¹² W = 1 pW

W = [kg - m2 / s3 ]



I (intensity)

L I = IL = 10 log I / Iref

Iref = 10-¹² W/m² = 1x10-¹² kg/s³



Waves

PLANE:

∂ ²p = 1 ∂ ²p∂ x² c² ∂ t²

COMPLEXFORM OF THEHARMONICSOLUTION

P = Ae + Bej(wt-kx) j(wt+kx)



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

→→



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 – )

( ) =



Human FactorsRANGEOFAUDIBILITY:

Figure 2



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


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


Human Factors

Critical BandsFigure 5Menlo Scientific Acoustics


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


© 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



History



Reflectionx > 4 λ


Figure 8


Diffusion

x ≈ λ


Figure 9


Diffraction


Figure 10


Concave Reflector


Figure 11


Flat Reflector


Figure 12


Convex Reflector


Figure 13


Room Modes


Figure 14 Figure 16

Figure 15


Reverberant Decaylarge room


Figure 17


Reverberant Decaysmall room


Figure 18


Materials


Figure 19


Small Rooms

Modes

Shape

Reflection management



TIME METRICS

Reverberation Time (RT60)

Bass Ratio (BR)

Large Rooms



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



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



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)



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



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







Figure 14: Ballou, p 91






List of Figures



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

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© 2002 Menlo Scientific Acoustics, Inc. 40

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