Introduction to Acoustics

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British Medical Ultrasound Society (BMUS) 895 bubble collapse 287 bubble oscillation 287 bubbles – compressible liquid 278 – incompressible liquid 276 – Minnaert frequency 277 – Rayleigh–Plesset equation 276 bubbles and bubbly media 162 bubbly liquid 275 – Burgers–Korteweg–de Vries equation 281 – Korteweg–de Vries equation 279 Burgers equation 268 C CAATI (computed angle-of-arrival transient imaging) 17 CAC (ceiling attenuation class) 422 calibration 1064, 1068 – condenser microphone 1028 caterpillar – sound detection 786 Catgut Acoustical Society 554, 600 causality requirement 517 cavitation 6 cavity modes 593 CCD (charge-coupled device) 1103 CDF (cumulative distribution function) 512 ceiling attenuation class (CAC) 422 celeste 649 cello 560 central limit theorem 513 central moment 513 – kurtosis 513 –skewness 513 cepstrum 517 cerebral hemispheres 361 CFD (computational fluid dynamics) 142 change sensitivity 488 channel vocoder 724 chaotic sound waves 292 – in musical instruments 293 – in speech production 293 charge-coupled device (CCD) 1103 Chinese gongs 654 Chinese Opera Gongs 656 chirping – animal sonar 797 Chladni pattern 1101 – guitar 586 – holography 586 – rectangular plate 585 – violin plates 586 Chladni’s Law 10, 653 cicada sound production 789 circular membranes 919 circulation of sound energy 1070 clarinet 550, 602, 622, 637 clarinet model 733 clavichord 560, 561 closure, perceptual 494 CMU (concrete masonry unit) 407 CN (cochlear nucleus) 435, 436, 452 CND (cumulative normal distribution) 512 cochlea 4, 429, 430, 434, 437 cochlear – amplification 439, 440, 448 – amplifier 439, 446 – frequency map 437 – nucleus (CN) 435, 436, 452 – transduction 436, 437 coherence 215 coherence of changes, role in perceptual grouping 488 col legno 562 coloratura singing 674 comb filter 732 combination of structures 926 combination tones 449, 553 combustion – pulsed 248 common fate, principle of 493 communication – vibrational 788 communication with sound 2 commuted synthesis 732 complex exponential representation 1066 complex instantaneous intensity 1056 complex notation 240 complex representation 1054 complex sound intensity 1056 complex wave 504 compliance 241 compression 439, 442, 449, 452 computational fluid dynamics (CFD) 142 computed angle-of-arrival transient imaging (CAATI) 17 computer music language 737 computer speech recognition 3 concatenative synthesis 717 CONCAWE (CONservation of Clean Air and Water in Europe) 134 concert halls 4 concrete masonry unit (CMU) 407 condenser microphone – calibration 1027 – functional implementation 1024 – mechanical response 1025 – open-circuit sensitivity 1028 – practical considerations 1027 – reciprocity pressure calibration 1026 – theoretical considerations 1026 – theory 1024 conditional probability density 513 conducting jacket 738 conical tube 606 – input impedance 607 – Q-values 606 – truncation 607 CONservation of Clean Air and Water in Europe (CONCAWE) 134 conservation of sound energy 1054 conservative system 905 consonants 687 context dependence of acoustic properties of vowels and consonants – vowel quality 693 continuity equation – lossless 240 – thermoacoustic 242 control of intonation (speech melody) 699 convolution 509, 521 – of the Fourier transforms 509 cornet 640 correlation matrix 1078 cost function 934 coupling – air-jet to air column 633 – air-membrane 643 – body-air cavity 592 – instrument-room acoustic 600 – string–body 575 – string–string 580 – vocal tract 627 CPT (current procedural terminology) 847 cricket 789 – sound production 790 critical angle of shadow zone formation 133 critical distance-reverberation distance 347 critical frequency 396, 938 cross synthesis 721 Subject Index 1169 Subject Index
1170 Subject Index Subject Index cross-correlation 511 cross-fingering 617 cross-synthesizing vocoder 724 crustacean 797 crystalline elastic constant 219 CSDM (cross-spectral-density matrix) 182 cubic nonlinearity 949 cumulative distribution function (CDF) 512 cumulative normal distribution (CND) 512 current procedural terminology (CPT) 847 cut-off-frequency 616 cylindric spreading 115 cylindrical coupler 1034 cylindrical pipe – closed resonance 602 – tube impedance 602 cymbals 655 D D’Alembert’s solution 916 DAC (digital-to-analog converter) 714, 769 damped sounds 483 damping – Coulomb 945 – hysteretic 947 – localized 941 –matrix 908 – modal projection 940 – proportional 941 – weak 941 deep scattering layer (DSL) 160 deep sound channel (DSC) 149 deep venous thrombosis (DVT) 878 degree of freedom (DOF) 902 Deiter’s cell 447, 448 density – Gaussian 512 deterministic (sines) components 720 detuning parameter 952 DF (directivity factor) 115 DFT 729 DFT (discrete Fourier transform) 719 DI (directivity index) 115, 347 diaphragm – impedance 800 difference limen 478 diffraction 215 diffuse sound field 1057 digital recording 548 – aliasing 548 – dynamic range 548 –files 549 – Nyquist frequency 548 – resolution 548 – sampling rate 548 – sampling system 550 – sound 549 – sound file 548 – windowing functions 549 digital signal processing (DSP) 724, 752 digital speckle photography (DSP) 1104 digital speckle-pattern interferometry (DSPI) 1103 DigitalDoo 737 digital-to-analog converter (DAC) 714, 769 digitized data 520 diphones 717 Dirac delta function 507, 904, 916 directed reflection sequence (DRS) 340 directional sensitivity 429, 431 directional tone colour 599 directionality – violin 598 directivity factor (DF) 115 directivity index (DI) 115, 347 discharge rate 441, 442 discrete Fourier transform (DFT) 719 discrete systems 907 disjoint allocation, principle of 493 dispersion equation 921, 922, 936 dispersion relation 279, 282, 517 dispersive system 516 dissipation 249 distortion tones 449 DLS (downloadable sounds) 714, 736 DOF (degree of freedom) 902 DOF (motional degree of freedom) 1127 dominance, pitch 482 downsampling 716 downloadable sounds (DLS) 714, 736 dramatic and lyric soprano 676 driving-point admittance 910, 912 DRS (directed reflection sequence) 340 drum sticks 644 drums – air loading 643 – circcular membrane modes 642 – excitation stick 644 – radiation 647 dry air standard 1047 DSC (deep sound channel) 149 DSL (deep scattering layer) 160 DSP (digital signal processing) 724, 752 DSP (digital speckle photography) 1104 DSPI (digital speckle-pattern interferometry) 1103 Duffing equation 949, 950 dulcimer 561 duration discrimination 476 DVT (deep venous thrombosis) 878 dynamic capability 1063 dynamic range 434, 442 E eardrum 429, 430, 432, 433 early decay time (EDT) 307, 379 EARP (equal-amplitude random-phase) 520 earthquakes: P-waves and N-waves 2 echoe suppression 485 echo-location –bats 796 ECMUS (European Committee for Medical Ultrasound Safety) 895 edge tones 636 Edison, Thomas 14 EDT (early decay time) 307, 379 EDV (end diastolic velocity) 876 EEG (electroencephalography) 352 effect of loudness on glottal source 679 effect of subglottal pressure on fundamental frequency 674 effective area 433 effective cross sectional area 430 efferent 436 efferent synapse 449 EFSUMB (European Federation of Societies for Ultrasound in Medicine and Biology) 895 eigenfrequency 909 eigenmodes 909, 914 – string vibrations 557 elastic energy 905, 950 elasticity effects on ground impedance 125
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Springer Handbook of Acoustics
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Springer Handbook of Acoustics Thom
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Foreword The present handbook cover
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List of Authors Iskander Akhatov No
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Philippe Roux Université Joseph Fo
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XIV Contents 3.7 Attenuation of Sou
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XVI Contents 10 Concert Hall Acoust
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XVIII Contents 17.8 Physical Modeli
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XX Contents 24.5 Free-Field Microph
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XXII List of Abbreviations K KDP po
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Introduction 1. Introduction to Aco
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of noise have been the subject of c
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in order to understand how objectiv
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A Brief 2. A Brief History of Acous
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of 350 m/s for the speed of sound [
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number and relative strength of its
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To his contemporaries, Koenig was p
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Probably the most important use of
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piezoelectric ceramic compositions
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surveys together [2.46]. Masking of
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ther of computer music, since he de
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Basic 3. Linear Basic Linear Acoust
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M average molecular weight n unit v
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a) b) S v.n ∆t ∆S V |v| ∆t n
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temperature, q =−κ∇T , (3.16)
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The equivalent density M/V is conse
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Basic Linear Acoustics 3.3 Equation
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Because any vector field may be dec
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The latter and (3.84), in a manner
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assumed to have no ambient motion,
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Because the friction associated wit
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3.5 Waves of Constant Frequency One
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3.5.4 Time Averages of Products Whe
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as well as symmetry considerations,
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The auxiliary internal variables th
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Then the transient at a distant pos
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ω ′ = 0, and this is consistent
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1.0 10 -1 10 -2 10 -3 10 -4 10 -5 A
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This yields the interpretation that
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direction of propagation when a pla
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so the time-averaged incident energ
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Although the simple result of (3.31
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ut, also in keeping with the linear
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equation, the two differential equa
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Rodrigues relation, one has �1
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for the derivative.) In the asympto
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The differential scattering cross s
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elow) is F(t) = (2c) 1/2 �t −
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0.5 0 -0.5 -1.0 -1.5 0 Y0(η) (π/2
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is the Wronskian for the Bessel and
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The function qS is termed the sourc
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The appropriate identification for
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where jℓ is the spherical Bessel
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this subtlety taken into account, o
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U(x) Basic Linear Acoustics 3.15 Wa
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is ordinarily valid. With these ass
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along rays. These can be regarded a
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A(x0) x0 A(x) Fig. 3.53 Sketch of a
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possible, and one where neither the
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which is independent of the z-coord
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[3.108], and Carslaw [3.109]. In th
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where C(X)andS(X) are the Fresnel i
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Fig. 3.60 Characteristic diffractio
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of elastic solids, Trans. Camb. Phi
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3.101 J.B. Keller: Geometrical acou
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114 Part A Propagation of Sound Par
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Underwater 5. Underwater Acoustics
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5.1 Ocean Acoustic Environment The
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Long-Range Propagation Paths Figure
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tal direction, there is no loss ass
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equivalent circuit, as shown in Fig
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Attenuation á (dB/km) 1000 100 10
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5.2.5 Ambient Noise There are essen
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ubble natural acoustic resonance ω
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a bubbly medium (and for the simple
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As discussed, because detection inv
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(1/A)∇ 2 A ≪ K 2 )sothat(5.34)
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water, where the deep sound channel
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egion in the form p(r, z) = ψ(r, z
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5.4.6 Propagation and Transmission
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tegration interval. The source puls
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5.6 SONAR Array Processing Signal p
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former output is: �∞ b(θ,t) =
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Fig. 5.37 Angle-versus-time represe
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5.7 Active SONAR Processing Depth M
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a factor when there is a reverberan
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depth measurements that correspond
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along the cross-shelf track taken b
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time as a result of multiple paths,
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technique is very sensitive, and ex
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Fig. 5.57a,b Typical echogram obtai
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Frequency (Hz) 150 100 50 0 0 a) b)
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out. These data allow for study of
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5.59 G. Raleigh, J.M. Cioffi: Spati
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Physical 6. Physical Acou Acoustics
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where I is the intensity of the sou
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Wave velocity The wall exerts a dow
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destructively interfered with one a
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or: � � p2 � rms SPL = 10 log
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6.1.4 Wave Propagation in Solids Si
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where c is again the wave speed and
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measured. Some resonances are cause
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as 50 µmto5µm through one oscilla
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the number of false positives and m
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with the small mass), and frequency
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Laser Lens 1 Circular aperture Fig.
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Ground ring Insulator Sample Resist
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Energy ratio 1.0 0.8 0.6 0.4 Calcul
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terms. In this equation γ is the r
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directly. The nonlinearity paramete
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Thermoacoust 7. Thermoacoustics The
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Table 7.1 The acoustic-electric ana
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walls of the pores. (Positive G ind
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a) b) c) C reso d) δtherm e) p 0 U
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a) b) UA,l c) d) E 0 Q A Q A TA TA
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tor. This eliminates the need to le
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to this consumption of acoustic pow
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The traditional Stirling refrigerat
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Washington 1986) pp. 550-554, Softw
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258 Part B Physical and Nonlinear A
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Acoustics 9. Acoustics in Halls for
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parameters, so we can assist in bui
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weeks or even years is less reliabl
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9.3.1 Reverberation Time Reverberan
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selected). A distance different fro
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ing sound, as will naturally be exp
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of the sound fields. Consequently,
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e derived from interrupted noise de
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Acoustics in Halls for Speech and M
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espectively, can be calculated from
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ated by the architects. However, on
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of C and G. However, as all the ind
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F b d F n I S Fb Fn S d F n/F b d/d
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HS S èn ã d0 P0 rn Position of ey
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Time T (s) 2.5 2 1.5 1 5 10 15 Acou
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floor can be tilted to reduce volum
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ÄLcurv (dB) 10 8 6 4 2 0 -2 -4 -6
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Seating capacity 2662 1 915 + 324 2
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4 3 2 1 Acoustics in Halls for Spee
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cially in auditoria with T values l
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esonance (AR)andmultichannel reverb
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Concert 10. Concert Hall Acoustics
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Concert Hall Acoustics Based on Sub
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0 0 Concert Hall Acoustics Based on
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mately by Concert Hall Acoustics Ba
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10.1.5 Specialization of Cerebral H
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The other (n − 1) bits indicated
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As for the conflicting requirements
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have mainly been concerned with tem
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a) c) S S -4.3 -2.8 -2.0 -3.5 -3dB
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a model of the auditory-brain syste
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Building 11. Building Acou Acoustic
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Pressure Maximum Minimum 0 D Distan
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Table 11.1 Absorption coefficients
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Absorption coefficient α 1 0 Frequ
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is of key importance in rooms where
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Table 11.4 Transmission loss and ST
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TL of wall - (TL of door, window or
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Table 11.7 Generalized noise reduct
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Masking sound pressure level (dB) 5
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As for the room criterion (RC) meth
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11.5 Noise Control Methods for Buil
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Neoprene pads (30 durometer) with a
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Concrete Caulk around perimeter Vib
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Trim board to conceal gap (fasten o
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Gypsum board partition (as schedule
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Double-layer ribbed or waffle neopr
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11.6 Acoustical Privacy in Building
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Table 11.9 AI,SIIandPIforopenplanof
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Electronic sound masking in plenum
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E 1179 Standard Specification for S
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430 Part D Hearing and Signal Proce
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Psychoacoust 13. Psychoacoustics Ps
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Absolute threshold (dB SPL) 100 90
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the signal. By using this off-cente
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is as a crude indicator of the exci
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Relative response (dB) 100 90 80 70
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In a variation of this procedure, t
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Level of matching noise (dB) 100 90
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13.4 Temporal Processing in the Aud
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Most models include an initial stag
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The components were either uniforml
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(Frequency DL)/ERBN 0.2 0.1 0.05 0.
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elaborate place models have been pr
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13.6 Timbre Perception 13.6.1 Time-
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the duplex theory of sound localiza
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harmonic (by shifting the frequency
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sive. While some studies have been
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sentences (see Fig. 13.20). They va
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components is usually only perceive
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References 13.1 ISO 389-7: Acoustic
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13.74 D. Ronken: Monaural detection
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asymmetric function, J. Acoust. Soc
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13.211 J. Vliegen, A.J. Oxenham: Se
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534 Part E Music, Speech, Electroac
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The 16. The Human Human Voice in Sp
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uation, the effect of gravity is in
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piratory muscles (the internal inte
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Mean Ps (cm H2O) 50 40 30 20 10 0 D
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Glottal flow Closed Opening Open Cl
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Transglottal airflow (l/s) 0.4 0.2
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Mean spectrum level (dB) -30 -40 -5
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20 10 0 -10 -20 -30 -40 -50 0 i y u
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Mean level (dB) 0 -10 -20 -30 -40 1
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This topic was addressed by Ladefog
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Fig. 16.29 Acoustic consequences of
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Bass i e u Alto Tenor o ε œ æ Th
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100 80 60 40 20 0 -20 100 80 60 40
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tours for [� ]and[Ù ] sampled at
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Rapp [16.100] asked three native sp
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Utterance command T0 T3 Accent comm
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The # symbol indicates the possibil
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Second formant frequency (Hz) 2500
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tional rather than absolute (à la
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16.7 P. Ladefoged, M.H. Draper, D.
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esonance imaging: Vowels, J. Acoust
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16.139 A. Eriksson: Aspects of Swed
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Computer 17. Computer Mu Music This
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Quantum step Amplitude Quantization
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Some might notice that linear inter
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pers, textbooks, patents, etc. Furt
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0:00.0 0.5 0 Computer Music 17.3 Ad
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(0,0) (0,1) (1,1) (0,2) (1,2) (0,3)
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synthesizing vocoder. The main diff
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x(n) + z -1 z -1 Scattering junctio
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230 Hz FOF 1100 Hz FOF 1700 Hz FOF
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0 y + - Computer Music 17.8 Physica
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-1 (1-ß )×length Velocity + Veloc
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0 -30 (dB) -60 0 1.5 3 4.5 (kHz) Fi
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17.10 Composition The history of co
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and variance of the features can be
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17.20 J.L. Kelly Jr., C.C. Lochbaum
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Audio 18. Audio and Electroacoustic
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Alexander Graham Bell filed his pat
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on magnetic stripes. A common arran
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60 40 20 0 SPL-sound pressure level
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Interaural intensity difference (dB
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with equalization, without incurrin
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Fig. 18.8 Sine wave with crossover
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18.3.8 Dynamic Range Dynamic range
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Directly actuated type Diaphragm ty
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effective pickup pattern of the arr
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attempts to apply complementary com
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Most of the issues relating to spea
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nificant design considerations. At
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Some appreciation of the performanc
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pre-digital reverberators were elec
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and ‘s’ in English text - may b
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content of rest of the signal spect
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cross the head, in opposite directi
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18.2 J. Sterne: The Audible Past (D
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18.71 T. Sporer: Creating, assessin
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786 Part F Biological and Medical A
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Medical 21. Medical Acous Acoustics
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21.1 Introduction to Medical Acoust
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Auscultation location Right & left
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portance. The Strouhal number has b
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Fig. 21.3 Phono-cardiograph transdu
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Amplitude 8 6 4 2 0 -2 -4 -6 Displa
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λ1 = c1 / fus θ1 λ2 = c2 / fus
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lood flow can be resolved if the si
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vided in the image thickness direct
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not as predicted, because the wave
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Fig. 21.18a,b Quadrature Doppler de
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a) b) c) 100 0 V mV 10 0 a = 13 a =
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Ultrasound contact gel Position enc
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a) 10 cm b) c) 10 cm Fig. 21.32a-c
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a) Pin B Pin A Ultrasound line b) M
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Organ Patient Ultrasound transducer
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systems cannot tell the difference
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40 µm can be resolved. For a 10 kH
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a) b) c) d) Medical Acoustics 21.4
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Fig. 21.54 Doppler spectral wavefor
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10 20 30 10 20 30 Pre-exercise B-mo
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Vibrations in a punctured artery De
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the veins and diffuse into the inte
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21.5.3 Agitated Saline and Patent F
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transported by those cells and/or r
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1 0.8 0.6 0.4 0.2 0 Relative power
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High intensity focused ultrasound h
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a) b) c) Fig. 21.74a-c B-mode imagi
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provided simple metrics for the lik
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thickness of the carotid arteries,
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Structural 22. Structural Acoustics
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Structural Acoustics and Vibrations
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Magnitude (arb. units) 1.4 1.2 1.0
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This does not include the case wher
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the mass matrix is taken to be cons
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Magnitude (dB) -10 -30 -50 0 1 2 3
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where D(ω) = ω 4 − 2iω 3�
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form y(x, t) = � Φn(x)qn(t) . (2
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first to solve the wave equation (2
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5 3 1 -1 -3 -5 0 1 2 3 4 5 6 7 8 9
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conditions at each end) are necessa
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from which we can derive through (2
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In this case, the eigenfrequencies
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of radiation modes and their link w
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Finally, the displacement is ˜ξ(x
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notes the value of this eigenmode a
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Pm = ˙Q H [Rs + Ra] ˙Q , (22.262)
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where and Ra = 2ζaω0 M Z(s) = zL
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Radiated Power. The mean acoustic p
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(22.318) can be written ξ(x, y, t)
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Denoting the eigenfrequencies and e
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Magnitude (arb. units) 3 2 1 0 -1 -
Page 942 and 943:
for any real symmetric tensor Xij.
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F(N) 1 0.5 0 -0.5 -1 -1 -0.8 -0.6 -
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whose solution is θ1 = A cos ωτ.
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4.5 3.5 2.5 1.5 A 0.5 0 0.5 1.0 1.5
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Equations (22.423) are usually writ
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3. As the amplitude reaches the top
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Shallow Spherical Shells and Plates
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22.20 L. Cremer, M. Heckl: Structur
Page 958 and 959:
Noise Noise is discussed in terms o
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where the overbars represent time a
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Typical outdoor setting A-weighted
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90 dB(A)” is widely used, and imp
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Microphone, amplifier and A/D conve
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When each segment of the measuremen
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found from � LW = Lp + 10 log A +
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surement method is the ultimate use
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An intensity analyzer is more compl
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23.2.5 Criteria for Noise Emissions
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Table 23.5 Table of limit values fr
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a) Air flows freely to rotor Weak t
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Static efficiency normalized to its
Page 984 and 985:
ful applications. Good results are
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Table 23.8 Crossover speeds for var
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Reduction of airplane engine noise
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A variety of materials are used to
Page 992 and 993:
∆LF (dB) 0 -10 -20 α -30 0.05 0.
Page 994 and 995:
Absorption coefficient 1.0 0.8 0.6
Page 996 and 997:
high enough that there is little so
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23.4.4 Criteria for Noise Immission
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Table 23.10 (cont.) Some features o
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Noise 23.4 Noise and the Receiver 1
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view of administrative procedures r
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provides recommendations for a foll
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sound power levels of noise sources
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23.68 ISO: ISO 9296:1988 Acoustics
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in impedance tubes - Part 2: Transf
Page 1014 and 1015:
23.194 Commission of the European C
Page 1016 and 1017:
1022 Part H Engineering Acoustics P
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Sound 25. Intens Sound Intensity So
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Under such conditions the intensity
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a) Pressure and particle velocity 0
Page 1052 and 1053:
τ is a dummy time variable. The ca
Page 1054 and 1055:
Error in intensity (dB) 5 0 -5 -10
Page 1056 and 1057:
8 7 6 5 4 3 2 1 0 -1 -2 -3 Error du
Page 1058 and 1059:
crophones are calibrated with a pis
Page 1060 and 1061:
Sound power level (dB re 1 pW) 72 7
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it is relatively straightforward si
Page 1064 and 1065:
intensity normal to the source. Thi
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25.9 W. Maysenhölder: The reactive
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25.77 ISO: ISO 11205 Acoustics - No
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Optical 27. Optical Methods Metho f
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course also present in ordinary hol
Page 1096 and 1097:
Optical Methods for Acoustics and V
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50 100 150 200 250 300 350 400 450
Page 1104 and 1105:
a) b) Optical Methods for Acoustics
Page 1106 and 1107:
nm 1000 0 -1000 150 y (mm) 100 50 O
Page 1108 and 1109: Optical Methods for Acoustics and V
Page 1110 and 1111: Optical Methods for Acoustics and V
Page 1112 and 1113: Laser Optical Methods for Acoustics
Page 1114 and 1115: References 27.1 E.F.F. Chladni: Die
Page 1116 and 1117: 27.75 E.-L.Johansson, L. Benckert,
Page 1118 and 1119: 1128 Part H Engineering Acoustics P
Page 1130 and 1131: About the Authors Iskander Akhatov
Page 1132 and 1133: Neville H. Fletcher Chapter F.19 Au
Page 1134 and 1135: Brian C. J. Moore Chapter D.13 Univ
Page 1136 and 1137: Detailed Contents List of Abbreviat
Page 1138 and 1139: 3.8.3 Acoustic Power ..............
Page 1140 and 1141: 4.8.3 Typical Speed of Sound Profil
Page 1142 and 1143: 7.3 Engines .......................
Page 1144 and 1145: 10 Concert Hall Acoustics Based on
Page 1146 and 1147: 13.4 Temporal Processing in the Aud
Page 1148 and 1149: 15.2.5 String-Bridge-Body Coupling
Page 1150 and 1151: 19.6 Birds ........................
Page 1152 and 1153: 22.4.5 Combinations of Elementary S
Page 1154 and 1155: 24.8 Overall View on Microphone Cal
Page 1156 and 1157: Subject Index 3 dB bandwidth 463 A
Page 1160 and 1161: electric circuit analogues - acoust
Page 1162 and 1163: hyperspeech 703 hypospeech 703 I IA
Page 1164 and 1165: - participation factors 909 - stiff
Page 1166 and 1167: - musical instruments 541 - musical
Page 1168 and 1169: - nonlinear vibrations 957 - plate
Page 1170 and 1171: subjective preference theory 353 su
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Introduction to Acoustics

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