Introduction to Acoustics

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esonance (AR)andmultichannel reverberation (MCR), which appeared in the 1960s, this delay was provided by letting the loop gain of a large number of microphone– loudspeaker channels be tuned to just below the feedback limit. By spacing the microphones and loudspeakers far apart in the room (normally close to the ceiling), the sound would spend sufficient time traveling several times between loudspeakers and microphones for an audible prolongation of the reverberation to be perceived. In more-modern systems, electronic delays and reverberators are normally used. In order to create the illusion of diffuse reverberation coming from the room itself, a large number of loudspeakers with low directivity must be distributed over the main surfaces in the room, as illustrated in Fig. 9.56. Since many speakers are needed, each can be fairly small and with limited acoustic power capability. The density and placement of these speakers as well as the balancing of their levels is essential to prevent localization of individual loudspeakers from any seat. Regarding the microphones, these may be highly directive, but they must be placed quite far from the sound sources (and preferably out of sight) in order to cover the stage without the reverberant level being strongly dependent on the position of the sound source. In view of what was explained in Sect. 9.8.1 about the measures needed to reduce the risk of feedback in loudspeaker systems, it is no wonder that most reverberation-enhancement manufacturers have to implement a solid strategy against uncontrolled feedback. One very efficient approach is to introduce time-varying delays in the sound-processing equipment, as this seems to destroy sharp room resonances when they start to build up to form a hauling frequency. Still, most enhancement systems work with a loop gain close to the feedback limit (which is actually participating actively in increasing the reverberation time), which is acceptable as long as it is under control and does not cause audible coloration of the sound. References 9.1 A.C. Gade: Subjective Room Acoustic Experiments with Musicians. PhD thesis, Rep. No. 32 (Technical University of Denmark, Copenhagen 1982) 9.2 W.C. Sabine: Collected Papers on Acoustics (Pininsula, Los Altos 1994), Reissued 9.3 L.L. Beranek: Concert Halls and Opera Houses, Music Acoustics and Architecture, 2nd edn. (Springer, Berlin, New York 2004) Reverberation time (s) 4 3.5 3 2.5 2 1.5 1 125 Acoustics in Halls for Speech and Music References 349 Demo Church Large hall Opera Small hall Chamber Jazz Speech Off 250 500 1000 2000 4000 1/1 octave centre frequency (Hz) Fig. 9.57 Reverberation time values measured in a hall for different settings of the reverberation enhancement system (LARES) It is essential for the acceptance of enhancement systems that neither audience nor performers experience the sound as coming from a loudspeaker system. Likewise, artefacts such as coloration due to feedback or the poor frequency characteristics of speakers are unacceptable. The maximum increase in reverberation time possible with feedback-based systems like AR and MCR was typically about 50%. With modern digital reverberators, a much larger range can be achieved, as shown in Fig. 9.57. Increasing the reverberation time by a factor of three or more is not impossible. However, the illusion, when you still see the physical, much-dryer room around you, tends to break down when the value increases much above the 50%, which ironically is what the old systems could produce. From a purist standpoint, reverberation enhancement can be regarded as an acoustic prosthesis, but in many cases a pragmatic approach to the use of these systems can increase the range of programs that a cultural venue can host. 9.4 M.F.E. Barron: Auditorium Acoustics and Architectural Design (Spun, London 1993) 9.5 H. Kuttruff: Room Acoustics (Applied Science, London 1976) 9.6 ISO: ISO 3382, Acoustics – Measurement of the Reverberation Time of Rooms with Reference to Other Acoustical Parameters (ISO, Geneva 1997) Part C 9
350 Part C Architectural Acoustics Part C 9 9.7 M. Vorländer: International Round Robin on Room Acoustical Computer Simulations, Proc. 15th ICA (Trondheim, Norway 1995) pp. 689–692 9.8 J.S. Bradley, G.A. Soloudre: The influence of late arriving energy on spetial impression, J. Acoust. Soc. Am. 97(4), 2263–2271 (1995) 9.9 L.L. Beranek: Music, Acoustics and Architecture (Wiley, New York 1962) 9.10 Personal communication (summer 2006) 9.11 A.C. Gade: Investigations of musicians’ room acoustic conditions in concert halls I, methods and laboratory experiments, Acustica 69, 193–203 (1989) 9.12 A.C. Gade: Investigations of musicians’ room acoustic conditions in concert halls II, Field experiments and synthesis of results, Acustica 69, 249–262 (1989) 9.13 T. Houtgast, H.J.M. Steeneken: A tool for evaluating auditoria, Brüel Kjær Tech. Rev. 3, 3–12 (1985) 9.14 J.S. Bradley: Predictors of speech intelligibility in rooms, J. Acoust. Soc. Am. 80, 837–845 (1986) 9.15 M.R. Schroeder: New method of measuring reverberation time, J. Acoust. Soc. Am. 37, 409 (1965) 9.16 J.S. Bradley: Accuracy and reproducibility of auditorium acoustics measures, Proc. IOA 10, 399–406 (1988), Part 2 9.17 K. Sekigouchi, S. Kimura, T. Hanyuu: Analysisi of sound field on spatial information using a fourchannel microphone system based on regular tetrahedron peak point method, Appl. Acoust. 37, 305–323 (1992) 9.18 D. de Vries, A.J. Berkhout, J.J. Sonke: Array Technology for Measurement and Analysis of Sound Fields in Enclosures, AES 100th Convention 1996 Copenhagen, Preprint 4266 (R-4) (AES, San Francisco 1996) 9.19 C.M. Harris: Absorption of air versus humidity and temperature, J. Acoust. Soc. Am. 40, 148–159 (1966) 9.20 C.W. Kosten: The mean free path in room acoustics, Acustica 10, 245(1960) 9.21 L.L. Beranek: Analysis of Sabine and Eyring equations and their applications to concert hall audience and chair absorption, J. Acoust. Soc. Am. 120 (2006) 9.22 L.L. Beranek, T. Hidaka: Sound absorption in concert halls by seats, occupied and unoccupied, and by the hall’s interior surfaces, J. Acoust. Soc. Am. 104, 3169–3177 (1998) 9.23 S. Sakamoto, T. Yokota, H. Tachibana: Numerical sound field analysis in halls using the finite difference time domain method. In: Proc. Int. Symp. Room Acoustics: Design and Science (RADS), Awaji Island (ICA, Kyoto 2004) 9.24 F. Spandöck: Raumakustische Modellversuche, Ann. Phys. 20, 345 (1934) 9.25 A.C. Gade: Room acoustic properties of concert halls: quantifying the influence of size, shape and absorption area, J. Acoust. Soc. Am. 100, 2802 (1996) 9.26 M. Barron, L.-J. Lee: Energy relations in Concert Auditoria, J. Acoust. Soc. Am. 84, 618–628 (1988) 9.27 W.-H. Chiang: Effects of Various Architectural Parameters on Six Room Acoustical Measures in Auditoria, PhD thesis (University of Florida, Gainesville 1994) 9.28 W. Fasold, H. Winkler: Bauphysikalische Entwurfslehre, Band 5; Raumakustik (Verlag Bauwesen, Berlin 1976) 9.29 Z. Maekawa, P. Lord: Environmental and Architectural Acoustics (Spon, London 1994) 9.30 W. Furrer, A. Lauber: Raum- und Bauakustik Lärmabwehr (Birkhaüser, Basel 1976) 9.31 J.H. Rindel: Anvendt Rumakustik, Note 4201, Oersted DTU (Technical University of Denmark, Copenhagen 1984), (In Danish) 9.32 L.I. Makrinenko: Acoustics of Auditoriums in Public Buildings (ASA, Melville 1994) 9.33 J. Sadowski: Akustyka architektoniczna (PWN, Warszawa 1976) 9.34 J.H. Rindel: Acoustic design of reflectors in Auditoria, Note 4212 Oersted DTU (Technical University of Denmark, Copenhagen 1999) 9.35 M.R. Schroeder: Binaural dissimilarity and optimum ceilings for concert halls: More lateral sound diffusion, J. Acoust. Soc. Am. 65, 958–963 (1979) 9.36 J.R. Hyde: Segerstrom Hall in Orange County – Design, Measurements and Results after years of operation, Proc. IOA, Vol. 10 (IOA, St. Albans 1988), Part 2
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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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Page 312 and 313: Acoustics 9. Acoustics in Halls for
Page 314 and 315: parameters, so we can assist in bui
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Page 326 and 327: e derived from interrupted noise de
Page 328 and 329: Acoustics in Halls for Speech and M
Page 330 and 331: espectively, can be calculated from
Page 332 and 333: ated by the architects. However, on
Page 334 and 335: of C and G. However, as all the ind
Page 336 and 337: F b d F n I S Fb Fn S d F n/F b d/d
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Page 352 and 353: Seating capacity 2662 1 915 + 324 2
Page 356 and 357: 4 3 2 1 Acoustics in Halls for Spee
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Page 364 and 365: Concert Hall Acoustics Based on Sub
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Page 368 and 369: mately by Concert Hall Acoustics Ba
Page 372 and 373: 10.1.5 Specialization of Cerebral H
Page 374 and 375: The other (n − 1) bits indicated
Page 376 and 377: As for the conflicting requirements
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Page 402 and 403: Table 11.1 Absorption coefficients
Page 404 and 405: Absorption coefficient α 1 0 Frequ
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Page 408 and 409: 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 -
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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
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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
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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
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∆LF (dB) 0 -10 -20 α -30 0.05 0.
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Absorption coefficient 1.0 0.8 0.6
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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
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23.194 Commission of the European C
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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
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τ is a dummy time variable. The ca
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Error in intensity (dB) 5 0 -5 -10
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8 7 6 5 4 3 2 1 0 -1 -2 -3 Error du
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crophones are calibrated with a pis
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Sound power level (dB re 1 pW) 72 7
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it is relatively straightforward si
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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
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Optical Methods for Acoustics and V
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50 100 150 200 250 300 350 400 450
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a) b) Optical Methods for Acoustics
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nm 1000 0 -1000 150 y (mm) 100 50 O
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Laser Optical Methods for Acoustics
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References 27.1 E.F.F. Chladni: Die
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27.75 E.-L.Johansson, L. Benckert,
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About the Authors Iskander Akhatov
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Neville H. Fletcher Chapter F.19 Au
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Brian C. J. Moore Chapter D.13 Univ
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Detailed Contents List of Abbreviat
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3.8.3 Acoustic Power ..............
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4.8.3 Typical Speed of Sound Profil
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7.3 Engines .......................
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10 Concert Hall Acoustics Based on
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13.4 Temporal Processing in the Aud
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15.2.5 String-Bridge-Body Coupling
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19.6 Birds ........................
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22.4.5 Combinations of Elementary S
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24.8 Overall View on Microphone Cal
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Subject Index 3 dB bandwidth 463 A
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British Medical Ultrasound Society
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electric circuit analogues - acoust
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hyperspeech 703 hypospeech 703 I IA
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- participation factors 909 - stiff
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- musical instruments 541 - musical
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- nonlinear vibrations 957 - plate
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subjective preference theory 353 su
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Introduction to Acoustics

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