Introduction to Acoustics

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1032 Part H Engineering Acoustics Part H 24.4 measured by interferometry. The cavity is manufactured with precision optical fabrication. The uncertainty in the equivalent volume of such a cavity is estimated to be approximately 20 ppm. For less stringent applications the three optical flats can be replaced with adaptor rings [24.25] or with three cavities of known volumes. The equivalent volume of the cavity can then be determined by interpolation. This method has been commercialized with a similar procedure that relied on two couplers (long and short couplers) in the Brüel and Kjær 5998 reciprocity apparatus. With the sensitivities of the microphone pairs obtained with the two couplers, the microphone cavity depths are then adjusted numerically until the final microphone sensitivities obtained with the two couplers are nearly identical or very close. 24.4.3 Capillary Tube Correction For microphone calibration, the preferred expression [24.38,40] adopted for the acoustic input impedance of an open capillary tube is: Zc = Zt tanh(ζ Lc) , (24.35) Table 24.2 Real part of Zc in GPa s/m 3 (ANSI S1.15: 2005, and IEC 61094-2:1992-03), tube dimensions in millimeters ℓC = 50 Frequency ℓC = 100 where Zt is the complex characteristic impedance of a capillary tube with infinite length, Lc is the length of the capillary tube, ζ is the complex propagation coefficient for plane waves in a tube, and Zt = � �1/2 Ã1/Ã2 , (24.36) ζ = � Ã1 Ã2 �1/2 . (24.37) Ã1 and Ã2 are complex quantities; Ã1 represents viscosity loss at the walls and inertia of the gas medium, and Ã2 represents heat conduction loss at the walls and the compliance of the gas medium, where Ã1 = i ωρ πrc 2 Ã2 = iω πr2 c ρc 2 � 1 − 2J1(kcrc) �−1 kcrc J0(kcrc) , (24.38) � 1 + 2 Bkcrc (γ − 1) j1(Bkcrc) j0(Bkcrc) rc = 0.1667 rc = 0.20 rc = 0.25 (Hz) rc = 0.1667 rc = 0.20 rc = 0.25 3.018 1.457 0.597 20 6.041 2.916 1.195 3.019 1.457 0.597 25 6.044 2.919 1.196 3.020 1.458 0.597 31.5 6.049 2.922 1.198 3.022 1.459 0.598 40 6.059 2.928 1.201 3.025 1.460 0.599 50 6.072 2.937 1.205 3.029 1.463 0.600 63 6.094 2.951 1.212 3.036 1.467 0.602 80 6.130 2.975 1.225 3.047 1.473 0.605 100 6.185 3.011 1.243 3.063 1.482 0.610 125 6.270 3.069 1.272 3.093 1.499 0.620 160 6.422 3.173 1.326 3.137 1.524 0.633 200 6.643 3.331 1.408 3.207 1.564 0.654 250 6.989 3.595 1.550 3.326 1.631 0.689 315 7.542 4.066 1.817 3.534 1.750 0.750 400 8.353 4.944 2.381 3.871 1.943 0.849 500 9.068 6.288 3.535 4.504 2.314 1.034 630 8.670 7.336 5.631 5.807 3.113 1.435 800 6.375 5.311 4.375 8.332 4.890 2.378 1000 4.353 3.005 1.925 12.120 9.008 5.385 1250 3.545 2.127 1.146 The data used for this table are: c = 345.7m/s, γ = 1.40, ρ = 1.186 kg/m 3 , η = 18.3×10 −6 Pa s, αt = 21 × 10 −6 m 2 /s The values given in this table are valid at the reference environmental conditions: 23 ◦ C, 101.325 kPa and 50% RH � , (24.39) J0 and J1 are, respectively, the zeroth- and first-order cylindrical Bessel functions of the first kind for complex arguments, rc is tube radius (m), kc = (−iωρ/η) 1/2 is the complex wave number (m −1 ), B =[η/(ραt)] 1/2 , αt is the thermal diffusivity of the gas media (m 2 /s).
Table 24.2 (continued) ℓC = 50 Frequency ℓC = 100 Microphones and Their Calibration 24.4 Corrections 1033 rc = 0.1667 rc = 0.20 rc = 0.25 (Hz) rc = 0.1667 rc = 0.20 rc = 0.25 9.191 7.926 6.740 1600 4.171 2.410 1.196 4.326 3.021 1.951 2000 6.325 4.409 2.527 2.694 1.637 0.893 2500 4.979 3.717 2.768 2.807 1.580 0.783 3150 4.411 2.661 1.392 5.923 3.536 1.749 4000 5.238 4.019 3.075 5.946 4.825 3.903 5000 5.059 3.262 1.770 3.306 1.939 1.011 6300 4.578 2.920 1.672 6.571 5.375 4.137 8000 4.695 3.034 1.749 4.184 2.465 1.258 10 000 4.977 3.363 1.952 3.902 2.539 1.540 12 500 4.760 3.331 2.271 4.043 2.590 1.534 16 000 4.753 3.263 2.137 4.535 2.813 1.517 20 000 4.844 3.324 2.023 0.097 0.074 0.049 20 0.096 0.114 0.090 0.122 0.092 0.061 25 0.120 0.143 0.112 0.153 0.116 0.077 31.5 0.151 0.180 0.141 0.195 0.147 0.098 40 0.191 0.228 0.180 0.244 0.184 0.123 50 0.238 0.285 0.225 0.307 0.232 0.155 63 0.299 0.359 0.283 0.390 0.295 0.197 80 0.376 0.455 0.360 0.488 0.369 0.246 100 0.465 0.569 0.452 0.610 0.461 0.308 125 0.569 0.710 0.567 0.782 0.592 0.396 160 0.701 0.905 0.731 0.980 0.743 0.496 200 0.824 1.123 0.923 1.228 0.933 0.623 250 0.916 1.380 1.170 1.556 1.186 0.792 315 0.888 1.664 1.500 1.990 1.527 1.021 400 0.479 1.842 1.922 2.511 1.948 1.306 500 –0.684 1.11 2.200 3.189 2.532 1.711 630 –2.739 –0.777 0.926 3.987 3.353 2.325 800 –3.890 –3.152 –2.510 4.280 4.213 3.186 1000 –3.031 –2.595 –2.130 1.338 3.162 3.730 1250 –1.382 –1.157 –0.944 –5.333 –4.384 –3.281 1600 0.429 0.456 0.282 –4.500 –3.768 –2.956 2000 0.260 0.971 1.221 –1.996 –1.663 –1.280 2500 –1.702 –1.552 –1.344 0.491 0.244 0.051 3150 0.205 0.199 0.053 2.428 2.283 1.692 4000 –1.074 –0.864 –0.524 –2.803 –2.434 –1.954 5000 0.208 0.438 0.406 0.186 –0.037 –0.190 6300 –0.070 –0.095 –0.219 –1.245 –0.607 0.209 8000 –0.041 –0.027 –0.138 0.872 0.643 0.336 10 000 –0.056 0.152 0.212 –0.542 –0.699 –0.764 12 500 –0.281 –0.295 –0.281 –0.210 –0.399 –0.532 16 000 –0.174 –0.187 –0.228 0.430 0.349 0.142 20 000 –0.109 –0.001 0.035 The data used for this table are: c = 345.7m/s, γ = 1.40, ρ = 1.186 kg/m 3 , η = 18.3×10 −6 Pa s, αt = 21 × 10 −6 m 2 /s The values given in this table are valid at the reference environmental conditions: 23 ◦ C, 101.325 kPa and 50% RH Part H 24.4
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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 -
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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
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
Page 976 and 977: 23.2.5 Criteria for Noise Emissions
Page 978 and 979: Table 23.5 Table of limit values fr
Page 980 and 981: a) Air flows freely to rotor Weak t
Page 982 and 983: Static efficiency normalized to its
Page 984 and 985: ful applications. Good results are
Page 986 and 987: Table 23.8 Crossover speeds for var
Page 988 and 989: Reduction of airplane engine noise
Page 990 and 991: 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
Page 998 and 999: 23.4.4 Criteria for Noise Immission
Page 1000 and 1001: Table 23.10 (cont.) Some features o
Page 1002 and 1003: Noise 23.4 Noise and the Receiver 1
Page 1004 and 1005: view of administrative procedures r
Page 1006 and 1007: provides recommendations for a foll
Page 1008 and 1009: sound power levels of noise sources
Page 1010 and 1011: 23.68 ISO: ISO 9296:1988 Acoustics
Page 1012 and 1013: 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
Page 1046 and 1047: Sound 25. Intens Sound Intensity So
Page 1048 and 1049: Under such conditions the intensity
Page 1050 and 1051: 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
Page 1062 and 1063: it is relatively straightforward si
Page 1064 and 1065: intensity normal to the source. Thi
Page 1066 and 1067: 25.9 W. Maysenhölder: The reactive
Page 1068 and 1069: 25.77 ISO: ISO 11205 Acoustics - No
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1084 Part H Engineering Acoustics P
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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
Page 1136 and 1137:
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
Page 1160 and 1161:
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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