Introduction to Acoustics

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crophones are calibrated with a pistonphone in the usual manner. However, because of the serious influence of phase mismatch the pressure-residual intensity index should also be determined. The IEC standard for sound intensity instruments and its North American counterpart [25.18, 19] specify minimum values of the acceptable pressure-residual intensity index for the probe as well as for the processor; according to the results of a test the instruments are classified as being of class 1 or class 2. The test involves subjecting the two microphones of the probe to identical pressures in a small cavity driven with wide-band noise. A similar test of the processor involves feeding the same signal to the two channels. The pressure and intensity response of the probe should also be tested in a plane propagating wave as a function of the frequency, and the directional response of the probe is required to follow the ideal cosine law within a specified tolerance. According to the two standards a special test is required in the frequency range below 400 Hz: the intensity probe should be exposed to the sound field in a standingwave tube with a specified standing wave ratio (24 dB for probes of class 1). When the sound intensity probe is drawn through this interference field the sound intensity indicated by the measurement system should be within a certain tolerance. Figure 25.16a illustrates how the sound pressure, the particle velocity and the sound intensity vary with 115.0 110.0 105.0 100.0 95.0 (dB) Frequency Space Mic type 259 Hz 12 mm 4165 P v SWR: 24.1 dB Icor Mic A: 4165.1090562 Mic B: 4165.1090599 I a) Level (dB) b) Error (dB) Sound Intensity 25.3 Measurement of Sound Intensity 1065 File: File55 Date: 12 Jun 91, JIC-2 Amb. pressure: 1008 hPa 90.0 0 90 180 (cm) Position x LP (max) LI (field) LP (min) Fig. 25.17 Response of a sound intensity probe exposed to a standing wave: sound pressure, particle velocity, intensity, and phase-corrected intensity (After [25.50]) 5 0 –5 10 dB One wavelength Fig. 25.16 (a) Sound pressure level (solid line), particle velocity level (dashed line), and sound intensity level (dashdotted line) in a standing wave with a standing-wave ratio of 24 dB (b) Estimation error of a sound intensity measurement system with a residual pressure-intensity index of 14 dB (positive and negative residual intensity) (After [25.49]) Part H 25.3
1066 Part H Engineering Acoustics Part H 25.3 position in a one-dimensional interference field with a standing-wave ratio of 24 dB. It is apparent that the pressure-intensity index varies strongly with the position in such a sound field. Accordingly, the influence of a given phase error depends on the position, as shown in the calculations presented in Fig. 25.16b. Figure 25.17 shows an example of measurements with an intensity probe drawn through a standing-wave tube. The standing-wave test will also reveal other sources of error than phase mismatch, for example, the influence of an unacceptably high vent sensitivity of the microphones [25.51]. 25.3.2 The p–u Measurement Principle A p–u sound intensity measurement system combines two fundamentally different transducers, a pressure microphone and a particle velocity transducer. The sound intensity is simply the time average of the instantaneous product of the pressure and particle velocity signal, Ir = 〈p(t)ur(t)〉 t = 1/2Re � pu ∗� r , (25.31) where the latter expression is based on the complex exponential representation. In the frequency domain the expression takes the form Ir(ω) = Spu(ω). (25.32) Equation (25.32) gives the same result as (25.31) when the intensity spectrum is integrated over the frequency band of concern. A p–u sound intensity probe that combined a pressure microphone with a transducer based on the convection of an ultrasonic beam by the particle velocity flow was produced by Norwegian Electronics for some years [25.2, 52], but the device was somewhat bulky, very sensitive to airflow, and difficult to calibrate, and production was stopped in the middle of the 1990s. More recently, a micromachined transducer called the Microflown has become available for measurement of the particle velocity [25.15], and an intensity probe based on this device in combination with a small pressure microphone is now in commercial production [25.16]; see Fig. 25.18. The Microflown particle velocity transducer consists of two short, thin, closely spaced wires, heated to about 300 ◦ C [25.15]. Their resistance depends on the temperature. A particle velocity signal in the perpendicular direction changes the temperature distribution instantaneously, because one of the wires will be cooled more than the other by the airflow. The frequency response of this device is relatively flat up to a corner Fig. 25.18 A p–u sound intensity probe (by Microflown Technologies, The Netherlands) frequency of the order of 1 kHz caused by diffusion effects related to the distance between the two wires. A second corner frequency at about 10 kHz is caused by the thermal heat capacity of the wires. Between 1 and 10 kHz there is a roll-off of 6 dB per octave. The particle velocity transducer is combined with a small electret condenser microphone in the 1/2 inch sound intensity probe shown in Fig. 25.18. The velocity transducer is mounted on a small, solid cylinder, and the condenser microphone is mounted inside another, hollow cylinder. The geometry of this arrangement increases the sensitivity of the velocity transducer. Unlike Norwegian Electronics’ intensity probe the Microflown probe is very small – in fact much smaller than a standard p–p probe. Thus it is possible to measure very close to a vibrating surface with this device. At the time of writing there is still relatively little experimental evidence of the practical utility of the Microflown intensity probe, but it seems to be promising [25.17]. Figure 25.19 shows the results of sound power measurements with a Microflown intensity probe in comparison with similar results made with a Brüel & Kjær p–p sound intensity probe. A variant of the p–u method, the surface intensity method, combines a pressure microphone with a transducer that measures the vibrational displacement, velocity or acceleration of a solid surface, for example with an accelerometer or a laser vibrometer [25.53–55]; see Fig. 25.20. Obviously, this method can only give the normal component of the sound intensity near vibrating surfaces. A disadvantage of the surface intensity method is that sound fields near complex sources are often very
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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
Page 892 and 893:
a) b) c) Fig. 21.74a-c B-mode imagi
Page 894 and 895:
provided simple metrics for the lik
Page 896 and 897:
thickness of the carotid arteries,
Page 898 and 899:
Structural 22. Structural Acoustics
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Structural Acoustics and Vibrations
Page 902 and 903:
Magnitude (arb. units) 1.4 1.2 1.0
Page 904 and 905:
This does not include the case wher
Page 906 and 907:
the mass matrix is taken to be cons
Page 908 and 909:
Magnitude (dB) -10 -30 -50 0 1 2 3
Page 910 and 911:
where D(ω) = ω 4 − 2iω 3�
Page 912 and 913:
form y(x, t) = � Φn(x)qn(t) . (2
Page 914 and 915:
first to solve the wave equation (2
Page 916 and 917:
5 3 1 -1 -3 -5 0 1 2 3 4 5 6 7 8 9
Page 918 and 919:
conditions at each end) are necessa
Page 920 and 921:
from which we can derive through (2
Page 922 and 923:
In this case, the eigenfrequencies
Page 924 and 925:
of radiation modes and their link w
Page 926 and 927:
Finally, the displacement is ˜ξ(x
Page 928 and 929:
notes the value of this eigenmode a
Page 930 and 931:
Pm = ˙Q H [Rs + Ra] ˙Q , (22.262)
Page 932 and 933:
where and Ra = 2ζaω0 M Z(s) = zL
Page 934 and 935:
Radiated Power. The mean acoustic p
Page 936 and 937:
(22.318) can be written ξ(x, y, t)
Page 938 and 939:
Denoting the eigenfrequencies and e
Page 940 and 941:
Magnitude (arb. units) 3 2 1 0 -1 -
Page 942 and 943:
for any real symmetric tensor Xij.
Page 944 and 945:
F(N) 1 0.5 0 -0.5 -1 -1 -0.8 -0.6 -
Page 946 and 947:
whose solution is θ1 = A cos ωτ.
Page 948 and 949:
4.5 3.5 2.5 1.5 A 0.5 0 0.5 1.0 1.5
Page 950 and 951:
Equations (22.423) are usually writ
Page 952 and 953:
3. As the amplitude reaches the top
Page 954 and 955:
Shallow Spherical Shells and Plates
Page 956 and 957:
22.20 L. Cremer, M. Heckl: Structur
Page 958 and 959:
Noise Noise is discussed in terms o
Page 960 and 961:
where the overbars represent time a
Page 962 and 963:
Typical outdoor setting A-weighted
Page 964 and 965:
90 dB(A)” is widely used, and imp
Page 966 and 967:
Microphone, amplifier and A/D conve
Page 968 and 969:
When each segment of the measuremen
Page 970 and 971:
found from � LW = Lp + 10 log A +
Page 972 and 973:
surement method is the ultimate use
Page 974 and 975:
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
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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 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
Page 1092 and 1093: Optical 27. Optical Methods Metho f
Page 1094 and 1095: course also present in ordinary hol
Page 1096 and 1097: Optical Methods for Acoustics and V
Page 1102 and 1103: 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 1120 and 1121:
Page 1122 and 1123:
Page 1124 and 1125:
Page 1126 and 1127:
Page 1128 and 1129:
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 1158 and 1159:
British Medical Ultrasound Society
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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