Introduction to Acoustics

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a) b) Optical Methods for Acoustics and Vibration Measurements 27.2 Measurement Principles and Some Applications 1113 y c) y π/2 0 –π/2 Phase Fig. 27.10a–c Air mode (0, 4, 0) in the rectangular transparent box in Fig. 27.8 [27.60]. (a) View along the shortest side; (b) view along the next shortest side; (c) phase along the x−axis in (a) measured by phase-modulated TV holography. (Reprint by S. Hirzel Verlag, Stuttgart) ple product 2k(n − n0)L. If not, the integral equation in (27.7) remains and tomography has to be used to reveal the distribution, see for instance Appendix B in [27.23]. Figs. 27.9 and 27.10 show measured standing waves inside the transparent box in Fig. 27.8 for two different air modes [27.60]. Fig. 27.11 shows standing waves inside a guitar body with a transparent top and back plate measured by phase-modulated TV holography [27.61]. a) b) c) y If instead a probing laser ray is passing through the box in Fig. 27.8 in the x-direction, it will experience a time-varying phase change. A small frequency shift is thus generated by the standing aerial waves inside the box. This shift can be detected by a laser vibrometer; compare Sect. 27.2.5. 27.2.3 Reciprocity and TV Holography An indirect pointwise method to measure the sound distribution from an instrument is to use reciprocity [27.62] combined with, for instance, TV holography [27.63]. An advantage of this method is that, even in a quite large spatial volume, radiativity [27.64] can be recorded. This is valuable since audible acoustical waves at low frequencies can have very long wavelengths. An experiment using reciprocity and TV holography can be performed as follows. A movable loudspeaker at constant (unit) driving conditions excites, say a stringed instrument, from different positions outside it. The corresponding out-of-plane velocity component at the bridge foot is measured by TV holography for the specific excited vibration pattern. Then, it can be argued using reciprocity that, if a constant (unit) driving force now instead is acting at the bridge foot, it will create a sound pressure of the same magnitude as the measured velocity component at the same place as the loudspeaker was placed. By moving the loudspeaker around when Fig. 27.11a–c Standing aerial waves inside a transparent guitar cavity measured by phase-modulated TV holography [27.61]; (a) covered sound hole (1195 Hz); (b) open sound hole (1182 Hz); (c) phase distribution along the y-axis in (b) . (Reprint from S Hirzel Verlag, Stuttgart). –π/2 y 0 π/2 Phase Part H 27.2
1114 Part H Engineering Acoustics Part H 27.2 measuring the vibration amplitude at the bridge foot, the radiativity is estimated. Experiences from the violin experiments in [27.63] were: • Radiativity is measured in an ordinary laboratory both close to and at quite large distances from the instrument; • the mode shape is simultaneously recorded, • the violin radiativity is measured as being almost spherical up to the 500 Hz, • complicated radiativity patterns result at higher modes. Important conditions for dynamic reciprocity measurements are that the system is linear, passive and that the vibration system has stable equilibrium positions. 27.2.4 Pulsed TV Holography – Pulsed Lasers Freeze Propagating Bending Waves, Sound Fields and Other Transient Events Pulsed lasers, like the traditional Q-switched ruby laser, emit one, two or more very short pulses (each pulse only some tenths of a ns long) of coherent laser light with a very high intensity. Most mechanical or acoustical events are frozen at such short exposure times. The time between the pulses can be set from about 10 µs to 800 µs with a ruby laser (during the burning time of the laser exciting flash lamps) and over a much broader range with a twin-cavity Nd:YAG laser. By double exposing a photographic plate of a transient event with two such pulses, one pulse of the object in the start position and another some time after the start, a double-exposed hologram is obtained. Both fields are reconstructed simultaneously with a continuous He–Ne laser. The technique is called pulsed holographic interferometry [27.12] and compares two states of an object. The optical setups used with pulsed lasers are in principle the same as with continuous ones with an object and a reference beam, compare Figs. 27.1 and 27.4. Both traditional recording on photographic plates (double-exposed hologram interferometry) and all-electronic methods (pulsed TV holography using a CCD chip for the recording as in TV holography) are available, although there are some differences. First, positive lenses are avoided and usually replaced by negative ones, since gas ions may otherwise occur at the focal points of positive lenses with the very strong light irradiances. With negative lenses light rays can be arranged so they seem to emanate from 125 µs Fig. 27.12 Transient bending wave propagation in a violin body, 125 µs after impact start. The top of the bridge is impacted horizontally by a 5 mm steel ball at the end of a 30 cm-long pendulum (seen in the figure as a thin line). In the top plate a hill and a valley centered on the two bridge feet can be seen. In the back plate the fringes are centered at the soundpost, which rapidly transfers the impact from the bridge to the back of the violin [27.65]. (Reprint American Institute of Physics, 10/22/04) a virtual focal point. Secondly, to use the temporal phasestepping technique with a moving mirror, such as PM in Fig. 27.4 is not applicable; there is simply not enough time to move them to record a sequence. Instead quantitative measuring data are obtained with a Fourier method where a small angle between the reference light and the object light is introduced to produce a modulated carrier wave at the CCD detector [27.66]. By Fourier filtering it is then possible to extract quantitative data. In Fig. 27.12 [27.65], the transient bending wave response of a violin body to an impact is visualized with pulsed hologram interferometry. The instrument is impacted at the top of the bridge with a small pendulum. This is a crude and simple model of one of the pulses from the pulse train that is produced by the stick–slip bow–string interaction when the instrument is played. It is obvious that energy is effectively transferred to the back plate by the soundpost of the instrument and that the back is acting more like a monopole source. The top plate, on the other hand, is excited by the rocking motion of the bridge with a hill at one foot and a valley at the other, more like a dipole source. Interesting information about the violin is pictured in this way. The pulsed TV holography setup is quite similar to ordinary TV holography (Fig. 27.4) inthatitisall electronic, it uses fast CCD cameras and is computer op-
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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
Page 906 and 907:
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
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
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(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.
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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
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Page 1020 and 1021:
Page 1022 and 1023:
Page 1024 and 1025:
Page 1026 and 1027:
Page 1028 and 1029:
Page 1030 and 1031:
Page 1032 and 1033:
Page 1034 and 1035:
Page 1036 and 1037:
Page 1038 and 1039:
Page 1040 and 1041:
Page 1042 and 1043:
Page 1044 and 1045:
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
Page 1070 and 1071: 1078 Part H Engineering Acoustics P
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 1106 and 1107: nm 1000 0 -1000 150 y (mm) 100 50 O
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 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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