Introduction to Acoustics

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Computer 17. Computer Mu Music This chapter covers algorithms, technologies, computer languages, and systems for computer music. Computer music involves the application of computers and other digital/electronic technologies to music composition, performance, theory, history, and perception. The field combines digital signal processing, computational algorithms, computer languages, hardware and software systems, acoustics, psychoacoustics (low-level perception of sounds from the raw acoustic signal), and music cognition (higher-level perception of musical style,form,emotion,etc.).Althoughmostpeople would think that analog synthesizers and electronic music substantially predate the use of computers in music, many experiments and complete computer music systems were being constructed and used as early as the 1950s. Because of this rich legacy, and the large number of researchers working on digital audio (primarily in speech research laboratories), there are a large number of algorithms for synthesizing sound using computers. Thus, a significant emphasis in this chapter will be placed on digital sound synthesis and processing, first providing Pulse code modulation (PCM) isthemeansforsampling and retrieval of audio in computers, and PCM synthesis uses combinations of prerecorded waveforms to reconstruct speech, sound effects, and music instrument sounds, based largely on the work of Joseph Fourier, who gave us a technique for formulating any waveform from sine waves. Additive synthesis uses fundamental waveforms (often sine waves), to construct more complicated waves. PCM and sinusoidal (Fourier) additive synthesis are often called nonparametric techniques. The word parametric in this context means that an algorithm with a few (but hopefully expressive) parameters can be used to generate a large variety of waveforms and spectral properties by varying the parameters. Since PCM involves recording and playing back waveforms, no actual expressive parameters are avail- 17.1 Computer Audio Basics ......................... 714 17.2 Pulse Code Modulation Synthesis .......... 717 17.3 Additive (Fourier, Sinusoidal) Synthesis . 719 17.4 Modal (Damped Sinusoidal) Synthesis .... 722 17.5 Subtractive (Source-Filter) Synthesis...... 724 17.6 Frequency Modulation (FM) Synthesis .... 727 17.7 FOFs, Wavelets, and Grains................... 728 17.8 Physical Modeling (The Wave Equation) . 730 17.9 Music Description and Control............... 735 17.10 Composition........................................ 737 17.11 Controllers and Performance Systems .... 737 17.12 Music Understanding and Modeling by Computer .................. 738 17.13 Conclusions, and the Future ................. 740 References .................................................. 740 an overview of the representation of audio in digital systems, then covering most of the popular algorithms for digital analysis and synthesis of sound. able in PCM systems. Similarly, Fourier’s theorem says that we can represent any waveform with a sum of sine waves, but in fact it might take a huge number of sine waves to represent a particular waveform accurately. So, without further work to parameterize PCM samples or large groups of additive sine waves, these techniques are nonparametric. Modal synthesis recognizes the fact that many vibrating systems exhibit a relatively few strong sinusoidal modes (natural frequencies) of vibration. Rigid bars and plates, plucked strings, and other structures are good candidates for modal synthesis, where after being excited (struck, plucked, etc.) the vibration/sound generation is restricted to a limited set of exponentially decaying sine waves. Modal synthesis is considered by some to be parametric, since the number of sine waves needed is often quite limited. Others claim that modal 713 Part E 17
714 Part E Music, Speech, Electroacoustics Part E 17.1 synthesis is nonparametric, since there is no small set of meaningful and expressive parameters that control variation in the sound. Subtractive synthesis begins with spectrally complex waveforms (such as pulses or noise), and uses filters to shape the spectrum and waveform to the desired result. Subtractive synthesis works particularly well for certain classes of sounds, such as human speech, where a spectrally rich source (pulses of the vocal folds) is filtered by a time-varying filter (the acoustic tube of the vocal tract). Subtractive synthesis is parametric, because only a few descriptive numbers control such a model. For example, a subtractive speech model might be controlled by numbers expressing how pitched versus noisy the voice is, the voice pitch, the loudness, and 8–10 locations of the resonances of the vocal tract. Using only a dozen or so variable numbers (parameters), a rich variety of vowel and consonant sounds can be synthesized. Frequency modulation (FM) synthesis exploits properties of nonlinearity to generate complex spectra and waveforms from much simpler ones. Modulating the frequency or phase of a sine wave (the carrier) by another sine wave (the modulator) causes multiple sideband sinusoids to appear at frequencies related to the ratio of the carrier and modulator frequencies. Thus an important parameter in FM is the carrier:modulator (C:M) ratio, and another is the amount (index) of modulation, which when increased causes the number of sidebands to increase. Wavelets are waveforms that are usually compact in time and frequency. They are viewed by some as related 17.1 Computer Audio Basics Typically, digital audio signals are formed by sampling analog (continuous in time and amplitude) signals at regular intervals in time, and then quantizing the amplitudes to discrete values. The process of sampling a waveform, holding the value, and quantizing the value to the nearest number that can be digitally represented (as a specific integer on a finite range of integers) is called analogto-digital (A to D, or A/D) conversion [17.1]. A device that does A/D conversion is called an analog-to-digital converter (ADC). Coding and representing waveforms in sampled digital form is called pulse code modulation (PCM), and digital audio signals are often called PCM audio. The process of converting a sampled signal back into an analog signal is called digital-to-analog conversion (D to A, or D/A), and the device is called to the fundamental unit of sound, by others as convenient building blocks for constructing sonic textures, and by others as related to important small events in nature and acoustics. Formes d’onde formantiques (FOFs, French for formant wave functions) are special wavelets that model the individual resonances of the vocal tract, and thus have been successfully used for modeling speech and singing. Physical models solve the wave equation in space and time to generate waveforms in the same ways that physical acoustics does. Efficient techniques combining discrete simulation of physics with modern digital filtering techniques allow models of plucked strings, wind instruments, percussion, the vocal tract, and many other musical systems to be solved efficiently by computers. After the presentation and examples of the main synthesis algorithms, some industry standards for representing and manipulating musical data in computerized systems will be discussed. The musical instrument digital interface (MIDI), downloadable sounds (DLS), open sound control (OSC), structured audio orchestra language (SAOL), and other score and control standards will be briefly covered. Some languages and systems for computer music composition are discussed, including the historical MusicX languages, and many modern languages such as Cmusic and MAX/MSP, followed by a few real-time performance and interaction systems. Finally, some aspects of computer modeling of human listening and systems for machine-assisted and automatic composition are covered. a digital-to-analog converter (DAC). Low-pass filtering (smoothing the samples to remove unwanted high frequencies) is necessary to reconstruct the sampled signal back into a smooth continuous-time analog signal. This filtering is usually contained in the DAC hardware. The time between successive samples is usually denoted by T. Sampling an analog signal first requires filtering it to remove unwanted high frequencies (more on this shortly), holding the value steady for a period while a stable measurement can be made, then associating the analog value with a digital number (coding). Analog signals can have any of the infinity of realnumbered amplitude values. Since computers work with fixed word sizes (8 bit bytes, 16 bit words, etc.), digital signals can only have a finite number of amplitude val-
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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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Page 666 and 667: 662 Part E Music, Speech, Electroac
Page 672 and 673: The 16. The Human Human Voice in Sp
Page 674 and 675: uation, the effect of gravity is in
Page 676 and 677: piratory muscles (the internal inte
Page 678 and 679: Mean Ps (cm H2O) 50 40 30 20 10 0 D
Page 680 and 681: Glottal flow Closed Opening Open Cl
Page 682 and 683: Transglottal airflow (l/s) 0.4 0.2
Page 684 and 685: Mean spectrum level (dB) -30 -40 -5
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Page 702 and 703: Utterance command T0 T3 Accent comm
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Page 712 and 713: esonance imaging: Vowels, J. Acoust
Page 714 and 715: 16.139 A. Eriksson: Aspects of Swed
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Page 720 and 721: Some might notice that linear inter
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Page 744 and 745: 17.20 J.L. Kelly Jr., C.C. Lochbaum
Page 746 and 747: Audio 18. Audio and Electroacoustic
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Page 754 and 755: Interaural intensity difference (dB
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Page 760 and 761: 18.3.8 Dynamic Range Dynamic range
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attempts to apply complementary com
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Most of the issues relating to spea
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nificant design considerations. At
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Some appreciation of the performanc
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pre-digital reverberators were elec
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and ‘s’ in English text - may b
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content of rest of the signal spect
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cross the head, in opposite directi
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18.2 J. Sterne: The Audible Past (D
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18.71 T. Sporer: Creating, assessin
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786 Part F Biological and Medical A
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Medical 21. Medical Acous Acoustics
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21.1 Introduction to Medical Acoust
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Auscultation location Right & left
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portance. The Strouhal number has b
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Fig. 21.3 Phono-cardiograph transdu
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Amplitude 8 6 4 2 0 -2 -4 -6 Displa
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λ1 = c1 / fus θ1 λ2 = c2 / fus
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lood flow can be resolved if the si
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vided in the image thickness direct
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not as predicted, because the wave
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Fig. 21.18a,b Quadrature Doppler de
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a) b) c) 100 0 V mV 10 0 a = 13 a =
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Ultrasound contact gel Position enc
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a) 10 cm b) c) 10 cm Fig. 21.32a-c
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a) Pin B Pin A Ultrasound line b) M
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Organ Patient Ultrasound transducer
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systems cannot tell the difference
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40 µm can be resolved. For a 10 kH
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a) b) c) d) Medical Acoustics 21.4
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Fig. 21.54 Doppler spectral wavefor
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10 20 30 10 20 30 Pre-exercise B-mo
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Vibrations in a punctured artery De
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the veins and diffuse into the inte
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21.5.3 Agitated Saline and Patent F
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transported by those cells and/or r
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1 0.8 0.6 0.4 0.2 0 Relative power
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High intensity focused ultrasound h
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a) b) c) Fig. 21.74a-c B-mode imagi
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provided simple metrics for the lik
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thickness of the carotid arteries,
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Structural 22. Structural Acoustics
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Structural Acoustics and Vibrations
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Magnitude (arb. units) 1.4 1.2 1.0
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This does not include the case wher
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the mass matrix is taken to be cons
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Magnitude (dB) -10 -30 -50 0 1 2 3
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where D(ω) = ω 4 − 2iω 3�
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form y(x, t) = � Φn(x)qn(t) . (2
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first to solve the wave equation (2
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5 3 1 -1 -3 -5 0 1 2 3 4 5 6 7 8 9
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conditions at each end) are necessa
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from which we can derive through (2
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In this case, the eigenfrequencies
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of radiation modes and their link w
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Finally, the displacement is ˜ξ(x
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notes the value of this eigenmode a
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Pm = ˙Q H [Rs + Ra] ˙Q , (22.262)
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where and Ra = 2ζaω0 M Z(s) = zL
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Radiated Power. The mean acoustic p
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(22.318) can be written ξ(x, y, t)
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Denoting the eigenfrequencies and e
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Magnitude (arb. units) 3 2 1 0 -1 -
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for any real symmetric tensor Xij.
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F(N) 1 0.5 0 -0.5 -1 -1 -0.8 -0.6 -
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whose solution is θ1 = A cos ωτ.
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4.5 3.5 2.5 1.5 A 0.5 0 0.5 1.0 1.5
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Equations (22.423) are usually writ
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3. As the amplitude reaches the top
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Shallow Spherical Shells and Plates
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22.20 L. Cremer, M. Heckl: Structur
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Noise Noise is discussed in terms o
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where the overbars represent time a
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Typical outdoor setting A-weighted
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90 dB(A)” is widely used, and imp
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Microphone, amplifier and A/D conve
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When each segment of the measuremen
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found from � LW = Lp + 10 log A +
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surement method is the ultimate use
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An intensity analyzer is more compl
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23.2.5 Criteria for Noise Emissions
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Table 23.5 Table of limit values fr
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a) Air flows freely to rotor Weak t
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Static efficiency normalized to its
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ful applications. Good results are
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Table 23.8 Crossover speeds for var
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Reduction of airplane engine noise
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A variety of materials are used to
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∆LF (dB) 0 -10 -20 α -30 0.05 0.
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Absorption coefficient 1.0 0.8 0.6
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high enough that there is little so
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23.4.4 Criteria for Noise Immission
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Table 23.10 (cont.) Some features o
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Noise 23.4 Noise and the Receiver 1
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view of administrative procedures r
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provides recommendations for a foll
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sound power levels of noise sources
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23.68 ISO: ISO 9296:1988 Acoustics
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in impedance tubes - Part 2: Transf
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23.194 Commission of the European C
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1022 Part H Engineering Acoustics P
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Sound 25. Intens Sound Intensity So
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Under such conditions the intensity
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a) Pressure and particle velocity 0
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τ is a dummy time variable. The ca
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Error in intensity (dB) 5 0 -5 -10
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8 7 6 5 4 3 2 1 0 -1 -2 -3 Error du
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crophones are calibrated with a pis
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Sound power level (dB re 1 pW) 72 7
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it is relatively straightforward si
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intensity normal to the source. Thi
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25.9 W. Maysenhölder: The reactive
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25.77 ISO: ISO 11205 Acoustics - No
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Optical 27. Optical Methods Metho f
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course also present in ordinary hol
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Optical Methods for Acoustics and V
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50 100 150 200 250 300 350 400 450
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a) b) Optical Methods for Acoustics
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nm 1000 0 -1000 150 y (mm) 100 50 O
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Laser Optical Methods for Acoustics
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References 27.1 E.F.F. Chladni: Die
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27.75 E.-L.Johansson, L. Benckert,
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About the Authors Iskander Akhatov
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Neville H. Fletcher Chapter F.19 Au
Page 1134 and 1135:
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
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electric circuit analogues - acoust
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hyperspeech 703 hypospeech 703 I IA
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- participation factors 909 - stiff
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- musical instruments 541 - musical
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- nonlinear vibrations 957 - plate
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subjective preference theory 353 su
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Introduction to Acoustics

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