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Vibration and sound
01 Jan 1948-
TL;DR: In this paper, the Simple Oscillator is described as a simple system with a simple unit function and a simple harmonic motion, and the case of small coupling is discussed, as well as normal modes of vibration.
Abstract: CHAPTER II THE SIMPLE OSCILLATOR 3. Free Oscillations The General Solution. Initial Conditions. Energy of Vibration 4. Damped Oscillations The General Solution. Energy Relations 5. Forced Oscillations The General Solution. Transient and Steady State. Impedance and Phase Angle. Energy Relations. Electromechanical Driving Force. Motional Impedance. Piezoelectric Crystals. 6. Response to Transient Forces Representation by Contour Integrals. Transients in a Simple System. Complex Frequencies. Calculating the Transients. Examples of the Method. The Unit Function. General Transient. Some Generalizations. Laplace Transfoms. 7. Coupled Oscillations The General Equation. Simple Harmonic Motion. Normal Modes of Vibration. Energy Relations. The Case of Small Coupling. The Case of Resonance. Transfer of Energy. Forced Vibrations. Resonance and Normal Modes. Transient Response. Problems
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TL;DR: Historically, physical models have led to prohibitively expensive synthesis algorithms, and commercially available synthesizers do not yet appear to make use of them, but as computers become faster and cheaper, and as algorithms based on physical models become more e cient, the authors may expect to hear more from them.
Abstract: Historically, physical models have led to prohibitively expensive synthesis algorithms, and commercially available synthesizers do not yet appear to make use of them. These days, most synthesizers use either processed digital recordings (\sampling synthesis") or an abstract algorithm such as Frequency Modulation (FM). However, as computers become faster and cheaper, and as algorithms based on physical models become more e cient, we may expect to hear more from them.
533 citations
Cites background from "Vibration and sound"
...In the case of the acoustic tube (Morse 1936; Markle and Gray 1976), we have the analogous relations p+(n) = Ru+(n) p (n) = Ru (n) where p+(n) is the right-going traveling longitudinal pressure wave, p (n) is the left-going pressure wave, and u (n) are the left and right-going volume velocity waves....
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...The vibrational energy per unit length along the string, or wave energy density (Morse 1936) is given by the sum of potential and kinetic energy densities: W (t; x) = 1 2 Ky02(t; x) + 1 2 _y2(t; x) Sampling across time and space, and substituting traveling wave components, one can show in a few…...
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...Sti ness in a vibrating string introduces a restoring force proportional to the fourth derivative of the string displacement (Morse 1936; Cremer 1984): y = Ky00 y0000 where, for a cylindrical string of radius a and Young's modulus Q, the moment constant is equal to = Q a4=4....
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...The Ideal Struck String The ideal struck string (Morse 1936) involves a zero initial string displacement but a nonzero initial velocity distribution....
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...The Ideal Plucked String The ideal plucked string (Morse 1936) is de ned as an initial string displacement and a zero initial velocity distribution....
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TL;DR: The theoretical principles of an imaging modality that uses the acoustic response of an object to a highly localized dynamic radiation force of an ultrasound field, named ultrasound-stimulated vibro-acoustography (USVA), are described and the point-spread function of the imaging system is presented.
Abstract: We describe theoretical principles of an imaging modality that uses the acoustic response of an object to a highly localized dynamic radiation force of an ultrasound field. In this method, named ultrasound-stimulated vibro-acoustography (USVA), ultrasound is used to exert a low-frequency (in kHz range) force on the object. In response, a portion of the object vibrates sinusoidally in a pattern determined by its viscoelastic properties. The acoustic emission field resulting from object vibration is detected and used to form an image that represents both the ultrasonic and low-frequency (kHz range) mechanical characteristics of the object. We report the relation between the emitted acoustic field and the incident ultrasonic pressure field in terms of object parameters. Also, we present the point-spread function of the imaging system. The experimental images in this report have a resolution of about 700 μm, high contrast, and high signal-to-noise ratio. USVA is sensitive enough to detect object motions on the order of nanometers. Possible applications include medical imaging and material evaluation.
455 citations
TL;DR: In this article, the effects of confining pressure, pore pressure, degree of saturation, strain amplitude, and frequency on seismic attenuation in sandstone bars were studied experimentally.
Abstract: Seismic wave attenuation in rocks was studied experimentally, with particular attention focused on frictional sliding and fluid flow mechanisms. Sandstone bars were resonated at frequencies from 500 to 9000 Hz, and the effects of confining pressure, pore pressure, degree of saturation, strain amplitude, and frequency were studied. Observed changes in attenuation and velocity with strain amplitude are interpreted as evidence for frictional sliding at grain contacts. Since this amplitude dependence disappears at strains and confining pressures typical of seismic wave propagation in the earth, we infer that frictional sliding is not a significant source of seismic attenuation in situ. Partial water saturation significantly increases the attenuation of both compressional (P) and shear (S) waves relative to that in dry rock, resulting in greater P‐wave than S‐wave attenuation. Complete saturation maximizes S‐wave attenuation but causes a reduction in P‐wave attenuation. These effects can be interpreted in term...
439 citations
01 Jan 1990
TL;DR: In this paper, it was shown that the dynamics of the inertia-laden flows leading to various modes of oscillation within the vocal tract are neither passive nor acoustic, and that the pressure across any cross section of the tract is constant and does not exhibit the differentials expected from the markedly different separated flows across that same cross section.
Abstract: Much of what speech scientists believe about the mechanisms of speech production and hearing rests less on an experimental base than on a centuries-old faith in linear mathematics. Based on experimental evidence we believe that the momentum waves, or the interactions of the inertia-laden flows leading to various modes of oscillation, within the vocal tract are neither passive nor acoustic. Measurements of flow within the vocal tract indicate that acoustic impedance, or the pressure-flow ratio, is violated. The pressure across any cross section of the tract is constant and does not exhibit the differentials expected from the markedly different separated flows across that same cross section. There has been little proof that the ear is primarily a frequency analyzer, or any solid explanation given for its extraordinary sensitivity. Finally, nonlinear processing techniques, that are less prey to Fourier artifacts, are described.
376 citations
TL;DR: In this article, the authors presented an analytical model for support loss in clamped-free (C-F) and clampedclamped (C -C) micromachined beam resonators with in-plane flexural vibrations.
Abstract: This paper presents an analytical model for support loss in clamped–free (C–F) and clamped–clamped (C–C) micromachined beam resonators with in-plane flexural vibrations. In this model, the flexural vibration of a beam resonator is described using the beam theory. An elastic wave excited by the shear stress of the beam resonator and propagating in the support structure is described through the 2D elastic wave theory, with the assumption that the beam thickness (h) is much smaller than the transverse elastic wavelength (λT). Through the combination of these two theories and the Fourier transform, closed-form expressions for support loss in C–F and C–C beam resonators are obtained. Specifically, closed-form expression for the support loss in a C–C beam resonator is derived for the first time. The model suggests lower support quality factor (Qsupport) for higher order resonant modes compared to the fundamental mode of a beam resonator. Through comparison with experimental data, the validity of the presented analytical model is demonstrated. © 2003 Elsevier B.V. All rights reserved.
374 citations