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Jun 2011

Volume 129, Issue 6, pp. EL217-4101

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Rupture of anterior cruciate ligament monitored by acoustic emission

D. G. Aggelis, N. K. Paschos, N. M. Barkoula, A. S. Paipetis, T. E. Matikas, and A. D. Georgoulis

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL217-EL222 (2011); (6 pages) | Cited 2 times

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The scope of this study is to relate the acoustic emission (AE) during rupture of human soft tissue (anterior cruciate ligament, ACL) to the mechanisms leading to its failure. The cumulative AE activity highlights the onset of serious damage, while other parameters, show repeatable tendencies, being well correlated with the tissue’s mechanical behavior. The frequency content of AE signals increases throughout the experiment, while other indices characterize between different modes of failure. Results of this preliminary study show that AE can shed light into the failure process of this tissue, and provide useful data on the ACL reconstruction.
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43.40.Le Techniques for nondestructive evaluation and monitoring, acoustic emission
43.80.Qf Medical diagnosis with acoustics
43.80.Vj Acoustical medical instrumentation and measurement techniques
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Engaging concert hall acoustics is made up of temporal envelope preserving reflections

Tapio Lokki, Jukka Pätynen, Sakari Tervo, Samuel Siltanen, and Lauri Savioja

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL223-EL228 (2011); (6 pages) | Cited 6 times

Online Publication Date: 11 May 2011

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Strong, exciting, and engaging sound is perceived in the best concert halls. Here, it is shown that wideband early reflections that preserve the temporal envelope of sound contribute to the clear and open acoustics with strong bass. Such reflections are fused with the direct sound due to the precedence effect. In contrast, reflections that distort the temporal envelope render the sound weak and muddy because they partially break down the precedence. The presented findings are based on the earlier psychoacoustics research, and confirmed by a perceptual evaluation with six simulated concert halls that have same monaural room acoustical parameter values according to ISO3382-1.
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43.55.Hy Subjective effects in room acoustics, speech in rooms
43.55.Fw Auditorium and enclosure design
43.66.Jh Timbre, timbre in musical acoustics
43.66.Nm Phase effects
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A statistical model of horizontal auditory localization performance data

Garnett P. McMillan, Gabrielle Saunders, and Timothy E. Hanson

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL229-EL235 (2011); (7 pages)

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Horizontal localization experiments are used to evaluate the listener’s ability to locate the position of a sound source, and determine how signal characteristics affect this ability. These experiments generate circular, bimodal, and repeated data that are challenging to statistically analyze. A two-part mixture of wrapped Cauchys is proposed for these data, with the effects of signal type and position on localization bias, precision, and front-back confusion modeled using regression. The model is illustrated using mid- (1.0–2.0 kHz) and high- (3.0–6.0 kHz) frequency narrow band noises localization collected among ten normal hearing listeners.
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43.66.Qp Localization of sound sources
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A particle filtering approach for spatial arrival time tracking in ocean acoustics

Rashi Jain and Zoi-Heleni Michalopoulou

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL236-EL241 (2011); (6 pages) | Cited 3 times

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The focus of this work is on arrival time and amplitude estimation from acoustic signals recorded at spatially separated hydrophones in the ocean. A particle filtering approach is developed that treats arrival times as “targets” and tracks their “location” across receivers, also modeling arrival time gradient. The method is evaluated via Monte Carlo simulations and is compared to a maximum likelihood estimator, which does not relate arrivals at neighboring receivers. The comparison demonstrates a significant advantage in using the particle filter. It is also shown that posterior probability density functions of times and amplitudes become readily available with particle filtering.
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43.60.Hj Time-frequency signal processing, wavelets
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Effects of speaking style on speech intelligibility for Mandarin-speaking cochlear implant users

Yongxin Li, Guoping Zhang, Hou-yong Kang, Sha Liu, Deming Han, and Qian-Jie Fu

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL242-EL247 (2011); (6 pages)

Online Publication Date: 16 May 2011

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Cochlear implant (CI) users’ speech understanding may be influenced by different speaking styles. In this study, speech recognition was measured in Mandarin-speaking CI and normal-hearing (NH) subjects for sentences produced according to four styles: slow, normal, fast, and whispered. CI subjects were tested using their clinical processors; NH subjects were tested while listening to a four-channel CI simulation. Performance gradually worsened with increasing speaking rate and was much poorer with whispered speech. CI performance was generally similar to NH performance with the four-channel simulation. Results suggest that some speaking styles, especially whispering, may negatively affect Mandarin-speaking CI users’ speech understanding.
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43.71.Bp Perception of voice and talker characteristics
43.71.Es Vowel and consonant perception; perception of words, sentences, and fluent speech
43.71.Ky Speech perception by the hearing impaired
43.64.Me Effects of electrical stimulation, cochlear implant
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Limits of coherence-based aeroacoustic analysis in the presence of distributed sources

Chris Bahr and Louis N. Cattafesta

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL248-EL253 (2011); (6 pages) | Cited 1 time

Online Publication Date: 16 May 2011

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Coherence-based analysis techniques utilizing a small number of microphones are often applied in aeroacoustic measurements. These techniques can remove statistically incoherent noise, electronic or hydrodynamic, from acoustic signals measured by microphones, at significantly lower cost than array methods. However, the assumptions involved in the usage of the ordinary coherence function technically limit analysis to a single-source field. In the presence of multiple sources the coherence function breaks down and ordinary analysis techniques under-predict true acoustic levels. This phenomenon is demonstrated mathematically and illustrated using experimental trailing edge noise data.
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43.50.Cb Noise spectra, determination of sound power
43.60.Cg Statistical properties of signals and noise
43.28.Lv Statistical characteristics of sound fields and propagation parameters
43.60.Gk Space-time signal processing, other than matched field processing
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Eddy-current non-inertial displacement sensing for underwater infrasound measurements

Dimitri M. Donskoy and Benjamin A. Cray

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL254-EL259 (2011); (6 pages) | Cited 1 time

Online Publication Date: 16 May 2011

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A non-inertial sensing approach for an Acoustic Vector Sensor (AVS), which utilizes eddy-current displacement sensors and operates well at Ultra-Low Frequencies (ULF), is described here. In the past, most ULF measurements (from mHertz to approximately 10 Hertz) have been conducted using heavy geophones or seismometers that must be installed on the seafloor; these sensors are not suitable for water column measurements. Currently, there are no readily available compact and affordable underwater AVS that operate within this frequency region. Test results have confirmed the validity of the proposed eddy-current AVS design and have demonstrated high acoustic sensitivity.
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43.20.Ye Measurement methods and instrumentation
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Focused sound from three-dimensional sound propagation effects over a submarine canyon

Linus Y. S. Chiu, Ying-Tsong Lin, Chi-Fang Chen, Timothy F. Duda, and Brian Calder

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL260-EL266 (2011); (7 pages) | Cited 3 times

Online Publication Date: 16 May 2011

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Ship noise data reveal an intensification of the near-surface sound field over a submarine canyon. Numerical modeling of sound propagation is used to study the effect. The noise data were collected during an ocean acoustic and physical oceanography experiment northeast of Taiwan in 2009. In situ measurements of water sound–speed profiles and a database of high-resolution bathymetry are used in the modeling study. The model results suggest that the intensification is caused by three-dimensional sound focusing by the concave canyon seafloor. Uncertainties in the model results from unsampled aspects of the environment are discussed.
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43.30.Es Velocity, attenuation, refraction, and diffraction in water, Doppler effect
43.20.El Reflection, refraction, diffraction of acoustic waves
43.30.Nb Noise in water; generation mechanisms and characteristics of the field
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Development and validation of the Mandarin speech perception test

Qian-Jie Fu, Meimei Zhu, and Xiaosong Wang

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL267-EL273 (2011); (7 pages)

Online Publication Date: 23 May 2011

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Currently there are few standardized speech testing materials for Mandarin-speaking cochlear implant (CI) listeners. In this study, Mandarin speech perception (MSP) sentence test materials were developed and validated in normal-hearing subjects listening to acoustic simulations of CI processing. Percent distribution of vowels, consonants, and tones within each MSP sentence list was similar to that observed across commonly used Chinese characters. There was no significant difference in sentence recognition across sentence lists. Given the phonetic balancing within lists and the validation with spectrally degraded speech, the present MSP test materials may be useful for assessing speech performance of Mandarin-speaking CI listeners.
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43.64.Me Effects of electrical stimulation, cochlear implant
43.71.Es Vowel and consonant perception; perception of words, sentences, and fluent speech
43.71.Gv Measures of speech perception (intelligibility and quality)
43.71.Ky Speech perception by the hearing impaired
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Experimental validation of the sound transmission of rectangular baffled plates with general elastic boundary conditions

Dayi Ou and Cheuk Ming Mak

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL274-EL279 (2011); (6 pages) | Cited 1 time

Online Publication Date: 23 May 2011

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Several prediction methods have recently been developed for systematically studying the effects of general boundary conditions on the sound transmission loss (STL) of plate-like structures. But corresponding experimental validation studies remain scarce owing to the difficulty of obtaining accurate boundary conditions for practical structures. This paper presents a convincing experiment conducted on a baffled plate system to validate the STL prediction model in a previous paper by Yu et al. [Noise Control Eng. J. 58(2), 187–200, 2010]. A method is proposed to determine the boundary conditions of this system, and experimental STL compares well with the predictions based on the identified boundary condition.
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43.55.Ti Sound-isolating structures, values of transmission coefficients
43.20.Tb Interaction of vibrating structures with surrounding medium
43.55.Rg Sound transmission through walls and through ducts: theory and measurement
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Evaluation of similarity effects in informational masking

Thomas Y. Lee and Virginia M. Richards

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. EL280-EL285 (2011); (6 pages) | Cited 1 time

Online Publication Date: 23 May 2011

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The degree of similarity between signal and masker in informational masking paradigms has been hypothesized to contribute to informational masking. The present study attempted to quantify “similarity” using a discrimination task. Listeners discriminated various signal stimuli from a multitone complex and then detected the presence of those signals embedded in a multitone informational masker. Discriminability negatively correlated with detection threshold in an informational masking experiment, indicating that similarity between signal and the masker quality contributed to informational masking. These results suggest a method for specifying relevant signal attributes in informational masking paradigms involving similarity manipulations.
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43.66.Dc Masking
43.66.Ba Models and theories of auditory processes
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The design of a harmonic percussion ensemble (L)

Neil McLachlan

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3441-3444 (2011); (4 pages)

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The primary oscillators of tuned percussion instruments are rigid structures that exhibit bending waves. Bending waves do not naturally occur at harmonically related frequencies, which may lead to uncertainty associated with the intended pitch of the instrument. Despite millennia of development across many cultures, tuned percussion instruments rarely exhibit harmonic tuning of the first three or more partials. This letter presents three percussion instruments that have three or more harmonically tuned partials, and provides an overview of the methods used to tune the partials and manufacture the instruments at relatively low production costs. These instruments form the basis of new percussion instrument ensembles for educational, recreational, and professional use.
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43.40.Ey Vibrations of shells
43.75.Kk Bells, gongs, cymbals, mallet percussion, and similar instruments

Masked auditory thresholds in three species of birds, as measured by the auditory brainstem response (L)

Isabelle C. Noirot, Elizabeth F. Brittan-Powell, and Robert J. Dooling

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3445-3448 (2011); (4 pages) | Cited 3 times

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Auditory brainstem responses (ABRs) were recorded in adult budgerigars, canaries, and zebra finches in quiet and in three levels of white noise for tone stimuli between 1 and 4 kHz. Similar to behavioral results, masked ABR thresholds increased linearly with increasing noise levels. When the three species are considered together, ABR-derived CRs were higher than behavioral CRs by 18–23 dB between 2 and 4 kHz and by about 30 dB at 1 kHz. This study clarifies the utility of using ABRs for estimating masked auditory thresholds in natural environmental noises in species that cannot be tested behaviorally.
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43.64.Ri Evoked responses to sounds
43.64.Wn Effects of noise and trauma on the auditory system

On the acoustic-radiation-induced strain and stress in elastic solids with quadratic nonlinearity (L)

Jianmin Qu, Laurence J. Jacobs, and Peter B. Nagy

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3449-3452 (2011); (4 pages) | Cited 3 times

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This letter demonstrates that an eigenstrain is induced when a wave propagates through an elastic solid with quadratic nonlinearity. It is shown that this eigenstrain is intrinsic to the material, but the mean stress and the total mean strain are not. Instead, the mean stress and total means strain also depend on the boundary conditions, so care must be taken when using the static deformation to measure the acoustic nonlinearity parameter of a solid.
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43.25.Dc Nonlinear acoustics of solids
43.25.Qp Radiation pressure
43.25.Ba Parameters of nonlinearity of the medium
43.25.Zx Measurement methods and instrumentation for nonlinear acoustics

Forward scatter target strength extraction in a marine environment (L)

J. A. Bucaro, L. Kraus, B. H. Houston, H. Simpson, and A. Sarkissian

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3453-3456 (2011); (4 pages)

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A 48 m rail with a moving receiver was used to measure forward scattering from a spherical shell lying on the bottom in the Gulf of Mexico. The target was mid-way between the source and rail, on a line from the source bisecting the rail. The major obstacle to the measurement of forward scattering is the much stronger source signal which overlaps the scattered signal in space and time. Here, forward scattered target strength is obtained by processing the received signals using a wavenumber filter to remove the incident wave. The result compares favorably to that obtained from numerical predictions.
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43.20.Fn Scattering of acoustic waves
43.30.Vh Active sonar systems

Bimodal listeners are not sensitive to interaural time differences in unmodulated low-frequency stimuli (L)

Anneke Lenssen, Tom Francart, Jan Brokx, and Jan Wouters

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3457-3460 (2011); (4 pages)

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Sensitivity to interaural time differences (ITDs) with unmodulated low-frequency stimuli was assessed in bimodal listeners who had previously shown to be good performers in ITD experiments. Two types of stimuli were used: (1) an acoustic sinusoid combined with an electric transposed signal and (2) an acoustic sinusoid combined with an electric clicktrain. No or very low sensitivity to ITD was found for these stimuli, even though subjects were highly trained on the task and were intensively tested in multiple test sessions. In previous studies with users of a cochlear implant (CI) and a contralateral hearing aid (HA) (bimodal listeners), sensitivity was shown to ITD with modulated stimuli with frequency content between 600 and 3600 Hz. The outcomes of the current study imply that in speech processing design for users of a CI in combination with a HA on the contralateral side, the emphasis should be more on providing salient envelope ITD cues than on preserving fine-timing ITD cues present in acoustic signals.
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43.66.Qp Localization of sound sources
43.66.Ts Auditory prostheses, hearing aids
43.64.Me Effects of electrical stimulation, cochlear implant

Near field acoustic holography with microphones on a rigid sphere (L)

Finn Jacobsen, Guillermo Moreno-Pescador, Efren Fernandez-Grande, and Jørgen Hald

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3461-3464 (2011); (4 pages)

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Spherical near field acoustic holography (spherical NAH) is a technique that makes it possible to reconstruct the sound field inside and just outside a spherical surface on which the sound pressure is measured with an array of microphones. This is potentially very useful for source identification. The sphere can be acoustically transparent or it can be rigid. A rigid sphere is somewhat more practical than an open sphere. However, spherical NAH based on a rigid sphere is only valid if it can be assumed that the sphere has a negligible influence on the incident sound field, and this is not necessarily a good assumption when the sphere is very close to a radiating surface. This Letter examines the matter through simulations and experiments.
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43.60.Pt Signal processing techniques for acoustic inverse problems
43.60.Jn Source localization and parameter estimation
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Axisymmetric scattering of scalar waves by spheroids

John Lekner and Rufus Boyack

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3465-3469 (2011); (5 pages)

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A phase shift formulation of scattering by oblate and prolate spheroids is presented, in parallel with the partial-wave theory of scattering by spherical obstacles. The crucial step is application of a finite Legendre transform to the Helmholtz equation in spheroidal coordinates. In the long-wavelength limit the spheroidal analog of the spherical scattering length immediately gives the cross section. Analytical results are readily obtained for scattering of Schrödinger particle waves by impenetrable spheroids, and for scattering of sound waves by acoustically soft spheroidal objects. The method is restricted to scattering by spheroids whose symmetry axis is coincident with the direction of the incident plane wave.
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43.20.Fn Scattering of acoustic waves

An efficient method for computing backscattering from Born objects of arbitrary shape

Edward H. Pees

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3470-3474 (2011); (5 pages)

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A method is presented for efficiently computing the propagating pressure field backscattered by an arbitrarily shaped, weakly scattering, three-dimensional object. This is accomplished by drawing upon a previously reported relationship between the boundary condition on a two-dimensional radiating aperture and the pressure propagating along an axis normal to the aperture, and the fundamental theorem of diffraction tomography, which relates the Fourier transform of an object function to its scattered pressure field. Together, these two results are used to derive an integral formula that expresses the pressure field backscattered from an object as a one-dimensional Fourier transform of its scattering amplitude. This formula is then utilized to compute the backscattered pressure field from a uniform fluid sphere in the first Born approximation; the results of which are compared to the rigorous partial wave expansion.
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43.20.Fn Scattering of acoustic waves
43.60.Pt Signal processing techniques for acoustic inverse problems
43.20.El Reflection, refraction, diffraction of acoustic waves
43.30.Gv Backscattering, echoes, and reverberation in water due to combinations of boundaries

Point mobility of a cylindrical plate incorporating a tapered hole of power-law profile

Daniel J. O’Boy, Elizabeth P. Bowyer, and Victor V. Krylov

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3475-3482 (2011); (8 pages)

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The paper describes the results of experimental measurements of point mobility carried out on circular plates containing tapered holes of quadratic power-law profile with attached damping layers. The obtained results are compared to the developed numerical model, as a means of validation. The profiles of the tapered hole in the plates are designed to replicate near zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation, also known as acoustic black hole effect. The driving point mobility measurements are provided, showing a comparison of the results for a constant thickness circular plate, a constant thickness plate with a layer of damping film applied and a plate with a quadratic power-law profile machined into the center, which is tested with a thin layer of elastic damping material attached. The results indicate a substantial suppression of resonant peaks, agreeing with a numerical model, which is based on the analytical solution available for the vibration of a plate with a central quadratic power-law profile. The paper contains results for the case of free boundary conditions on all edges of the plates, with emphasis placed on the predictions of resonant frequencies and the amplitudes of vibration and loss factor.
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43.20.Jr Velocity and attenuation of elastic and poroelastic waves
43.40.At Experimental and theoretical studies of vibrating systems
43.40.Dx Vibrations of membranes and plates
43.40.Tm Vibration isolators, attenuators, and dampers
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Two regimes of the parametrically self-exciting ultrasonic standing waves

Zinoviy Goldberg, Iliya Goldberg, and Alexander Goldberg

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3483-3489 (2011); (7 pages)

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This paper discusses a nonlinear multi-wave mechanism for the parametrically self-exciting standing waves in a plane-parallel liquid layer driven at one end of the layer. The dependence of this process on the number of parametrically self-exciting waves and the frequency detuning between the frequency “f” of the pump wave and the nearest natural frequency are analyzed. It is found that two regimes with different thresholds are possible. One of them is characterized by self-exciting subharmonic frequencies close to f/2 and the second has a much lower threshold and the presence of a self-exciting subharmonic at a frequency near to the smallest natural frequency. Three dimensionless parameters determining each regime are introduced.
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43.25.Gf Standing waves; resonance

Theoretical and numerical calculations for the time-averaged acoustic force and torque acting on a rigid cylinder of arbitrary size in a low viscosity fluid

Jingtao Wang and Jurg Dual

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3490-3501 (2011); (12 pages) | Cited 5 times

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In this paper, theoretical calculations as well as numerical simulations are performed for the time-averaged acoustic force and torque on a rigid cylinder of arbitrary size in a fluid with low viscosity, i.e., the acoustic boundary layer is thin compared to the cylinder radius. An exact analytical solution and its approximation are proposed in the form of an infinite series including Bessel functions. These solutions can be evaluated easily by a mathematical software package such as mathematica and matlab. Three types of incident waves, plane traveling wave, plane standing wave, and dual orthogonal standing waves, are investigated in detail. It is found that for a small particle, the viscous effects for an incident standing wave may be neglected but those for an incident traveling wave are notable. A nonzero viscous torque is experienced by the rigid cylinder when subjected to dual orthogonal standing waves with a phase shift even when the cylinder is located at equilibrium positions without imposed acoustic forces. Furthermore, numerical simulations are carried out based on the FVM algorithm to verify the proposed theoretical formulas. The theoretical results and the numerical ones agree with each other very well in all the cases considered.
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43.25.Qp Radiation pressure
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Closed form solutions for the acoustical impulse response over a masslike or an absorbing plane

Martin Ochmann

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3502-3512 (2011); (11 pages) | Cited 1 time

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The transient sound field caused by a Dirac delta impulse function above an infinite locally reacting plane can be calculated by applying the inverse Fourier transform of the corresponding half-space Green’s function in frequency domain. As a starting point, the representation given by Ochmann [J. Acoust. Soc. Am. 116(6), 3304–3311 (2004)] is used, which consists of discrete and continuous superposition of point sources. For a locally reacting plane with masslike character and also with pure absorbing behavior, it is possible to express the resulting impulse response in closed form. Such a result is surprising, because corresponding formulations in the frequency domain are not available yet. Hence, the first main result is the closed form solution Eq. ( 22 ) for an impulse response over an infinite plane with a pure imaginary impedance. The second main result is the closed form solution Eq. ( 53 ) for an impulse response over an infinite plane with a pure real impedance. As a particular application of both main results, a convolution technique is used for deriving formulas for point sources with a general time dependency. For special signals like an exponentially decaying time signal or a triangular shaped impulse, the resulting sound field can be presented in terms of elementary functions.
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43.28.En Interaction of sound with ground surfaces, ground cover and topography, acoustic impedance of outdoor surfaces
43.20.Px Transient radiation and scattering
43.20.Bi Mathematical theory of wave propagation
43.20.El Reflection, refraction, diffraction of acoustic waves

Comparison of methods for calculating the sound field due to a rotating monopole

M. A. Poletti and P. D. Teal

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3513-3520 (2011); (8 pages) | Cited 1 time

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A spherical harmonic expansion for the sound field due to a rotating oscillating point source has recently been derived. This paper provides further confirmation of the expansion results by comparing it with two known numerical approaches to determining the sound field. In the advanced time approach—applicable for Mach numbers below 1—the sound at transmission time determines the field at an observation point from the distance from source to observation point at the transmission time. In the retarded time approach the field at the observation point at the observation time is determined by solving for the retarded transmission times. The results from all three approaches are shown to be in good agreement. Expressions for the far-field instantaneous frequency are also derived and shown to agree with previous work.
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43.28.Py Interaction of fluid motion and sound, Doppler effect, and sound in flow ducts
43.25.Cb Macrosonic propagation, finite amplitude sound; shock waves
43.28.Mw Shock and blast waves, sonic boom
43.20.Bi Mathematical theory of wave propagation

Comparison of sound power radiation from isolated airfoils and cascades in a turbulent flow

Vincent P. Blandeau, Phillip F. Joseph, Gareth Jenkins, and Christopher J. Powles

J. Acoust. Soc. Am. Volume 129, Issue 6, pp. 3521-3530 (2011); (10 pages)

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An analytical model of the sound power radiated from a flat plate airfoil of infinite span in a 2D turbulent flow is presented. The effects of stagger angle on the radiated sound power are included so that the sound power radiated upstream and downstream relative to the fan axis can be predicted. Closed-form asymptotic expressions, valid at low and high frequencies, are provided for the upstream, downstream, and total sound power. A study of the effects of chord length on the total sound power at all reduced frequencies is presented. Excellent agreement for frequencies above a critical frequency is shown between the fast analytical isolated airfoil model presented in this paper and an existing, computationally demanding, cascade model, in which the unsteady loading of the cascade is computed numerically. Reasonable agreement is also observed at low frequencies for low solidity cascade configurations.
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43.28.Ra Generation of sound by fluid flow, aerodynamic sound and turbulence
43.50.Cb Noise spectra, determination of sound power
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