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Feb 2012

Volume 131, Issue 2, pp. EL87-1825

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Effects of low-pass filtering on intelligibility of periodically interrupted speech

Pranesh Bhargava and Deniz Başkent

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL87-EL92 (2012); (6 pages)

Online Publication Date: 13 Jan 2012

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The combined effect of low-pass filtering (cut-off frequencies between 500 and 3000 Hz) and periodic interruptions (1.5 and 10 Hz) on speech intelligibility was investigated. When combined, intelligibility was lower than each manipulation alone, even in some conditions where there was no effect from a single manipulation (such as the fast interruption rate of 10 Hz). By using young normal-hearing listeners, potential suprathreshold deficits and aging effects that may occur due to hearing impairment were eliminated. Thus, the results imply that reduced audibility of high-frequency speech components may partially explain the reduced intelligibility of interrupted speech in hearing impaired persons.
Show PACS
43.66.Mk Temporal and sequential aspects of hearing; auditory grouping in relation to music
43.71.Es Vowel and consonant perception; perception of words, sentences, and fluent speech
43.71.Rt Sensory mechanisms in speech perception
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Optimization of orthotropic distributed-mode loudspeaker using attached masses and multi-exciters

Guochao Lu, Yong Shen, and Ziyun Liu

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL93-EL98 (2012); (6 pages)

Online Publication Date: 13 Jan 2012

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Based on the orthotropic model of the plate, the method to optimize the sound response of the distributed-mode loudspeaker (DML) using the attached masses and the multi-exciters has been investigated. The attached masses method will rebuild the modes distribution of the plate, based on which multi-exciter method will smooth the sound response. The results indicate that the method can be used to optimize the sound response of the DML.
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43.38.Ja Loudspeakers and horns, practical sound sources
43.38.Ar Transducing principles, materials, and structures: general
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Perceptually based head-related transfer function database optimization

Brian F. G. Katz and Gaëtan Parseihian

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL99-EL105 (2012); (7 pages) | Cited 1 time

Online Publication Date: 13 Jan 2012

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In the context of binaural audio rendering, choosing the best head-related transfer function (HRTF) for an individual from large databases poses several problems. This study proposes a method to reduce the size of a given HRTF database. Participants, 45 in total, were asked to rate the quality of binaural synthesis for 46 HRTFs. The lack of reciprocity in the ratings was noted. Results were used to create a perceptually optimized HRTF subset which satisfied all participants’ judgments. The subset was validated using localization tests on a separate group of subjects with results showing reduced errors when subjects were given their best choice, rather than their worst choice HRTF.
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43.66.Pn Binaural hearing
43.66.Qp Localization of sound sources
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The magnetic resonance imaging subset of the mngu0 articulatory corpus

Ingmar Steiner, Korin Richmond, Ian Marshall, and Calum D. Gray

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL106-EL111 (2012); (6 pages)

Online Publication Date: 13 Jan 2012

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This paper announces the availability of the magnetic resonance imaging (MRI) subset of the mngu0 corpus, a collection of articulatory speech data from one speaker containing different modalities. This subset comprises volumetric MRI scans of the speaker’s vocal tract during sustained production of vowels and consonants, as well as dynamic mid-sagittal scans of repetitive consonant–vowel (CV) syllable production. For reference, high-quality acoustic recordings of the speech material are also available. The raw data are made freely available for research purposes.
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43.70.Aj Anatomy and physiology of the vocal tract, speech aerodynamics, auditory kinetics
43.70.Jt Instrumentation and methodology for speech production research
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Evidence of cue use and performance differences in deciphering dysarthric speech

Yu-kyong Choe, Julie M. Liss, Tamiko Azuma, and Pamela Mathy

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL112-EL118 (2012); (7 pages)

Online Publication Date: 13 Jan 2012

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There is substantial performance variability among listeners who transcribe degraded speech. Error patterns from 88 listeners who transcribed dysarthric speech were examined to identify differential use of syllabic strength cues for lexical segmentation. Transcripts from listeners were divided into four groups (ranging from Better- to Poorer- performing). Phrases classified as Higher- and Lower-intelligibility were analyzed separately for each performance group to assess the independent variable of severity. Results revealed that all four listener groups used syllabic strength cues for lexical segmentation of Higher-intelligibility speech, but only the Poorer listeners persisted with this strategy for the Lower-intelligibility phrases. This finding and additional analyses suggest testable hypotheses to address the role of cue-use and performance patterns.
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43.71.Gv Measures of speech perception (intelligibility and quality)
43.71.Bp Perception of voice and talker characteristics
43.71.Sy Spoken language processing by humans
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Comparing vowel perception and production in Spanish and Portuguese: European versus Latin American dialects

Kateřina Chládková and Paola Escudero

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL119-EL125 (2012); (7 pages)

Online Publication Date: 17 Jan 2012

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Recent acoustic descriptions have shown that Spanish and Portuguese vowels are produced differently in Europe and Latin America. The present study investigates whether comparable between-variety differences exist in vowel perception. Spanish, Peruvian, Portuguese, and Brazilian listeners were tested in a vowel identification task with stimuli sampled from the whole vowel space. The mean perceived first (F1) and second formant (F2) of every vowel category were compared across varieties. For both languages, perception exhibited the same between-variety differences as production for F1 but not F2, which suggests correspondence between produced F1 and perceived vowel height but not between F2 and frontness.
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43.71.Es Vowel and consonant perception; perception of words, sentences, and fluent speech
43.70.Mn Relations between speech production and perception
43.71.An Models and theories of speech perception
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Modification of the loop filter design for a plucked string instrument

Sangjin Cho, Hyungseob Han, Jongmyon Kim, Uipil Chong, and Sangbock Cho

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL126-EL132 (2012); (7 pages)

Online Publication Date: 17 Jan 2012

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A modified loop filter design method for plucked string instruments is introduced. Previous loop filter designs do not properly represent the frequency-dependent damping of a silk stringed instrument. To solve this problem, the modified method evaluates how many harmonics are required and which portion of the sound should be chosen to effectively replicate the instrument. Then, the most reasonable filter parameters are determined based on the frequency signal-to-noise ratio of the synthesized sound.
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43.75.Gh Plucked string instruments
43.75.Zz Analysis, synthesis, and processing of musical sounds
43.75.Yy Instrumentation and measurement methods for musical acoustics
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Sine-wave speech recognition in a tonal language

Yan-Mei Feng, Li Xu, Ning Zhou, Guang Yang, and Shan-Kai Yin

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL133-EL138 (2012); (6 pages)

Online Publication Date: 18 Jan 2012

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It is hypothesized that in sine-wave replicas of natural speech, lexical tone recognition would be severely impaired due to the loss of F0 information, but the linguistic information at the sentence level could be retrieved even with limited tone information. Forty-one native Mandarin-Chinese-speaking listeners participated in the experiments. Results showed that sine-wave tone-recognition performance was on average only 32.7% correct. However, sine-wave sentence-recognition performance was very accurate, approximately 92% correct on average. Therefore the functional load of lexical tones on sentence recognition is limited, and the high-level recognition of sine-wave sentences is likely attributed to the perceptual organization that is influenced by top-down processes.
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43.71.Gv Measures of speech perception (intelligibility and quality)
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Solving permutations in frequency-domain for blind separation of an arbitrary number of speech sources

Iván Durán-Díaz, Auxiliadora Sarmiento, Sergio Cruces, and Pablo Aguilera

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL139-EL144 (2012); (6 pages)

Online Publication Date: 23 Jan 2012

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Blind separation of speech sources in reverberant environments is usually performed in the time-frequency domain, which gives rise to the permutation problem: the different ordering of estimated sources for different frequency components. A two-stage method to solve permutations with an arbitrary number of sources is proposed. The suggested procedure is based on the spectral consistency of the sources. At the first stage frequency bins are compared with each other, while at the second stage the neighboring frequencies are emphasized. Experiments for perfect separation situations and for live recordings show that the proposed method improves the results of existing approaches.
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43.60.Pt Signal processing techniques for acoustic inverse problems
43.60.Gk Space-time signal processing, other than matched field processing
43.60.Np Acoustic signal processing techniques for neural nets and learning systems
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Frequency dependent beating patterns and amplitude increase during the approach of an internal wave packet

Jing Luo and Mohsen Badiey

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL145-EL149 (2012); (5 pages)

Online Publication Date: 23 Jan 2012

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A frequency-dependent beating pattern in the spectrogram of broadband signals transmitted during the approach of an internal wave packet to an acoustic propagating path is reported. An analytical expression relating the acoustic signal measurements and environmental parameters under certain conditions is obtained. Three-dimensional parabolic equation modeling results compare well with Shallow Water 2006 experiment data.
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43.30.Es Velocity, attenuation, refraction, and diffraction in water, Doppler effect
43.30.Dr Hybrid and asymptotic propagation theories, related experiments
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Broadband acoustic concentrator with multilayered alternative homogeneous materials

Yu-ran Wang, Hui Zhang, Shu-yi Zhang, Li Fan, and Hong-xiang Sun

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL150-EL155 (2012); (6 pages)

Online Publication Date: 26 Jan 2012

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A two-dimensional cylindrical acoustic concentrator is designed with multilayered alternative homogeneous materials, which can focus acoustic field and enhance acoustic energy in a given area. The frequency response analysis of the acoustic concentrator demonstrates that the acoustic energy can be concentrated within the device over a wide frequency band. Meanwhile, there are contradictory relations between the acoustic concentrating performances in the inner region and the scattering properties in the outer region of these concentrators. When the contradictory relations satisfy compromise balance, the concentration ratio can reach at least 70%.
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43.20.Fn Scattering of acoustic waves
43.40.Ey Vibrations of shells
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A selective array activation method for the generation of a focused source considering listening position

Min-Ho Song, Jung-Woo Choi, and Yang-Hann Kim

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL156-EL162 (2012); (7 pages)

Online Publication Date: 26 Jan 2012

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A focused source can provide an auditory illusion of a virtual source placed between the loudspeaker array and the listener. When a focused source is generated by time-reversed acoustic focusing solution, its use as a virtual source is limited due to artifacts caused by convergent waves traveling towards the focusing point. This paper proposes an array activation method to reduce the artifacts for a selected listening point inside an array of arbitrary shape. Results show that energy of convergent waves can be reduced up to 60 dB for a large region including the selected listening point.
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43.60.Tj Wave front reconstruction, acoustic time-reversal, and phase conjugation
43.66.Qp Localization of sound sources
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Multiuser interference cancellation in time-varying channels

S. E. Cho, H. C. Song, and W. S. Hodgkiss

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL163-EL169 (2012); (7 pages)

Online Publication Date: 26 Jan 2012

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In this letter, an adaptive time-reversal multichannel combiner is embedded within an iterative successive interference cancellation receiver. With the addition of matching pursuit, a sparse channel estimation technique, the combined receiver is shown to provide both temporal interference cancellation as well as spatial interference suppression in decoding simultaneous transmissions from separate users in a time-varying underwater acoustic environment. Experimental data collected during the KAM11 experiment illustrates that for a two-user multiple-access system, multiuser separation can be achieved.
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43.60.Dh Signal processing for communications: telephony and telemetry, sound pickup and reproduction, multimedia
43.60.Gk Space-time signal processing, other than matched field processing
43.60.Fg Acoustic array systems and processing, beam-forming
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Contrasting behavior between dispersive seismic velocity and attenuation: Advantages in subsoil characterization

Alimzhan Zhubayev and Ranajit Ghose

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL170-EL176 (2012); (7 pages) | Cited 1 time

Online Publication Date: 26 Jan 2012

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A careful look into the pertinent models of poroelasticity reveals that in water-saturated sediments or soils, the seismic (P and S wave) velocity dispersion and attenuation in the low field-seismic frequency band (20–200 Hz) have a contrasting behavior in the porosity-permeability domain. Taking advantage of this nearly orthogonal behavior, a new approach has been proposed, which leads to unique estimates of both porosity and permeability simultaneously. Through realistic numerical tests, the effect of maximum frequency content in data and the integration of P and S waves on the accuracy and robustness of the estimates are demonstrated.
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43.20.Jr Velocity and attenuation of elastic and poroelastic waves
43.30.Ky Structures and materials for absorbing sound in water; propagation in fluid-filled permeable material
43.40.Ph Seismology and geophysical prospecting; seismographs
43.28.We Measurement methods and instrumentation for remote sensing and for inverse problems
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Psychometric properties of the coordinate response measure corpus with various types of background interference

David A. Eddins and Chang Liu

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL177-EL183 (2012); (7 pages)

Online Publication Date: 26 Jan 2012

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The coordinate response measure (CRM) corpus has gained broad acceptance as a research tool for investigating speech intelligibility in background competition and has been widely used in studies of informational masking. The purpose of this study is to establish the psychometric characteristics of CRM target-word identification in various backgrounds with the goal of being able to determine when it is appropriate or not to use adaptive threshold procedures with the CRM corpus. Target-word identification performance based on adaptive tracking mapped directly onto the monotonic psychometric functions obtained for two-talker, four-talker, and cafeteria noise interferers.
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43.71.Gv Measures of speech perception (intelligibility and quality)
43.71.An Models and theories of speech perception
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Multifrequency species classification of acoustic-trawl survey data using semi-supervised learning with class discovery

M. Woillez, P. H. Ressler, C. D. Wilson, and J. K. Horne

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL184-EL190 (2012); (7 pages)

Online Publication Date: 26 Jan 2012

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Acoustic surveys often use multifrequency backscatter to estimate fish and plankton abundance. Direct samples are used to validate species classification of acoustic backscatter, but samples may be sparse or unavailable. A generalized Gaussian mixture model was developed to classify multifrequency acoustic backscatter when not all species classes are known. The classification, based on semi-supervised learning with class discovery, was applied to data collected in the eastern Bering Sea during summers 2004, 2007, and 2008. Walleye pollock, euphausiids, and two other major classes occurring in the upper water column were identified.
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43.30.Sf Acoustical detection of marine life; passive and active
43.60.Bf Acoustic signal detection and classification, applications to control systems
43.60.Lq Acoustic imaging, displays, pattern recognition, feature extraction
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Annoyance due to railway vibration at different times of the day

Eulalia Peris, James Woodcock, Gennaro Sica, Andrew T. Moorhouse, and David C. Waddington

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. EL191-EL196 (2012); (6 pages)

Online Publication Date: 26 Jan 2012

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The time of day when vibration occurs is considered as a factor influencing the human response to vibration. The aim of the present paper is to identify the times of day during which railway vibration causes the greatest annoyance, to measure the differences between annoyance responses for different time periods and to obtain estimates of the time of day penalties. This was achieved using data from case studies comprised of face-to-face interviews and internal vibration measurements (N = 755). Results indicate that vibration annoyance differs with time of day and that separate time of day weights can be applied when considering exposure–response relationships from railway vibration in residential environments.
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43.40.Ng Effects of vibration and shock on biological systems, including man
43.50.Qp Effects of noise on man and society
43.50.Sr Community noise, noise zoning, by-laws, and legislation
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On the use of an absorption layer for the angular spectrum approach (L)

Yun Jing

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 999-1002 (2012); (4 pages)

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Reducing the spatial aliasing error of the angular spectrum method by using an absorption layer is investigated in this paper. The acoustic equation including the absorption layer is presented and is transformed in the spatial frequency domain, where an implicit analytic solution is readily available. Its approximation, which is more suitable for numerical simulation, is derived and is numerically implemented. The comparisons between the present method and available methods demonstrate its validity and advantages.
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43.35.Bf Ultrasonic velocity, dispersion, scattering, diffraction, and attenuation in liquids, liquid crystals, suspensions, and emulsions
43.20.Bi Mathematical theory of wave propagation

The influence of age and high-frequency hearing loss on sensitivity to temporal fine structure at low frequencies (L)

Brian C. J. Moore, Brian R. Glasberg, Martin Stoev, Christian Füllgrabe, and Kathryn Hopkins

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1003-1006 (2012); (4 pages) | Cited 1 time

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Sensitivity to temporal fine structure (TFS) at low frequencies may be adversely affected by hearing loss at high frequencies even when absolute thresholds at low frequencies are within the normal range. However, in several studies suggesting this, the effects of hearing loss and age were confounded. Here, interaural phase discrimination (IPD) thresholds for pure tones at 500 and 750 Hz were measured for 39 subjects with ages from 61 to 83 yr. All subjects had near-normal audiometric thresholds at low frequencies, but thresholds varied across subjects at high frequencies. IPD thresholds were correlated with age. IPD thresholds for the test frequency of 750 Hz were weakly correlated with absolute thresholds at high frequencies, but these correlations became non-significant when the effect of age was partialed out. The results do not confirm that sensitivity to TFS at low frequencies is influenced by hearing loss at high frequencies, independently of age.
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43.66.Sr Deafness, audiometry, aging effects
43.66.Pn Binaural hearing

Evidence of the enhancement effect in electrical stimulation via electrode matching (L)

Matthew J. Goupell and Mitchell J. Mostardi

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1007-1010 (2012); (4 pages)

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The ability to match a pulsing electrode during multi-electrode stimulation through a research interface was measured in seven cochlear-implant (CI) users. Five listeners were relatively good at the task and two could not perform the task. Performance did not vary as a function of the number of electrodes or stimulation level. Performance on the matching task was not correlated to performance on an electrode-discrimination task. The listeners may have experienced the auditory enhancement effect, and this may have implications for speech recognition in noise for CI users.
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43.66.Ts Auditory prostheses, hearing aids
43.66.Mk Temporal and sequential aspects of hearing; auditory grouping in relation to music
43.66.Hg Pitch
43.66.Dc Masking

Effects of seeing the interlocutor on the production of prosodic contrasts (L)

Erin Cvejic, Jeesun Kim, and Chris Davis

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1011-1014 (2012); (4 pages)

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This study investigated whether the production of prosodic focus and phrasing contrasts was modified when interlocutors could only hear each other [auditory only (AO)], compared to when they could hear and see each other [face to face (FTF)]. The prosodic characteristics of utterances produced by six talkers were examined using both acoustic and perceptual measures (ratings of the degree of focus or clarity of the statement-question contrast). The acoustic measures showed a range of differences between narrow focus and between phrasing contrasts and some of these differences were greater in the AO setting than the FTF one. The listener’s ratings of focus and phrasing showed a clear difference between the AO and FTF conditions, with perceptual attributes of both narrow focus and echoic question phrasing being rated as clearer in the AO condition. To explain these results it is proposed that talkers compensate for the lack of visual prosodic cues in the AO condition by taking extra care (relative to FTF conditions) to ensure the effective transmission of prosodic cues.
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43.71.Sy Spoken language processing by humans
43.70.Mn Relations between speech production and perception
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Wave motion and dispersion phenomena: Veering, locking and strong coupling effects

Brian R. Mace and Elisabetta Manconi

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1015-1028 (2012); (14 pages)

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The dispersion curves describe wave propagation in a structure, each branch representing a wave mode. As frequency varies the wavenumbers change and a number of dispersion phenomena may occur. This paper characterizes, analyzes, and quantifies these phenomena in general terms and illustrates them with examples. Two classes of phenomena occur. Weak coupling phenomena—veering and locking—arise when branches of the dispersion curves interact. These occur in the vicinity of the frequency at which, for undamped waveguides, the dispersion curves in the uncoupled waveguides would cross: if two dispersion curves (representing either propagating or evanescent waves) come close together as frequency increases then the curves either veer apart or lock together, forming a pair of attenuating oscillatory waves, which may later unlock into a pair of either propagating or evanescent waves. Which phenomenon occurs depends on the product of the gradients of the dispersion curves. The wave mode shapes which describe the deformation of the structure under the passage of a wave change rapidly around this critical frequency. These phenomena also occur in damped systems unless the levels of damping of the uncoupled waveguides are sufficiently different. Other phenomena can be attributed to strong coupling effects, where arbitrarily light stiffness or gyroscopic coupling changes the qualitative nature of the dispersion curves.
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43.20.Bi Mathematical theory of wave propagation
43.20.Jr Velocity and attenuation of elastic and poroelastic waves
43.20.Hq Velocity and attenuation of acoustic waves
43.20.Mv Waveguides, wave propagation in tubes and ducts
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Contactless transport of matter in the first five resonance modes of a line-focused acoustic manipulator

Daniele Foresti, Majid Nabavi, and Dimos Poulikakos

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1029-1038 (2012); (10 pages)

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The first five resonance modes for transport of matter in a line-focused acoustic levitation system are investigated. Contactless transport was achieved by varying the height between the radiating plate and the reflector. Transport and levitation of droplets in particular involve two limits of the acoustic forces. The lower limit corresponds to the minimum force required to overcome the gravitational force. The upper limit corresponds to the maximum acoustic pressure beyond which atomization of the droplet occurs. As the droplet size increases, the lower limit increases and the upper limit decreases. Therefore to have large droplets levitated, relatively flat radiation pressure amplitude during the translation is needed. In this study, using a finite element model, the Gor’kov potential was calculated for different heights between the reflector and the radiating plate. The application of the Gor’kov potential was extended to study the range of droplet sizes for which the droplets can be levitated and transported without atomization. It was found that the third resonant mode (H3–mode) represents the best compromise between high levitation force and smooth pattern transition, and water droplets of millimeter radius can be levitated and transported. The H3–mode also allows for three translation lines in parallel.
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43.25.Uv Acoustic levitation
43.25.Qp Radiation pressure
43.25.Gf Standing waves; resonance
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Application of the Beilis–Tappert parabolic equation method to sound propagation over irregular terrain

Santosh Parakkal, Kenneth E. Gilbert, and Xiao Di

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1039-1046 (2012); (8 pages)

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The Beilis–Tappert (1979) parabolic equation method is attractive for irregular terrain because it treats surface variations in terms of a simple multiplicative factor (“phase screen”). However, implementing the exact sloping-surface impedance condition is problematic if one wants the computational efficiency of a Fourier parabolic equation algorithm. This article investigates an approximate flat-ground impedance condition that allows the Beilis–Tappert phase screen method to be used with a Fourier algorithm without any added complications. The exact sloping-surface impedance condition is derived and applied to propagation predictions over hills with maximum slopes from 5° to 22°. The predictions with the exact impedance condition are compared to predictions using the approximate flat-ground impedance condition. It is found that for slopes less than 15°–20°, the flat-ground impedance condition is sufficiently accurate. For slopes greater than approximately 20°, the limiting factor on numerical accuracy is not the flat-ground impedance approximation, but rather the narrow-angle approximation required by the Beilis–Tappert method. Thus, within the 20° limitation and using the flat-ground impedance condition with a Fourier parabolic equation, sound propagation over irregular terrain can be computed simply, efficiently, and accurately.
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43.28.En Interaction of sound with ground surfaces, ground cover and topography, acoustic impedance of outdoor surfaces
43.28.Js Numerical models for outdoor propagation
43.28.Fp Outdoor sound propagation through a stationary atmosphere, meteorological factors
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A Hamiltonian method for finding broadband modal eigenvalues

Haozhong Wang, Ning Wang, and Dazhi Gao

J. Acoust. Soc. Am. Volume 131, Issue 2, pp. 1047-1054 (2012); (8 pages)

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For shallow water waveguides over a layered elastic bottom, modal eigenvalues can be determined by searching the locations in the complex plane of the horizontal wave number at which the complex phase function is a multiple of π [C. T. Tindle and N. R. Chapman, J. Acoust. Soc. Am. 96, 1777–1782 (1994)]. In this paper, a Hamiltonian method is introduced for tracing the path in the complex plane along which the phase function keeps real. The Hamiltonian method can also be extended to compute the broadband modal eigenvalues or the modal dispersion curves in the Pekeris waveguide with fluid/elastic bottoms. For each proper or leaky normal mode, a different Hamiltonian is constructed in the complex plane and used to trace automatically the complex dispersion curve with the eigenvalue in a reference frequency as the initial value. In contrast to the usual methods, the dispersion curve for each mode is determined individually. The Hamiltonian method shows good performance by comparing with kraken.
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43.30.Bp Normal mode propagation of sound in water
43.30.Ma Acoustics of sediments; ice covers, viscoelastic media; seismic underwater acoustics
43.20.Mv Waveguides, wave propagation in tubes and ducts
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