Zhang R, Zhang Y, Nie L
… +4 more, Wang J, Tai Y, Wang L, Wang H
J Acoust Soc Am
· 2026 May · PMID 42133458
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Modulation recognition in underwater acoustic communication is challenging due to channel distortion and non-cooperative scenarios. This paper proposed a method based on Multi-Path ResNet to extract and fuse time-domain,...Modulation recognition in underwater acoustic communication is challenging due to channel distortion and non-cooperative scenarios. This paper proposed a method based on Multi-Path ResNet to extract and fuse time-domain, frequency-domain, and multi-order spectral features of received signals for improving recognition performance. Moreover, for practical non-cooperative applications, a per-class distance thresholding method was proposed to reject unknown modulation types by leveraging the proximity of intra-class samples in the logits space and establishing decision thresholds individually for each class. To validate the proposed methods, this paper conducted both simulation and sea trials. Simulations using measured underwater acoustic channels confirmed the superior performance of both proposed methods in shallow water. Deep-water sea trials in the Western Pacific collected and established a dataset of 6776 samples, on which the proposed system achieved the recognition accuracy of 64.1%, while the rejection accuracy for unknown categories reached 74.4%. Furthermore, the study also revealed that recognition performance is directly correlated with the delay spread and dynamic variation of channels, offering physical insights into improving deep learning-based modulation recognition in underwater acoustic communication.
Sanhaji M, Fellah ZEA, Franklin H
… +4 more, Achaoui Y, Bahich M, Depollier C, Ogam E
J Acoust Soc Am
· 2026 May · PMID 42133457
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This study derives the asymptotic behavior of dynamic tortuosity for arbitrary pore geometries filled with non-Newtonian fluid in both high- and low-frequency regimens. This derivation leads to the formulation of a gener...This study derives the asymptotic behavior of dynamic tortuosity for arbitrary pore geometries filled with non-Newtonian fluid in both high- and low-frequency regimens. This derivation leads to the formulation of a general model of dynamic tortuosity through the use of a simple transition function. The analytical model can be applied to complex shapes of pores filled with a non-Newtonian fluids, which so far not has been reported in the literature. Applied to the porelastic Biot theory, the model predicts the influence of non-Newtonian fluids on the modal dispersion of the dilatational waves. This integration provides insights into wave dynamics within the most general context of porous materials with complex pore geometries, offering a robust theoretical foundation for various practical applications.
J Acoust Soc Am
· 2026 May · PMID 42133456
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The Hawaiian phoneme inventory includes a consonant ('okina) typically described as glottal stop. Recent studies have found that 'okina is rarely produced with full glottal closure utterance-medially, and is instead prod...The Hawaiian phoneme inventory includes a consonant ('okina) typically described as glottal stop. Recent studies have found that 'okina is rarely produced with full glottal closure utterance-medially, and is instead produced as a period of creaky phonation. This study investigated the acoustic correlates of utterance-initial 'okina following a pause. Although visible creaky phonation did not occur for utterance-initial 'okina, several reliable acoustic correlates were found during the first vowels of utterances that started with 'okina. Vowels preceded by 'okina had higher fundamental frequency, more abrupt onsets of acoustic energy, greater acoustic energy both in the fundamental frequency and across all frequency ranges, lower harmonics-to-noise ratios, and higher jitter than vowels that started without a preceding 'okina. Linear discriminant analyses of the data showed that these acoustic correlates were able to correctly categorize ∼75% of productions. Although no concurrent articulatory data were collected, arguments are provided to suggest that 'okina is regularly produced as full glottal closure utterance-initially in Hawaiian, possibly because of effects of prosodic strengthening. We believe the present study is the first to establish a relationship between utterance-initial glottal stop and these acoustic effects on the following vowel.
Jézéquel Y, Bonnel J, Amice E
… +1 more, Chauvaud L
J Acoust Soc Am
· 2026 May · PMID 42133455
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Sound production is prevalent among marine invertebrates, yet acoustic behavior remains largely undocumented in polar species. Here is reported the first evidence of acoustic emissions in the snow crab Chionoecetes opili...Sound production is prevalent among marine invertebrates, yet acoustic behavior remains largely undocumented in polar species. Here is reported the first evidence of acoustic emissions in the snow crab Chionoecetes opilio, a commercially important crustacean inhabiting cold and deep marine environments. Using synchronized passive acoustic recordings and miniaturized carapace-mounted accelerometers, the study demonstrates that snow crabs emit broadband pulse trains, termed rasps. Laboratory experiments revealed a strong effect of light conditions, with rasps detected only under dark conditions. Some snow crabs produced long and highly repetitive rasp sequences (up to 200 rasps in 1 h), resulting in sustained emission rates that, as far as can be determined, have not been described at this temporal scale in marine invertebrates. A complementary field experiment confirmed rasp production in situ, and accelerometer recordings allowed attribution of signals to a single individual within a group, highlighting strong inter-individual variability. The temporal structure of rasps was comparatively irregular, suggesting that internal friction-based mechanisms, such as gastric mill activity, may be involved. While the ecological role of snow crab rasps remains unknown, these findings expand current knowledge of crustacean acoustic behavior and provide a foundation for future research on sound production and its ecological relevance in polar marine invertebrates.
Li J, Chen S, Zheng C
… +4 more, Chang Y, Zhou D, Li F, Hao C
J Acoust Soc Am
· 2026 May · PMID 42133454
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Ultrasound is increasingly explored to regulate protein-small molecule interactions, yet the relative importance of acoustic parameters under practical liquid sonication remains unclear. This study used a bovine serum al...Ultrasound is increasingly explored to regulate protein-small molecule interactions, yet the relative importance of acoustic parameters under practical liquid sonication remains unclear. This study used a bovine serum albumin-toluidine blue O (BSA-TBO) model system to quantify parameter-dependent spectroscopic responses after establishing a baseline binding state. A 20 kHz probe sonicator recorded changes in the fluorescence peak intensity of bovine serum albumin and BSA-TBO as a function of treatment time, ultrasonic power, and duty cycle, while a bath sonicator qualitatively compared peak-intensity responses at 25, 40, and 59 kHz. Temperature-matched heating controls, together with circular dichroism and synchronous fluorescence measurements, were used to test whether the parameter-dependent fluorescence response was dominated by bulk thermal effects. Under the present setup and geometry, ultrasonic power was the dominant factor; duty cycle and treatment time acted as secondary modulators via temporal delivery and cumulative exposure, whereas frequency effects were weaker and non-monotonic across the tested discrete points. These results provide guidance for parameter selection and optimization in ultrasound-regulated protein-ligand systems.
J Acoust Soc Am
· 2026 May · PMID 42133453
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Acoustic vowel dynamics have some speaker-identifying characteristics, which have been ascribed to individual properties of articulatory strategies: formant transitions have a particular shape because speakers move their...Acoustic vowel dynamics have some speaker-identifying characteristics, which have been ascribed to individual properties of articulatory strategies: formant transitions have a particular shape because speakers move their articulators, using specific and practised movements. However, there is little existing evidence that different articulatory strategies systematically affect formant dynamics. The present study corroborates the link between the two. Ultrasound tongue imaging data from 36 speakers of Northern-Anglo English are used to identify distinct articulatory strategies for the production of palatal vowel /i/. Tongue shape in /i/ is found to be a significant predictor of formant dynamics in diphthongs with a palatal offglide. The observed relationships can be explained by the characteristics of articulatory movement conditioned by vocal tract shape. Greater articulatory displacement of tongue root and/or dorsum produces greater distortion from the mean tongue shape in palatal vowels, and it also requires higher articulatory velocities, resulting in relatively earlier and steeper formant transitions. The results contribute to the conceptual understanding of individuality in speech, by illuminating the regularising and individual aspects of articulatory compensation.
Tajima K, Amano S, Kitahara M
… +5 more, Yoneyama K, Maki K, Kawahara H, Kondo M, Yamakawa K
J Acoust Soc Am
· 2026 May · PMID 42132894
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The present study investigated characteristics of pop-out voice, i.e., a type of voice that stands out in the presence of other competing sounds. First, Japanese listeners heard a Japanese sentence produced by various sp...The present study investigated characteristics of pop-out voice, i.e., a type of voice that stands out in the presence of other competing sounds. First, Japanese listeners heard a Japanese sentence produced by various speakers mixed with babble noise and rated the subjective degree of pop-out. Results showed wide variation in pop-out scores across the sentences, despite normalized intensity. Second, detection thresholds were measured by presenting the sentences to listeners at various speech-to-noise ratios. Results demonstrated that sentences with higher pop-out rank were more easily detectable than those with lower pop-out rank, both for Japanese listeners and for English listeners with no proficiency in Japanese. Furthermore, detection thresholds were lower for Japanese than English listeners. Third, intelligibility was measured with Japanese listeners using the same sentences. Results confirmed that sentences with higher pop-out ranks were more intelligible. Furthermore, correlations between intelligibility and detection thresholds were moderate. Finally, acoustic analysis revealed that pop-out voice was associated with higher relative power in the 0.85-4.0 kHz frequency band. These results suggest that pop-out voice is driven by acoustic information, which enhances perceptual salience, and by linguistic information, which further enhances detectability for native listeners.
J Acoust Soc Am
· 2026 May · PMID 42118720
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Online secondary path modeling is essential for the robust performance of adaptive active noise control (ANC) systems. The Overall Modeling Algorithm (OMA) simultaneously models both the primary and secondary paths durin...Online secondary path modeling is essential for the robust performance of adaptive active noise control (ANC) systems. The Overall Modeling Algorithm (OMA) simultaneously models both the primary and secondary paths during control filter adaptation, featuring a simple algorithm structure and no need for auxiliary noise. While previous studies have analyzed its convergence only in broadband ANC systems, the convergence behavior in narrowband ANC (NANC) systems remains unclear. Therefore, this paper analyzes the convergence of OMA in NANC systems in both the time and frequency domains. The results show that OMA-based NANC systems converge when the lengths of the modeled primary path, the modeled secondary path, and the control filter are each at least twice the number of noise frequencies. If the modeled path length equals the true path length, full-band convergence can be achieved when the number of noise frequencies is at least half of the path length. This indicates that complete secondary path information can be obtained using only a limited number of tonal signals. The theoretical analysis is validated through simulations and experiments under various NANC scenarios.
J Acoust Soc Am
· 2026 May · PMID 42118719
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Knowledge is lacking about the way humans process acoustic information conveyed by flowing water in natural settings. To address this issue, the sound of a river was recorded in a Mediterranean forest three times per day...Knowledge is lacking about the way humans process acoustic information conveyed by flowing water in natural settings. To address this issue, the sound of a river was recorded in a Mediterranean forest three times per day and for two seasons along a 100 m transect from a river segment and at two further locations (150 and 200 m) on a different transect. Stimuli were presented diotically to listeners tasked to detect presence of water. A two-interval, two-alternative forced-choice paradigm was used to measure detection performance, where the target and standard stimuli corresponded to samples from the 100 m transect and samples from the two further locations on the other transect, respectively. Each listener was tested on a single trial only. Absolute level cues were removed. Detection performance measured for this habitat varied mainly with distance from the river segment and season. The empirical data were compared to those simulated by a model calculating time-averaged texture statistics at the output of a cochlear and a modulation filterbank and predicting performance via a template-matching decision strategy. The results indicate that the sparsity of envelope fluctuations and the coordination of temporal-envelope fluctuations across perceptual channels are diagnostic cues for water detection in natural environments.
J Acoust Soc Am
· 2026 May · PMID 42112824
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Frequency band importance weights were estimated for isolated consonant-vowel-consonant words presented in auditory-only and audiovisual modalities. Acoustic speech stimuli were filtered into six one-octave bands centere...Frequency band importance weights were estimated for isolated consonant-vowel-consonant words presented in auditory-only and audiovisual modalities. Acoustic speech stimuli were filtered into six one-octave bands centered at 250, 500, 1000, 2000, 4000, and 8000 Hz. Twenty-one adults with typical hearing and vision completed a word repetition task in both modalities with two bands presented on each trial. Generalized linear mixed models with logistic link functions were used to estimate the weight of each band and the effect of modality on weight. In both modalities, band importance was highest for the 2000 Hz band and progressively declined for bands further from 2000 Hz. There were significant band by modality interactions for the four highest frequency bands, reflecting a decrease in weighting of high-frequency acoustics in audiovisual conditions. Exploratory analyses of phoneme-level accuracy revealed that visual speech cues impacted frequency importance weighting for both consonant and vowel perception. Study results are consistent with the idea that the bands redundant with visual cues have relatively less impact on audiovisual speech intelligibility than auditory-only speech intelligibility and suggest that auditory-only assessments of band importance fail to capture differences in band importance that occur when visual speech cues are available to support speech recognition.
Liu Y, Zhang X, Luo Z
… +3 more, Wang Z, Li Z, Xu L
J Acoust Soc Am
· 2026 May · PMID 42112823
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Adaptive beamformers such as the minimum-variance distortionless response (MVDR) are highly sensitive to mismatches in both the sample covariance matrix (SCM) and the array steering vector. This paper proposes a closed-l...Adaptive beamformers such as the minimum-variance distortionless response (MVDR) are highly sensitive to mismatches in both the sample covariance matrix (SCM) and the array steering vector. This paper proposes a closed-loop Neural-MVDR framework for direction-of-arrival estimation that enforces a distortionless constraint consistent with a physically parameterized array model. The method requires no offline supervised pretraining on external labeled datasets. Instead, it performs per-frame, self-supervised adaptation at test time. For each incoming snapshot, it alternates among steering-vector refinement, robust SCM reconstruction parameterized by a lightweight neural module, and analytical MVDR spectral estimation. Experiments on synthetic data and the SWellEx-96 S5 event demonstrate improved robustness compared with the conventional beamformer, conventional MVDR, and representative robust MVDR variants based on eigenspace suppression, covariance matrix tapering, and oracle-approximating shrinkage, respectively.
Espy-Wilson C, Loganathan K, Seneviratne N
… +1 more, Benway N
J Acoust Soc Am
· 2026 May · PMID 42112822
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This study investigates the impact of Major Depressive Disorder and its characteristic psychomotor slowing on speech intelligibility. The speech-in-noise intelligibility task involved 176 native English-speaking listener...This study investigates the impact of Major Depressive Disorder and its characteristic psychomotor slowing on speech intelligibility. The speech-in-noise intelligibility task involved 176 native English-speaking listeners and 9 speakers with speech from 2 speaker states: very severe depression and in remission. Speaker intelligibility was rated across three signal-to-noise-ratio levels (-2, 0, and +2 dB). The findings suggest that depressed speech is at least as intelligible as in-remission speech. Linear mixed-effects modeling showed no significant difference in overall intelligibility between the two speaker states. Additional acoustic analysis used vocal tract variables to quantify underlying articulatory coordination. Acoustic and articulatory analyses revealed that depressed speech exhibits "simpler" articulatory coordination, characterized by reduced coarticulation and less target undershoot, challenging the conventional view that depression necessarily leads to poorly articulated speech.
J Acoust Soc Am
· 2026 May · PMID 42112821
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Objective hearing diagnostics in asymmetric hearing often require masking the better ear. Currently, no guideline for masking levels for narrowband chirps used in evoked response audiometry is available. The present stud...Objective hearing diagnostics in asymmetric hearing often require masking the better ear. Currently, no guideline for masking levels for narrowband chirps used in evoked response audiometry is available. The present study investigated which levels of a broadband noise are required to mask narrowband chirps. In a psychoacoustic experiment with 12 normal-hearing adults and an electrophysiological experiment using auditory steady-state responses with 12 single-sided deaf adults, air-conducted and bone-conducted narrowband chirp trains were presented at a repetition rate of 40 Hz. Both experiments showed similar results. Masking levels depended on the center frequency of the narrowband chirps as well as the transducer used to present the chirps. In the psychoacoustic experiment, noise levels of 36.0, 27.4, 28.3, and 30.6 dB above the chirp level were measured for air-conducted chirp trains of center frequencies 500, 1000, 2000, and 4000 Hz, respectively. For bone-conducted chirp trains, noise levels of 53.4, 38.1, 29.1, and 42.2 dB above the chirp level were necessary to mask the signals. The masker levels measured in this study can be used in the clinical routine to enhance the diagnostic quality of hearing assessments in patients with asymmetric hearing loss.
Fatela J, Heimes A, Vorländer M
… +2 more, Masullo M, Maffei L
J Acoust Soc Am
· 2026 May · PMID 42101143
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Geometrical acoustics methods provide efficient techniques to estimate sound propagation properties in virtual spaces. Advances based on acoustic radiance transfer principles facilitate the simulation of environments wit...Geometrical acoustics methods provide efficient techniques to estimate sound propagation properties in virtual spaces. Advances based on acoustic radiance transfer principles facilitate the simulation of environments with complex scattering distributions via the implementation of bidirectional reflectance distribution functions (BRDF). Though significant work has been developed in the optimization of such methods, the effects of complex BRDF implementation have seldom been studied. In this article, two scattering distribution modeling approaches are compared, based on random incidence and bidirectional scattering coefficients, respectively. Their implementation in an acoustic radiosity (AR) simulation tool is discussed. The simulation of a single façade shows that random-incidence modeling in the radiosity tool aligns with state-of-the-art ray-tracing (RT) simulation. Bidirectional scattering approach results of retro-reflective surface simulations are closest to a reference wave-based simulation output, meaning they capture more of the spatial details of the scattering distribution. The simulation of a street canyon scene further highlights how the choice of scattering modeling leads to significant differences in the energy time curve. The results evidence minor artifacts due to the AR and RT implementations. Major computational performance metrics are also assessed.
Beni A, Bresciani APC, Christophe J
… +1 more, Schram C
J Acoust Soc Am
· 2026 May · PMID 42101142
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The trade-off between performance and noise emissions has progressively established itself as a key factor in the emergence of Urban Air Mobility. This work addresses the relationship between the propulsive efficiency an...The trade-off between performance and noise emissions has progressively established itself as a key factor in the emergence of Urban Air Mobility. This work addresses the relationship between the propulsive efficiency and noise emissions of drone-sized coaxial, co-rotating propellers operating in hover, for varying phase offset ϕ and axial separation Δz between the rotors. Experimentally, an antagonistic behavior emerged between power loading and broadband noise, while a modulation of the tonal noise with varying phase offset was observed. The physical mechanism modulating tonal noise is explained using an analytical approach accounting for the acoustic interferences that occur for unevenly spaced rotors, based on Goldstein's formulation for the tonal noise generated by rotating dipole sources. Furthermore, a combination of a commercial panel method and a rotating dipole source model is proposed as a fast-turnaround approach to predict aerodynamic loads and tonal noise. The acoustic predictions obtained for the second shaft harmonic are consistent with the experimental trends, given the inherent limitations of the solver employed, and assess the potential of the proposed method for a multidisciplinary early-stage design phase.
J Acoust Soc Am
· 2026 May · PMID 42101141
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This paper addresses the challenge of pulse source localization in a deep sea bottom bounce area using multipath time differences via a vertical dual-hydrophone configuration. By analyzing the variation trends of multipa...This paper addresses the challenge of pulse source localization in a deep sea bottom bounce area using multipath time differences via a vertical dual-hydrophone configuration. By analyzing the variation trends of multipath time-delay differences with respect to source range and depth in deep sea bottom bounce area, a set of analytical expressions relating multipath time-delay differences to source range and depth is derived based on geometric relationships. Furthermore, by integrating ray tracing technology with simulated annealing and Bayesian inversion methods, source localization within the range-depth two-dimensional plane is achieved. Simulation results indicate that the source positions calculated using the geometric analytical expressions can provide starting values for the other two methods. The Bayesian inversion approach demonstrates higher accuracy in estimating source range compared to simulated annealing. However, simulated annealing yields better depth estimation results with higher concentration. Sea trial results confirm the effectiveness of both methods in localizing cooperative sources under high signal-to-noise ratio conditions.
Zhao Y, Kou Z, Liu M
… +3 more, Miller RJ, Czarnota GJ, Oelze ML
J Acoust Soc Am
· 2026 May · PMID 42089704
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Publisher ↗
Quantitative ultrasound (QUS) techniques provide tissue characterization and have applications in precision diagnostics and therapy monitoring. A common QUS approach estimates backscatter coefficients (BSCs) using the ex...Quantitative ultrasound (QUS) techniques provide tissue characterization and have applications in precision diagnostics and therapy monitoring. A common QUS approach estimates backscatter coefficients (BSCs) using the external reference phantom method, which does not adequately address attenuation and transmission losses. To address this issue, we previously utilized a 2 mm titanium bead as an in situ calibration reference with conventional focused wave (FW) imaging. Plane wave compounding (PWC), which transmits multiple angled plane waves, enables rapid image acquisition while maintaining quality, making it widely useful in Doppler and elastographic imaging. However, its role in BSC estimation with an in situ bead had not been investigated. We hypothesized that PWC would outperform FW, as diffraction effects vary more slowly away from the bead depth when using PWC. We tested this hypothesis by comparing BSC estimation in phantoms and in vivo rabbit mammary tumors. Results indicated that PWC with in situ calibration better compensated for attenuation loss and reduced variability in scatterer property estimates compared to FW. Specifically, the scatterer diameter variance was 15.2 μm2 when using PWC versus 45.4 μm2 when using FW where the focus was offset from the bead depth. These findings demonstrate the superiority of using PWC with an in situ calibration target for accurate, efficient BSC estimation.
J Acoust Soc Am
· 2026 May · PMID 42089703
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Publisher ↗
Adaptation to altered or non-individual head-related transfer functions (HRTFs) has been widely studied in individuals with normal hearing. Studies have shown that after an adaptation period, individuals can significantl...Adaptation to altered or non-individual head-related transfer functions (HRTFs) has been widely studied in individuals with normal hearing. Studies have shown that after an adaptation period, individuals can significantly improve their sound localization performance with altered cues. Recently, it has been shown that after training with one set of HRTFs, improvements can also be observed with another set, a phenomenon referred to as generalization. This study provides significantly more evidence of this phenomenon by including a larger number of participant groups and a longer training period compared to prior work. The experiment involved four groups of participants: two control groups (one with individual HRTFs, one with non-individual HRTFs) only performing localization tests and two training groups (one with individual HRTFs, one with non-individual HRTFs) completing both localization tests and training sessions. In all cases, the stimulus consisted of a male speech sentence reproduced binaurally. Both training groups showed significant and comparable improvements in localization performance. Moreover, generalization effects were observed and found to be similar between the two training groups.
J Acoust Soc Am
· 2026 May · PMID 42084650
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Range resolution defines the ability to discriminate multiple closely spaced surfaces from a single surface and is a fundamental determinant of dolphin biosonar performance. In this study, three bottlenose dolphins were...Range resolution defines the ability to discriminate multiple closely spaced surfaces from a single surface and is a fundamental determinant of dolphin biosonar performance. In this study, three bottlenose dolphins were trained to discriminate "phantom" echoes with a single highlight from those with two highlights. The inter-highlight interval of the two-highlight echo was varied to determine the discrimination threshold. Threshold measurements were conducted at echo delays corresponding to simulated target ranges of 2.5-80 m. Discrimination thresholds were 2-3 μs (∼2 mm) for two dolphins with a full-bandwidth of hearing. A third dolphin with high-frequency hearing loss had higher thresholds, between 3 and 5 μs (∼2-4 mm). Thresholds were independent of simulated range, which contrasts with previous reports that the dolphin's accuracy of range determination-as opposed to range resolution-is reduced beyond 10-20 m. Dolphin discriminations in the current study appeared to be based on a spectral cue that consisted of a low-pass filter effect at the highest audible frequencies in the two-highlight echoes. It is unknown if dolphins perceive highlight-dependent spectral interference patterns as a spatial separation of target features along a range axis.
Guo Z, Li J, Guo Y
… +8 more, Zhang S, Ma T, Wang G, Wang Q, Liu X, Zhang Z, Wei H, Wang L
J Acoust Soc Am
· 2026 May · PMID 42084284
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Publisher ↗
This paper adapts a well-established optical Fourier modal method to acoustics and proposes a Fourier modal method with an enhanced transmittance matrix for investigating the diffraction characteristics of multilayer two...This paper adapts a well-established optical Fourier modal method to acoustics and proposes a Fourier modal method with an enhanced transmittance matrix for investigating the diffraction characteristics of multilayer two-dimensional acoustic metamaterial gratings. This method analytically solves the acoustics equation in the Fourier domain and matches the analytical solutions at boundaries to obtain the overall diffraction information. Numerical results demonstrate that this method yields results consistent with those of the finite-element method for both oblique and normal incidence, while offering significant computational advantages compared with full-wave spatial discretization for relatively simple periodic unit-cell geometries. The primary practical value of the framework lies in the rapid prediction of the overall reflection and transmission of multilayer periodic acoustic gratings, which is particularly attractive for parameter sweeps and design optimization. When higher-order propagating channels are open, this method also provides direct access to the contributions of individual diffraction orders. The proposed framework therefore provides a fast and accurate tool for the analysis and design of multilayer acoustic-metamaterial gratings.