Pitch Perception Research Articles

Humans use local spectrotemporal correlations to detect rising and falling pitch.

To discern speech or appreciate music, the human auditory system detects how pitch increases or decreases over time. However, the algorithms used to detect changes in pitch, or pitch motion, are incompletely understood. Here, using psychophysics, computational modeling, functional neuroimaging, and analysis of recorded speech, we ask if humans detect pitch motion using computations analogous to those used by the visual system. We adapted stimuli from studies of vision to create novel auditory correlated noise stimuli that elicited robust pitch motion percepts. Crucially, these stimuli possess no persistent features across frequency or time, but do possess positive or negative local spectrotemporal correlations in intensity. In psychophysical experiments, we found clear evidence that humans judge pitch direction based on both positive and negative spectrotemporal correlations. The observed sensitivity to negative correlations is a direct analogue of illusory "reverse-phi" motion in vision, and thus constitutes a new auditory illusion. Our behavioral results and computational modeling led us to hypothesize that human auditory processing employs pitch direction opponency. fMRI measurements in auditory cortex supported this hypothesis. To link our psychophysical findings to real-world pitch perception, we analyzed recordings of English and Mandarin speech and discovered that pitch direction was robustly signaled by the same positive and negative spectrotemporal correlations used in our psychophysical tests, suggesting that sensitivity to both positive and negative correlations confers ecological benefits. Overall, this work reveals that motion detection algorithms sensitive to local correlations are deployed by the central nervous system across disparate modalities (vision and audition) and dimensions (space and frequency).

AcousTac: Tactile Sensing with Acoustic Resonance for Electronics-Free Soft Skin.

Sound is a rich information medium that transmits through air; people communicate through speech and can even discern material through tapping and listening. To capture frequencies in the human hearing range, commercial microphones typically have a sampling rate of over 40 kHz. These accessible acoustic technologies are not yet widely adopted for the explicit purpose of giving robots a sense of touch. Some researchers have used sound to sense tactile information, both monitoring ambient soundscape and with embedded speakers and microphones to measure sounds within structures. However, these options commonly do not provide a direct measure of steady state force or require electronics integrated somewhere near the contact location. In this work, we present AcousTac, an acoustic tactile sensor for electronics-free, force-sensitive soft skin. Compliant silicone caps and plastic tubes compose the resonant chambers that emit pneumatic-driven sound measurable with a conventional off-board microphone. The resulting frequency changes depend on the external loads on the compliant endcaps. The compliant cap vibrates with the resonant pressure waves and is a nonidealized boundary condition, initially producing a nonmonotonic force response. We characterize two solutions-adding a distal hole and mass to the cap-resulting in monotonic and nonhysteretic force readings with this technology. We can tune each AcousTac taxel to specific force and frequency ranges, based on geometric parameters including tube length, and thus uniquely sense each taxel simultaneously in an array. We demonstrate AcousTac's functionality on two robotic systems: a 4-taxel array and a 3-taxel astrictive gripper. Simple to implement with off-the-shelf parts, AcousTac is a promising concept for force sensing on soft robotic surfaces, especially in situations where electronics near the contact are not suitable. Equipping robots with tactile sensing and soft skin provides them with a sense of touch and the ability to safely interact with their surroundings.

3D morphology of an outer-hair-cell hair bundle increases its displacement and dynamic range

In mammals, outer-hair-cell hair bundles (OHBs) transduce sound-induced forces into receptor currents and are required for the wide dynamic range and high sensitivity of hearing. OHBs differ conspicuously in morphology from other types of bundles. Here, we show that the 3D morphology of an OHB greatly impacts its mechanics and transduction. An OHB comprises rod-like stereocilia, which pivot on the surface of its sensory outer hair cell. Stereocilium pivot positions are arranged in columns and form a V shape. We measure the pivot positions and determine that OHB columns are far from parallel. To calculate the consequences of an OHB’s V shape and far-from-parallel columns, we develop a mathematical model of an OHB that relates its pivot positions, 3D morphology, mechanics, and receptor current. We find that the 3D morphology of the OHB can halve its stiffness, can double its damping coefficient, and causes stereocilium displacements driven by stimulus forces to differ substantially across the OHB. Stereocilium displacements drive the opening and closing of ion channels through which the receptor current flows. Owing to the stereocilium-displacement differences, the currents passing through the ion channels can peak versus the stimulus frequency and vary considerably across the OHB. Consequently, the receptor current peaks versus the stimulus frequency. Ultimately, the OHB’s 3D morphology can increase its receptor-current dynamic range more than twofold. Our findings imply that potential pivot-position changes owing to development, mutations, or location within the mammalian auditory organ might greatly alter OHB function.

Timbral brightness perception investigated through multimodal interference

Brightness is among the most studied aspects of timbre perception. Psychoacoustically, sounds described as “bright” versus “dark” typically exhibit a high versus low frequency emphasis in the spectrum. However, relatively little is known about the neurocognitive mechanisms that facilitate these metaphors we listen with. Do they originate in universal magnitude representations common to more than one sensory modality? Triangulating three different interaction paradigms, we investigated using speeded classification whether intramodal, crossmodal, and amodal interference occurs when timbral brightness, as modeled by the centroid of the spectral envelope, and pitch height/visual brightness/numerical value processing are semantically congruent and incongruent. In four online experiments varying in priming strategy, onset timing, and response deadline, 189 total participants were presented with a baseline stimulus (a pitch, gray square, or numeral) then asked to quickly identify a target stimulus that is higher/lower, brighter/darker, or greater/less than the baseline after being primed with a bright or dark synthetic harmonic tone. Results suggest that timbral brightness modulates the perception of pitch and possibly visual brightness, but not numerical value. Semantically incongruent pitch height-timbral brightness shifts produced significantly slower reaction time (RT) and higher error compared to congruent pairs. In the visual task, incongruent pairings of gray squares and tones elicited slower RTs than congruent pairings (in two experiments). No interference was observed in the number comparison task. These findings shed light on the embodied and multimodal nature of experiencing timbre.

Perception and imitation of period-doubled phonation: Pitch and voice qualitya).

Period-doubled phonation, henceforth, period doubling, characterized by voicing periods that alternate in amplitudes and/or frequencies, is often perceived rough and with an indeterminate pitch. Lower pitch percept has been suggested by past studies when the degree of amplitude or frequency modulation increases. However, how listeners use period doubling when identifying linguistic tones remains unclear. The current study uses tasks of categorization with training, followed by imitation of tones manipulated with period doubling (with amplitude and frequency modulation, both separately and jointly) in a novel language. Native Mandarin and English speakers with different levels of music experience were tested. I show that period doubling leads to a low-tone bias in perception and imitation, especially as the modulation degree, particularly that of frequency, increases. Interestingly, interactions with stimulus f0 and modulation type show that in amplitude-modulated tokens, when compared to lower f0 (200 Hz), higher f0 (300 Hz) drives more low-tone responses. Period doubling is also imitated with lowered f0 and creaky quality. Language and music experience does not affect perceptual and imitative responses, suggesting that the perception of period doubling is not language-specific or conditioned by tonal knowledge. Period doubling likely signals low tones, even when the original f0 is high.

Cochlear Implantation in Single-Sided Deafness and Asymmetric Hearing Loss: 12 Months Follow-up Results of a European Multicenter Evaluation.

People with single-sided deafness (SSD) or asymmetric hearing loss (AHL) have particular difficulty understanding speech in noisy listening situations and in sound localization. The objective of this multicenter study is to evaluate the effect of a cochlear implant (CI) in adults with single-sided deafness (SSD) or asymmetric hearing loss (AHL), particularly regarding sound localization and speech intelligibility with additional interest in electric-acoustic pitch matching. A prospective longitudinal study at 7 European tertiary referral centers was conducted including 19 SSD and 16 AHL subjects undergoing cochlear implantation. Sound localization accuracy was investigated in terms of root mean square error and signed bias before and after implantation. Speech recognition in quiet and speech reception thresholds in noise for several spatial configurations were assessed preoperatively and at several post-activation time points. Pitch perception with CI was tracked using pitch matching. Data up to 12 months post activation were collected. In both SSD and AHL subjects, CI significantly improved sound localization for sound sources on the implant side, and thus overall sound localization. Speech recognition in quiet with the implant ear improved significantly. In noise, a significant head shadow effect was found for SSD subjects only. However, the evaluation of AHL subjects was limited by the small sample size. No uniform development of pitch perception with the implant ear was observed. The benefits shown in this study confirm and expand the existing body of evidence for the effectiveness of CI in SSD and AHL. Particularly, improved localization was shown to result from increased localization accuracy on the implant side.

Deficits in congenital amusia: Pitch, music, speech, and beyond

Congenital amusia is a neurodevelopmental disorder characterized by deficits of music perception and production, which are related to altered pitch processing. The present study used a wide variety of tasks to test potential patterns of processing impairment in individuals with congenital amusia (N = 18) in comparison to matched controls (N = 19), notably classical pitch processing tests (i.e., pitch change detection, pitch direction of change identification, and pitch short-term memory tasks) together with tasks assessing other aspects of pitch-related auditory cognition, such as emotion recognition in speech, sound segregation in tone sequences, and speech-in-noise perception. Additional behavioral measures were also collected, including text reading/copying tests, visual control tasks, and a subjective assessment of hearing abilities. As expected, amusics' performance was impaired for the three pitch-specific tasks compared to controls. This deficit of pitch perception had a self-perceived impact on amusics’ quality of hearing. Moreover, participants with amusia were impaired in emotion recognition in vowels compared to controls, but no group difference was observed for emotion recognition in sentences, replicating previous data. Despite pitch processing deficits, participants with amusia did not differ from controls in sound segregation and speech-in-noise perception. Text reading and visual control tests did not reveal any impairments in participants with amusia compared to controls. However, the copying test revealed more numerous eye-movements and a smaller memory span. These results allow us to refine the pattern of pitch processing and memory deficits in congenital amusia, thus contributing further to understand pitch-related auditory cognition. Together with previous reports suggesting a comorbidity between congenital amusia and dyslexia, the findings call for further investigation of language-related abilities in this disorder even in the absence of neurodevelopmental language disorder diagnosis.

Screened optimally tuned range separated hybrid functional for solvated low bandgap molecular systems.

The description of electronic properties of low bandgap molecular system is often performed by using density functional theory (DFT) and time dependent (TD) DFT calculations with the optimally tuned range-separated hybrid (OT-RSH) functional, as it contains the necessary ingredients to reliably predict charge transfer excitations. However, the range separating parameter (ω) is system-dependent and its optimization, including the chemical environment, is intricate. Refaely-Abramson et al. demonstrated that the gap renormalization in molecular crystals, a ground state property, can be represented by an OT-RSH functional screened by ɛstatic [Phys. Rev. B 88, 081204(R) (2013)], the zero frequency scalar dielectric constant. In this study, we propose the use of an OT-RSH functional screened by the scalar dielectric constant in the high frequency limit (OT-sRSH), ɛ∞, an appropriate constraint for vertical ionization energies or excitations in a dielectric environment. We have performed calculations for S,N-heteroacene derivatives in tetrahydrofuran and dichloromethane. The "unscreened" OT-RSH functional tends to underestimate experimental ionization potentials (IPs) and optical gaps (Egs) by up to 1.5 and 0.5eV, respectively. In contrast, OT-sRSH functional calculations underestimate IPs and Egs by only 0.4 and 0.2eV. We also compared the OT-sRSH results to explicitly solvated OT-RSH functional calculations for oligothiophenes in dioxane, benzene in ammonia, and methylene blue in water. We observe that both the approaches perform similarly for weakly interacting intermolecular systems and deviate for solvent-solute interacting systems, as expected. In conclusion, the OT-sRSH functional can describe molecular systems with environmental polarization effects accurately, a step toward describing realistic molecular systems.

A Narrative Analysis of J. G. Roederer’s The Physics and Psychophysics of Music

This paper conducts narrative analysis for the rhetorical critique of Roederer's <i>The Physics and Psychophysics of Music</i>, a prominent textbook of music science. It is possible to analyze implicit narratives even for texts in non-narrative genres. In science textbooks, implicit narratives can be analyzed in structural, educational, and research contexts. Roederer's satisfies structural coherence by composing a book in a way that deals with the perception of pitch, volume, timbre, and harmony according to the stages of sound generation, transmission, and acceptance in a structural context. In an educational context, a book is composed of content that students may be interested in for a scientific understanding of music to satisfy material coherence, and the validity of narrative fidelity is satisfied through the pursuit of reliable knowledge through experience data and improved observational equipment according to the method of constructing scientific knowledge. From the research context, we can confirmed that characterological coherence is secured by satisfying the truthfulness of narrative fidelity through the update of knowledge throughout the four editions, and by revealing that the knowledge of music science is being built through the activities of major researchers.

The cochlear hook region detects harmonics beyond the canonical hearing range.

Ultrasound, or sound at frequencies exceeding the conventional range of human hearing, is not only audible to mice, microbats, and dolphins, but also creates an auditory sensation when delivered through bone conduction in humans. Although ultrasound is utilized for brain activation and in hearing aids, the physiological mechanism of ultrasonic hearing remains unknown. In guinea pigs, we found that ultrasound above the hearing range delivered through ossicles of the middle ear evokes an auditory brainstem response and a mechano-electrical transduction current through hair cells, as shown by the local field potential called the cochlear microphonic potential (CM). The CM synchronizes with ultrasound, and like the response to audible sounds is actively and nonlinearly amplified. In vivo optical nano-vibration analysis revealed that the sensory epithelium in the hook region, the basal extreme of the cochlear turns, resonates in response both to ultrasound within the hearing range and to harmonics beyond the hearing range. The results indicate that hair cells can respond to stimulation at the optimal frequency and its harmonics, and the hook region detects ultrasound stimuli with frequencies more than two octaves higher than the upper limit of the ordinary hearing range.

Distortions in sound: Bridging acoustics and psychoacoustics in auditory perception

The field of acoustics encompasses the examination of sound, encompassing both its physical characteristics and the way in which humans perceive auditory input. Acoustics is the study of how sound waves are created and spread physically, while psychoacoustics connects these physical characteristics to our auditory perceptions. Comprehending these two features is essential for progress in audio technology and understanding auditory perception aberrations such as paracusia and diplacusis. This research consolidates information from multiple investigations to examine the interaction between acoustics and psychoacoustics. The technique entails examining the current body of literature on the fundamental principles governing sound waves, their interaction with various materials, and their movement across space. The examination of psychoacoustic elements involved the conversion of sound waves into brain impulses. The study also examines certain psychoacoustic phenomena, such as the sense of pitch and auditory distortions. By combining acoustic and psychoacoustic concepts, we can gain a thorough comprehension of how we perceive sound. Sound waves, generated by mechanical vibrations, pass through substances such as air, causing compression and rarefaction cycles that move at a speed of about 344 m/s at a temperature of 20°C. Psychoacoustics studies the perception of sound waves, specifically how they are processed by the ear and converted into neural signals that the brain can understand. The key findings reveal the subjective nature of pitch perception, where alterations in intensity or length impact the perceived frequency and the precise sensitivity of pitch discrimination. Furthermore, abnormalities such as paracusia and diplacusis emphasize the intricacies of auditory perception. The study highlights the significance of psychoacoustics in audio technology, where principles are utilized in audio compression and noise reduction to improve sound quality and clarity. The comprehensive comprehension of acoustics and psychoacoustics lays the groundwork for advancements in audio technology and the creation of auditory experiences.

Auditory cortical regions show resting-state functional connectivity with the default mode-like network in echolocating bats

Echolocating bats are among the most social and vocal of all mammals. These animals are ideal subjects for functional MRI (fMRI) studies of auditory social communication given their relatively hypertrophic limbic and auditory neural structures and their reduced ability to hear MRI gradient noise. Yet, no resting-state networks relevant to social cognition (e.g., default mode-like networks or DMLNs) have been identified in bats since there are few, if any, fMRI studies in the chiropteran order. Here, we acquired fMRI data at 7 Tesla from nine lightly anesthetized pale spear-nosed bats (Phyllostomus discolor). We applied independent components analysis (ICA) to reveal resting-state networks and measured neural activity elicited by noise ripples (on: 10 ms; off: 10 ms) that span this species' ultrasonic hearing range (20 to 130 kHz). Resting-state networks pervaded auditory, parietal, and occipital cortices, along with the hippocampus, cerebellum, basal ganglia, and auditory brainstem. Two midline networks formed an apparent DMLN. Additionally, we found four predominantly auditory/parietal cortical networks, of which two were left-lateralized and two right-lateralized. Regions within four auditory/parietal cortical networks are known to respond to social calls. Along with the auditory brainstem, regions within these four cortical networks responded to ultrasonic noise ripples. Iterative analyses revealed consistent, significant functional connectivity between the left, but not right, auditory/parietal cortical networks and DMLN nodes, especially the anterior-most cingulate cortex. Thus, a resting-state network implicated in social cognition displays more distributed functional connectivity across left, relative to right, hemispheric cortical substrates of audition and communication in this highly social and vocal species.

Directional sensitivity of bone conduction stimulation on the otic capsule in a finite element model of the human temporal bone

Sound transmission to the human inner ear by bone conduction pathway with an implant attached to the otic capsule is a specific case where the cochlear response depends on the direction of the stimulating force. A finite element model of the temporal bone with the inner ear, no middle and outer ear structures, and an immobilized stapes footplate was used to assess the directional sensitivity of the cochlea. A concentrated mass represented the bone conduction implant. The harmonic analysis included seventeen frequencies within the hearing range and a full range of excitation directions. Two assessment criteria included: (1) bone vibrations of the round window edge in the direction perpendicular to its surface and (2) the fluid volume displacement of the round window membrane. The direction of maximum bone vibration at the round window edge was perpendicular to the round window. The maximum fluid volume displacement direction was nearly perpendicular to the modiolus axis, almost tangent to the stapes footplate, and inclined slightly to the round window. The direction perpendicular to the stapes footplate resulted in small cochlear responses for both criteria. A key factor responsible for directional sensitivity was the small distance of the excitation point from the cochlea.

Acoustic metamaterials characterization via laser plasma sound sources

Phononic crystals and acoustic metamaterials are expected to become an important enabling technology for science and industry. Currently, various experimental methods are used for evaluation of acoustic meta-structures, such as impedance tubes and anechoic chambers. Here we present a method for the precise characterization of acoustic meta-structures that utilizes rapid broadband acoustic pulses generated by point-like and effectively massless laser plasma sound sources. The method allows for broadband frequency response and directivity evaluations of meta-structures with arbitrary geometries in multiple sound propagation axes while also enabling acoustic excitation inside the structure. Experimental results are presented from acoustic evaluations of various phononic crystals with band gaps in the audible range, notably also in the very low frequencies, validating the predictions of numerical models with high accuracy. The proposed method is expected to boost research and commercial adoption of acoustic metamaterials in the near future.

Modal approach to the dynamics of string instruments over the audible range

The present theoretical analysis addresses the dynamics of the bow instruments in the whole audible range of frequencies. Several scenarios are considered for the string-bridge-soundbox system: natural vibrations and frequency spectrum, external periodic excitation on some bridge point, and vibration induced by the bow rubbing. The single parts of the musical artifact are conveniently modelled and the bridge interfacing between the strings and the top plate of the soundbox is studied considering two possible vibrating modes of the bridge: a translational mode along its symmetry axis and a rotational mode around the waist centre. The bridge mechanical model is thus definable from both the kinematical and the dynamical aspects, and the relations between the forces and displacements of the strings and the sound box are formulated.The coupled natural modes of vibration are obtained in non-dissipative conditions, finding that the whole frequency spectrum is roughly given by the union of the uncoupled spectra, of the strings and the harmonic box. Then, introducing some level of dissipation, the frequency response to a transverse harmonic excitation on an arbitrary bridge point and the admittance on another arbitrary point of the instrument are studied, obtaining a useful tool to identify or verify the mechanical characteristics of the system. At last, the response to the bow excitation is analysed introducing an appropriate model for the nonlinear stick-slip contact between the bow and the strings and solving the motion equations by modal decomposition.

Medial superior olive in the rat: Anatomy, sources of input and axonal projections

Although rats and mice are among the preferred animal models for investigating many characteristics of auditory function, they are rarely used to study an essential aspect of binaural hearing: the ability of animals to localize the sources of low-frequency sounds by detecting the interaural time difference (ITD), that is the difference in the time at which the sound arrives at each ear. In mammals, ITDs are mostly encoded in the medial superior olive (MSO), one of the main nuclei of the superior olivary complex (SOC). Because of their small heads and high frequency hearing range, rats and mice are often considered unable to use ITDs for sound localization. Moreover, their MSO is frequently viewed as too small or insignificant compared to that of mammals that use ITDs to localize sounds, including cats and gerbils. However, recent research has demonstrated remarkable similarities between most morphological and physiological features of mouse MSO neurons and those of MSO neurons of mammals that use ITDs. In this context, we have analyzed the structure and neural afferent and efferent connections of the rat MSO, which had never been studied by injecting neuroanatomical tracers into the nucleus.The rat MSO spans the SOC longitudinally. It is relatively small caudally, but grows rostrally into a well-developed column of stacked bipolar neurons. By placing small, precise injections of the bidirectional tracer biotinylated dextran amine (BDA) into the MSO, we show that this nucleus is innervated mainly by the most ventral and rostral spherical bushy cells of the anteroventral cochlear nucleus of both sides, and by the most ventrolateral principal neurons of the ipsilateral medial nucleus of the trapezoid body. The same experiments reveal that the MSO densely innervates the most dorsolateral region of the central nucleus of the inferior colliculus, the central region of the dorsal nucleus of the lateral lemniscus, and the most lateral region of the intermediate nucleus of the lateral lemniscus of its own side. Therefore, the MSO is selectively innervated by, and sends projections to, neurons that process low-frequency sounds. The structural and hodological features of the rat MSO are notably similar to those of the MSO of cats and gerbils. While these similarities raise the question of what functions other than ITD coding the MSO performs, they also suggest that the rat MSO is an appropriate model for future MSO-centered research.

Design And Development Of Automated Electrical Circuit Fault Protector With Alarm System

In response to the critical need for fire and accident prevention in homes and establishments, this research presents an automated electrical circuit fault protector with an alarm system. The device automatically interrupts current flow upon detecting short circuits and overloads, safeguarding against potential hazards. Objectives include assessing sensitivity to faults, evaluating wireless remote-control performance, examining sound clarity, and ensuring voltage stability post-fault events. Equipped with a resettable system, the device allows manual or remote control. Using a developmental research method, data collection employed researcher-made observation and evaluation sheets. Thirty expert evaluators assessed the device. Micro testing revealed that the device was sensitive to faults and automatically triggered the alarm. With an overload rating of 1,500-3,000 watts, the device shuts off power automatically after the overload occurs and back to normal with a stable voltage once the problem was fixed, though this device was primarily designed only for micro-testing this device was customizable to user needs. Its alarm system boasts an audible range of up to 20 meters the same is through with remote control operation. Overall, the device effectively detects faults, incorporates an audible alarm, and supports remote operation, serving as a crucial safety measure against electrical mishaps and very acceptable in terms of design, composition, safety, and operating performance.

Seashells and sound waves: modelling soundscapes in Chacoan great-house communities

Humans inhabit rich social and physical worlds and archaeology is increasingly engaging with the multi-sensory experience of life in the past. In this article, the authors model the soundscapes of five Chacoan communities on the Colorado Plateau, where habitation sites cluster around monumental great houses. The work demonstrates that the audible range of a conch-shell trumpet blown from atop these great houses consistently maps the distribution of associated habitation sites. Staying within the audible reach of great houses may have helped maintain the social cohesion of communities in the past which, the authors argue, also has implications for the management of archaeological landscapes in the modern world.

Do rats (Rattus norvegicus) perceive octave equivalence, a critical human cross-cultural aspect of pitch perception?

Octave equivalence describes the perception that two notes separated by a doubling in frequency have a similar quality. In humans, octave equivalence is important to both music and language learning and is found cross-culturally. Cross-species studies comparing human and non-human animals can help illuminate the necessary pre-conditions to developing octave equivalence. Here, we tested whether rats (Rattus norvegicus) perceive octave equivalence using a standardized cross-species paradigm. This allowed us to disentangle concurring hypotheses regarding the evolutionary roots of this phenomenon. One hypothesis is that octave equivalence is directly connected to vocal learning, but this hypothesis is only partially supported by data. According to another hypothesis, the harmonic structure of mammalian vocalizations may be more important. If rats perceive octave equivalence, this would support the importance of vocal harmonic structure. If rats do not perceive octave equivalence, this would suggest that octave equivalence evolved independently in several mammalian clades due to a more complex interplay of different factors such as-but not exclusively-the ability to vocally learn. Evidence from our study suggests that rats do perceive octave equivalence, thereby suggesting that the harmonic vocal structure found in mammals may be a key pre-requisite for octave equivalence. Stage 1 approved protocol: the study reported here was originally accepted as a Registered Report and the study design was approved in Stage 1. We hereby confirm that the completed experiment(s) have been executed and analysed in the manner originally approved with any unforeseen changes in those approved methods and analyses clearly noted. The approved Stage 1 protocol can be found at: https://osf.io/gvf7c/?view_only=76dc1840f31c4f9ab59eb93cbadb98b7.

A Reduced Order Series Expansion for the BEM Incorporating the Boundary Layer Impedance Condition

When modeling sound waves in fluids it can be important to include the viscous and thermal losses originating from the fluids’ interaction with boundaries. In the audible frequency range, the thickness of the boundary layers is between a micrometer and a millimeter. As such the viscous and thermal losses are important when simulating the properties of small acoustical devices such as e.g. hearing aids or transducers. However, the inclusion of viscous and thermal losses is a computationally demanding task as it requires a fine discretization of the boundary layer in order to fully capture the complicated physical phenomena happening on the microscale. Recently, there has been developments to ease the computational demands using both the Finite Element Method and the Boundary Element Method, by approximating the losses using the Boundary Layer Impedance (BLI) boundary condition. In this paper, we extend previous developments for multi-frequency analysis using the Reduced Order Series Expansion Boundary Element Method to handle the BLI condition. This model follows a two-step procedure: Using a series expansion to decrease the assembly time of the BEM matrices and a projection to reduce the overall memory consumption of the model. Results from two acoustic interior problems show that the model decreases the total computational time by around 96% while using less than 15% of the memory. For both test setups the limiting factor of the accuracy was the reduction and not the series expansion.