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An equivalent circuit model has been developed to model a one-dimensional waveguide with many side-branch Helmholtz resonators. This waveguide constitutes a phononic crystal that has been shown to have decreased phase speed below the resonance frequency of an individual resonator. This decreased phase speed can be exploited to achieve super-resolution using broadband time reversal focusing techniques. It is shown that the equivalent circuit model is capable of quantifying this change in phase speed of the crystal and also the small-scale wave-resonator interactions within the crystal. The equivalent circuit model enables the parameterization of the physical variables and the optimization of the focusing bandwidth by balancing the combination of increasing resolution and decreasing amplitude near the resonance frequency. It is shown that the quality factor—in this case, the quality factor determined by the geometric shape of each resonator—controls the range of frequencies that are strongly affected by the Helmholtz resonators.

Sounds to Astound is an acoustics demonstration show, produced for the community twice yearly by the Brigham Young University Student Chapter of the Acoustical Society of America. The free, interactive demonstration show explores the science of sound for a target audience of fifth- to eighth-grade students. Introductory acoustics concepts, such as longitudinal wave motion, wave properties, propagation effects, and standing waves, are taught with live demonstrations, animations, and videos. The goal of this paper is to inspire and encourage readers in their outreach efforts by describing the purposes of Sounds to Astound and technical details of several entertaining and educational demonstrations. Lessons learned from a decade of these student-produced shows serve as an aid for future efforts and highlight the benefits of outreach efforts, particularly for the students involved.

Time reversal (TR) signal processing is an effective tool to exploit a reverberant environment for the intentional focusing of airborne, audible sound. A previous room acoustics TR study found preliminary evidence that above a certain focal amplitude the focal waveform begins to display signs of nonlinearity [Willardson, Anderson, Young, Denison, and Patchett, J. Acoust. Soc. Am. 143(2), 696–705 (2018)]. This study investigates that nonlinearity further by increasing the focal peak amplitudes beyond that previously observed. This increases the nonlinear characteristics, allowing for a closer inspection of their properties. An experiment is conducted using eight horn loudspeaker sources and a single receiver in a reverberation chamber. A maximum peak focal amplitude of 214.8 kPa (200.6 dBpk) is achieved. The focus signal waveforms are linearly scaled to observe and characterize the nonlinear amplification of the waveform. Frequency spectra of the peak focal amplitudes are plotted to observe changes in frequency content as the signals become nonlinear. A one-dimensional spatial scan of the focal region is conducted to observe properties of the converging and diverging waves. A proposal for a possible explanation involving free-space Mach stem formation is given.

Time reversal (TR) is a method of focusing wave energy at a point in space. The optimization of a TR demonstration is described, which knocks over one selected LEGO minifigure among other minifigures by focusing the vibrations within an aluminum plate at the target minifigure. The aim is to achieve a high repeatability of the demonstration along with reduced costs to create a museum exhibit. By comparing the minifigure's motion to the plate's motion directly beneath its feet, it is determined that a major factor inhibiting the repeatability is that the smaller vibrations before the focal event cause the minifigure to bounce repeatedly and it ends up being in the air during the main vibrational focal event, which was intended to launch the minifigure. The deconvolution TR technique is determined to be optimal in providing the demonstration repeatability. The amplitude, frequency, and plate thickness are optimized in a laboratory setting. An eddy current sensor is then used to reduce the costs, and the impact on the repeatability is determined. A description is given of the implementation of the demonstration for a museum exhibit. This demonstration illustrates the power of the focusing acoustic waves, and the principles learned by optimizing this demonstration can be applied to other real-world applications.

A phononic crystal acts as a dispersive medium with a phase speed that is lower than the bulk wave speed at frequencies below the resonance of a single resonator. Time reversal is used to compensate for the phase shifts caused by individual resonators as the waves enter the medium and enable focusing of acoustic waves among the crystal. An equivalent circuit, which can predict the dispersion and attenuation of the crystal model, is shown and compared to a full-wave finite-element simulation in frequency and time. The phase shift due to a single resonator is also depicted.

In acoustics, time-reversal processing is commonly used to exploit multiple scatterings in reverberant environments to focus sound to a specific location. Recently, the nonlinear characteristics of time-reversal focusing at amplitudes as high as 200 dB have been reported [Patchett and Anderson, J. Acoust. Soc. Am. 151(6), 3603–3614 (2022)]. These studies were experimental in nature and suggested that converging waves nonlinearly interact in the focusing of waves, leading to nonlinear amplification. This study investigates the nonlinear interactions and subsequent characteristics from a model-based approach. Utilizing both finite difference and finite-element models, it is shown that nonlinear interactions between high-amplitude waves lead to free-space Mach-wave coalescence of the converging waves. The number of waves used in both models represents a small piece of the full aperture of converging waves experimentally. Limiting the number of waves limits the number of Mach-stem formations and reduces the nonlinear growth of the focus amplitudes when compared to experiment. However, limiting the number of waves allows the identification of individual Mach waves. Mach wave coalescence leading to Mach-stem formation appears to be the mechanism behind nonlinear amplification of peak focus amplitudes observed in high-amplitude time-reversal focusing.

Super resolution is possible using resonators placed in the near field of time reversal focusing. This presentation addresses the problem that a two-dimensional Helmholtz resonator array in a three-dimensional reverberant environment has limited ability to produce a high-resolution spatial focus in the time reversal focusing of audible sound. Acoustic waves propagating out-of-plane with the resonator array are not as strongly modified by the resonators, partially negating the effect of the resonators. The use of a two-dimensional waveguide limits the out-of-plane propagation, leading to improved resolution. It is also shown that post processing using an orthogonal particle velocity decomposition of a spatial scan of the focusing can limit out-of-plane particle motion in the near field of the array, which bypasses the effect of the unwanted third spatial dimension of propagation. Each of these techniques results in a pressure field focus reconstruction that has a higher spatial resolution.

In acoustics, time reversal processing may be used to focus sound to a selected spatial location. Recently, the nonlinear characteristics of time-reversalfocusing at amplitudes as high as 200 dB have been reported [Patchett and Anderson, J. Acoust. Soc. Am., 151(6), (2022)]. These studies were experimental in nature and suggested that converging waves nonlinearly interact in the focusing of waves, leading to surprising observations of nonlinear amplification. This study investigates the nonlinear interactions and subsequent characteristics from a model-based approach. Utilizing both the k-Wave© package for MATLAB©, and COMSOL Multiphysics©, it is shown that nonlinear interactions between high-amplitude waves leads to free-space Mach-wave coalescence of the converging waves. The number of waves used in both models represents a small piece of the full aperture of converging waves experimentally. Limiting the number of waves limits the number of Mach-stem formations and reduces the nonlinear growth of thefocus amplitudes when compared to experiment. However, limiting the number of waves allows the identification of individual Mach waves. Mach wave coalescence leading to Mach-stem formation appears to be the mechanism behind nonlinear amplification of peak focus amplitudes observed in high amplitude time reversal focusing.

Poor acoustics in a classroom can lead to vocal strain and heath challenges for teachers using these rooms over many years. In some cases, voice amplification can be used to help alleviate vocal strain. The acoustics of various types of elementary and secondary school (K–12) classrooms in Utah were assessed with speech parameters calculated from impulse response measurements for teacher to student interactions (using a dodecahedron loudspeaker and microphone) as well as oral binaural impulse responses for the teacher’s perception of the room (using a KEMAR mannequin with a mouth simulator). The use of and impact on speech intelligibility of voice amplification was also investigated. This study is part of an overall effort to better assess the degree to which rooms with poor acoustics may impact vocal strain.

Time reversal (TR) is a signal processing technique that can be used to focus high amplitude sound or vibration at a desired location. TR focusing can be done with sources placed far from the desired focal location and the technique excels in complex environments. The impulse response between each source and the desired focal location must be obtained prior to the focusing and the environment must remain relatively unchanged for successful focusing. Multiple scattering or reverberation of waves off of many reflecting surfaces in the environment can actually be used advantageously by exploiting those reflections as additional image sources. This talk will provide an introduction to TR and then focus on the use of TR to provide high amplitude focusing of sound and vibration. Applications of high amplitude TR include lithotripsy of kidney stones, histotripsy of lesions, and locating cracks and defects in structures such as in human teeth, spent nuclear fuel storage casks, airplane wings, and automotive bearing caps. Recently, high amplitude TR of airborne sound has been studied in a reverberation chamber to generate a focused difference frequency and to study the nonlinear acoustics of the peak sound levels of 200 dB that have been attained.

Exciting structures with a broadband noise signal is a method used to assess a structure’s health and how it responds to the noise. Past work has shown that time reversal (TR) acoustics has provided a robust method to focus impulses at high amplitudes. Maximization of the highest possible amplitude while maintaining the desired spectral shape can be challenging. This study explores the benefits of using TR with equalization methods to a steady state broadband noise signal to acoustically excite structures. Tradeoffs exist between the possible amplitude of the focused noise and the duration of the noise and the amount of equalization employed. The spatial extent of the focusing will also be discussed. The use of TR to generate high amplitude broadband noise is compared to standard point application of noise equalization with the overall goal to use this high amplitude noise to excite structures under test.

School teachers’ voice problems are widespread and influence the learning process. Voice amplification systems in classrooms are a common response and a preventative strategy. The primary purpose of this study was to (1) determine the relationship between teacher vocal fatigue and use of classroom amplification; and (2) identify factors influencing amplification usage. Teachers throughout the US completed questionnaires regarding vocal health, classroom conditions, lifestyle habits, and access to and use of vocal amplification systems. Responses indicated that biological female teachers who used voice amplification or taught grades kindergarten to middle school were more likely to report higher levels of vocal fatigue. Further, teachers with access to amplification systems were more likely to use them if they were teachers in lower grade levels, who smoked occasionally, drank alcohol frequently, and taught in larger capacity classrooms. In conclusion, it maybe that those using the amplifications are using them because of pre-existing voice issues. Finally, the work-related factors associated with the use of amplification systems (e.g., grade level, classroom capacity) may be indicators of adjustments to reduce the occurrence of voice problems among teachers. Ongoing studies reviewing the available classroom amplification equipment and use from a school administrators perspective will be discussed.

Time reversal is a technique that allows the focusing of sound from a source to a remote location causing an impulsive focusing event. Using more sources and other amplitude-increasing techniques, the focusing of audible sound can reach over 200 dB peak. This can extinguish the flame on a single candle without affecting nearby lit candles. Most methods used to extinguish a flame using sound involve the nearfield and nonlinear airflow effects. Because time reversal focusing can occur far from the sources, the mechanism is different. Using high-speed video footage of the focal event, we can see the finer details of this millisecond scale focus interacting with the flame. Measuring the sound field during the focus event at and near the focal location also sheds light on the mechanism. So far, it has been seen that the focus pushes the flame outward, separating the plasma from its fuel source. The known formation of shock waves provides a possible explanation. Further research is being done to explore the cause of the extinguishing of the flame. This talk will show that not only is it possible to focus high amplitude sound waves but targeted flows of air as well.

The natural frequency resonances and sound radiation from one-dimensional acoustic systems are of great interest in the study of musical instruments, human vocal tract effects on speech, automotive exhaust pipes, duct systems for temperature control in buildings, and more. The impedance translation theorem is an approach that may be used to solve for the input impedance and therefore the resonance frequencies of one-dimensional systems. Equivalent circuits offer another approach to solving one-dimensional systems, though with equivalent circuits you can also solve for the response at any location in the system, including the radiated sound pressure. At Brigham Young University, there are two graduate level courses that teach these two techniques. One of the most challenging and memorable homework assignments from these courses is based on using one of these techniques to analyze a particular acoustic system and compare its response with the real thing. This paper discusses the basics of these two techniques and applies them to an analysis of phonemes produced by altering the human vocal tract. Details about the homework assignments are also given.

Time reversal (TR) is a signal processing technique often used to generate focusing at selected positions within reverberant environments. This study investigates the effect of the location of the focusing, with respect to the room wall boundaries, on the amplitude of the focusing and the uniformity of this amplitude when focusing at various room locations. This is done experimentally with eight sources and two reverberation chambers. The chambers are of differing dimensions and were chosen to verify the findings in different volume environments. Multiple spatial positions for the TR focusing are explored within the rooms' diffuse field, against a single wall, along a two-wall edge, and in the corners (three walls). Measurements of TR focusing at various locations within the room show that for each region of study, the peak amplitude of the focusing is quite uniform, and there is a notable and consistent increase in amplitude for each additional wall that is adjacent to the focal location. A numerical model was created to simulate the TR process in the larger reverberation chamber. This model returned results similar to those of the experiments, with spatial uniformity of focusing within the room and increases when the focusing is near adjacent walls.

Time reversal (TR) focusing of airborne ultrasound in a room is demonstrated. Various methods are employed to increase the amplitude of the focus. These methods include creating a small wooden box (or chamber) to act as a miniature reverberation chamber, using multiple sources, and using the clipping processing method. The use of a beam blocker to make the sources more omnidirectional is also examined, and it is found that for most source/microphone orientations, the use of a beam blocker increases the amplitude of the focus. A high-amplitude focus of 134 dB peak re 20 μPa sound pressure level with a center frequency of about 38 kHz is generated using TR. Using four sources centered at 36.1 kHz and another four sources centered at 39.6 kHz, nonlinear difference frequency content centered at 3.5 kHz is observed in the focus signal. The difference frequency amplitude grows quadratically with increasing primary frequency amplitude. When using beam blockers, the difference frequency content propagates away from the focal location with higher amplitude than when beam blockers are not used. This is likely due to the differences in the directionality of the converging waves during TR focusing.

Time Reversal (TR) is a technique that may be used to focus an acoustic signal at a particular point in space. The effect of transducer placement within a room as well as the layout of several sources are explored. Maximum focal amplitude and spatial clarity are found to increase when the focus location is dual coplanar to the source location while temporal quality is found to decrease in comparison to the case when source and focal location share only one plane. Maximum focal amplitude is found to be at a minimum when the focus location is at the critical distance and increases closer and farther away from the source, while temporal quality steadily decreases and spatial clarity steady increases farther from the source. The maximum focal amplitude and the temporal quality are not greatly affected by the type of array layout, but a circular array, even without half wavelength spacing, is ideal for maximizing spatial clarity.

Time reversal (TR) focusing used for nonlinear detection of cracks relies on the ability of the TR process to provide spatially localized, high-amplitude excitation. The high amplitude improves the ability to detect nonlinear features that are a signature of the motion of closed cracks. It follows that a higher peak focal amplitude than what can be generated with the traditional TR process will improve the detection capability. Modifying the time-reversed impulse response to increase the amplitude of later arrivals in the impulse response, while maintaining the phase information of all arrivals, increases the overall focal signal amplitude. A variety of existing techniques for increasing amplitude are discussed, and decay compensation TR, a technique wherein amplitude is increased according to the inverse of the amplitude envelope of the impulse response decay, is identified as the best modification technique for nonlinear crack detection. This technique increases the focal signal amplitude with a minor introduction of harmonic content, a drawback in two other methods studied, one-bit TR and clipping TR. A final study employs both decay compensation TR and traditional TR, focusing on a rod with stress corrosion cracking, and compares the merits of each in detecting nonlinearity from cracks in a real system.

Stainless steel containers are susceptible to stress corrosion cracking (SCC) under certain stress and corrosion conditions. Nonlinear ultrasonic techniques are very sensitive to the early presence of damage, more so than linear techniques. Nonlinear Resonant Ultrasound Spectroscopy (NRUS) is used here to measure a nonlinear shift in the resonance frequency due to a cumulative amount of SCC. Steel rods are immersed in a heated magnesium chloride solution and removed after different exposure times. NRUS measurements are conducted using the fundamental longitudinal mode of vibration. Rods exposed longer generally have a larger resonance frequency shift and are therefore more nonlinear. Thus NRUS might offer a means of detecting a cumulative SCC damage in a sample.

Graduate studies in acoustics at Brigham Young University prepare students for industry, research, and academia by complementing in-depth coursework with publishable research. Coursework provides a solid foundation in core acoustical principles and practices and measurement skills, including a strong foundation in experimental techniques and technical writing. Labs across the curriculum cover calibration, directivity, scattering, absorption, laser Doppler vibrometry, experimental methods for dynamic structures, lumped-element mechanical systems, equivalent circuit modeling, arrays, filters, room acoustics, active noise control, and near-field acoustical holography. Recent thesis and dissertation topics include active noise control, directivity, room acoustics, energy-based acoustics, time reversal, nondestructive evaluation, vibration and acoustics of aerospace vehicles, biomedical applications, flow-based acoustics, voice production, aeroacoustics, sound propagation modeling, nonlinear propagation, high-amplitude noise analyses, machine and deep learning applied to ambient noise level prediction, crowd noise interpretation, and underwater acoustic source localization, and ocean environment classification. Graduate students are expected to present research at professional meetings and publish in peer-reviewed acoustics journals. Additionally, graduate students often serve as peer mentors to undergraduate students on related projects and may participate in field experiments to gain additional experience.@BYUAcoustics

Time reversal is used as an energy-focusing technique in nondestructive evaluation applications. Here, it is often of interest to evaluate small samples or samples that do not lend themselves to the bonding of transducers to their surfaces. A reverberant cavity, called a chaotic cavity, attached to the sample of interest provides space for the attachment of transducers as well as an added reverberant environment, which reverberation is critical to the quality of time reversal focusing. The goal of this research is to explore the dependence of the quality of the time reversal focusing on the size and geometric shape of the chaotic cavity used. An optimal chaotic cavity will produce the largest focusing amplitude, best spatial resolution, and linear focusing of the time reversed signal. Ultrasonic elastic-wave experiments are performed on a rectangular, cylindrical, and three-dimensional Sinai billiard prism samples, and experiments are repeated each time these samples are successively cut down to smaller volumes. As the size of the cavity decreases, the peak amplitude may increase or decrease depending on the normalization scheme employed. The higher the degree of ergodicity of the cavity, the higher the amplitude and quality focusing achieved.

This presentation will discuss the time reversal focusing of audible sound over an array of Helmholtz resonators. The presence of the resonators modifies the phase speed of waves, thereby lowering the effective wavelength, in the near field of the focus. It is shown experimentally what conditions are necessary to obtain super resolution. Frequencies above the resonators’ resonance frequency do not result in super resolution. In order to achieve super resolution in the plane of the resonators, the focused waves must be confined to propagate only in the plane of the resonators. When waves converged in three dimensions, super-resolution was not observed but when a 2-D waveguide was used, and super-resolution was observed.

This presentation will discuss the possibility of using path-diverting scatterers in time reversal focusing to achieve super resolution. In particular, use of a one-dimensional pipe system with varying lengths of diverting pipes is shown to decrease the effective wave speed. This provides insight, albeit in an extreme case, of how scatterers can force sound to travel a longer path as the waves converge to the focal location. As the effective wave speed decreases, the spatial extent of the focusing decreases, creating an apparent super resolution when compared to the speed of sound in an unaltered pipe system. Previous work achieved super resolution with what they described as scatterers, but it is likely that their scatterers are better classified as resonators, and consequently, it has yet to be shown that scatterers can be used to obtain super resolution.

Time reversal is a method often used to focus sound to a desired location within a reverberant environment. Recent high-amplitude focusing experiments have shown that when multiple sources are used simultaneously to generate a focus, the level reached (200 dB) is higher than if each source were focused individually with the signals being superposed computationally. An investigation into the temporal and spatial features and harmonic content of each method is presented in order to work toward an understanding of the mechanisms driving the nonlinear increases observed when the sources are combined acoustically as opposed to being summed in post-processing.

Time reversal (TR) is a process that can be used to generate high amplitude focusing of sound. It has been previously shown that using TR in reverberant environments to cause high amplitude foci will in fact have multiple nonlinear properties including waveform steepening and a nonlinear increase in peak pressure compressions. This study investigates the removal of one possible cause for these phenomena: free-space Mach stems. By isolating the focus into a 1-D system, the potential formation of Mach stems is eliminated so that remaining effects can be qualitatively observed. To achieve this, a system of pipes is used to restrict the focused waves to be planar in a 1-D reverberant environment. Preliminary results have shown that waveform steepening effects remain as expected but that the nonlinear increase in compression amplitudes disappears, which is consistent with the idea that free-space Mach stems cannot be formed in a 1-D system.

This presentation will outline the physical and practical considerations for conducting a COMSOL simulation of time reversal focusing in air. Attempts to obtain sub-diffraction-limited time reversal focusing, along with physical and practical consideration, will be presented. Physical considerations include end-corrections, resonator shape and placement, computational domain and anechoic terminations. Practical considerations include mesh size and temporal length. While conducting a time domain study in COMSOL, mesh size is related to the highest frequency and the simulation length is related to the lowest frequency. To maximize computational resources, the simulation uses a restricted bandwidth. Extending the bandwidth is accomplished by combining multiple simulations. Comparison to previous super resolution studies as well as the authors’ equivalent circuit model will also be discussed.

Time reversal (TR) is a signal processing technique that can be used for intentional sound focusing. While it has been studied in room acoustics, the application of TR to produce a high amplitude focus of sound in a room has not yet been explored. The purpose of this study is to create a virtual source of spherical waves with TR that are of sufficient intensity to study nonlinear acoustic propagation. A parameterization study of deconvolution, one-bit, clipping, and decay compensation TR methods is performed to optimize high amplitude focusing and temporal signal focus quality. Of all TR methods studied, clipping is shown to produce the highest amplitude focal signal. An experiment utilizing eight horn loudspeakers in a reverberation chamber is done with the clipping TR method. A peak focal amplitude of 9.05 kPa (173.1 dB peak re 20 μPa) is achieved. Results from this experiment indicate that this high amplitude focusing is a nonlinear process.

Time reversal (TR) focusing of high-amplitude airborne ultrasound can be used to create a difference frequency. Methods are employed to increase the amplitude of the focus. These methods include creating a miniature reverberation chamber, using multiple sources, and using the clipping processing method. The use of a beam blocker to make the sources more omnidirectional is also examined, and it is found that for most source/microphone orientations, the use of a beam blocker increases the amplitude of the focus. A high-amplitude focus of 134 dB peak re 20 μPa sound pressure level with a center frequency of about 38 kHz is generated using eight sources. Then, using four sources centered at 36.1 kHz and another four sources centered a 39.6 kHz, nonlinear difference frequency content centered at 3.5kHz is observed in the focus signal. The difference frequency amplitude grows quadratically with increasing primary frequency amplitude. When using beam blockers, the difference frequency content propagates away from the focal location with higher amplitude than when beam blockers are not used. This is likely due to the differences in the directionality of the converging waves during TR focusing.

Historically Black colleges and universities (HBCUs) have a long-standing history of engaging the African-American community. In most instances, these institutions are located in predominantly African-American communities. This article intends to offer a discussion of a pedagogical approach used at an HBCU, located in a large mid-Atlantic city. The purpose of this macro-assignment was an effort designed to prepare BSW students for macro-practice with communities through participation in service-learning projects that involved community engagement with urban communities. Outcomes reflect that students have a vested interest in working with underserved communities, which exemplifies the School of Social Work’s mission; said mission is to fully prepare urban social work leaders who are committed to the alleviation of human suffering, social justice, and the improvement of the quality of life for diverse urban populations.

This paper explores the feasibility of active control of noise from magnetic resonance imaging (MRI) systems using control sources placed outside of the region that MRI scanners are sensitive to ferrous materials. Active noise control (ANC) is shown here to be equivalent to the time reversal (TR) inverse filter technique with a 180° phase shift. Since TR is capable of remotely focusing sound energy to a point in space, it follows that ANC may also be remotely focused. This paper explores the remote delivery of a noise-canceling signal to a desired location (e.g. a patient’s ears). A parameterization study testing frequency dependence and signal length is conducted to determine the effectiveness of the remote delivery. The reduction of MRI noise using ANC is demonstrated using recordings of MRI noise. The parameterization and MRI noise reduction studies are conducted in a reverberation chamber and in a laboratory room with a lower reverberation time. Frequencies below 1 kHz and narrowband signals are easier to control, with reductions up to 20 dB. MRI noise is reduced by up to 18 dB in overall sound pressure level. These results utilized a single control loudspeaker; further reductions should be possible with multiple control sources.

Acoustic reflections in rooms are best understood and controlled when their causal surfaces have been accurately localized. Several in situ measurement techniques have been proposed over the years to pinpoint reflections via estimated directions of arrival at chosen field positions. The polar energy time curve (Polar ETC) is one approach requiring six cardioid impulse response measurements along the Cartesian axes about a point in a room. This paper presents a theoretical, numerical, and experimental investigation of its estimation errors due to simultaneous sound arrivals. Theoretical developments provide insights into their causes. Numerical examples based on the method of images explore conditions leading to the errors and likely error magnitudes. Experimental work using discrete planar reflectors in an anechoic chamber produced controlled reflections to further investigate the effects. An altazimuth-mounted laser and mirrors enabled reflection tracing and a means of measuring and comparing arrival directions to those estimated by the Polar ETC. The efforts demonstrate that the Polar ETC provides credible angular estimations for individual arrivals, but spurious results for most simultaneous arrivals. Single arrivals produce absolute errors of only a few degrees, while simultaneous arrivals of similar amplitudes produce errors ranging sporadically from a few degrees to many degrees.

The purpose of this research is to develop a visual demonstration of time reversal focusing of vibrations in a thin plate. Various plate materials are tested to provide optimal conditions for time reversal focusing. Specifically, the reverberation time in each plate and the vibration coupling efficiency from a shaker to the plate are quantified to illustrate why a given plate provides the best spatially confined focus as well as the highest focal amplitude possible. A single vibration speaker and a scanning laser Doppler vibrometer (SLDV) are used to provide the time reversal focusing. Table salt is sprinkled onto the plate surface to allow visualization of the high amplitude, spatially localized time reversal focus; the salt is thrown upward only at the focal position. Spatial mapping of the vibration focusing on the plate using the SLDV is correlated to the visual salt jumping demonstration. The time reversal focusing is also used to knock over an object when the object is placed at the focal position; some discussion of optimal objects to use for this demonstration are given.

Evidence of the ability to probe depth information of stress corrosion cracking (SCC) are presented using the time reversed elastic nonlinearity diagnostic (TREND). Depth estimation of SCC is important to determine when a stainless steel canister has been breached. TREND is a method to focus elastic energy to a point in space in order to probe that point for damage and its' depth penetration is used here to study depth information about SCC. High frequencies are used to probe near the surface, while low frequencies are used to probe deeper into a stainless steel section of a cylinder.

The Time Reversed Elastic Nonlinearity Diagnostic (TREND) has a long history of successful nondestructive detection of cracks in solids using nonlinear indicators. Recent research implemented TREND to find stress corrosion cracking (SCC) in the heat-affected zone adjacent to welds in stainless steel. SCC development around welds is likely to occur due to the temperature and chemical exposure of steel canisters housing spent nuclear fuel. The ideal SCC detection technique would quantify the size and extent of the SCC, rather than just locating it, as TREND has been used for in the past. The current paper explores TREND's ability to detect an assumed increase in SCC over time using 13 samples exposed to a magnesium chloride (MgCl2) bath for different lengths of time. The samples are then scanned with TREND and nonlinearity is quantified for each scan point and each sample. The results suggest that TREND can be used to not only locate SCC in the heat-affected zone, but also track an increase in nonlinearity, and thereby an increase in damage, in samples exposed to the MgCl2 solution for a longer duration.

Time Reversal (TR) is a technique that may be used to focus an acoustic signal at a particular point in space. While many variables contribute to the quality of TR focusing of sound in a particular room, the most important have been shown to be the number of sound sources, signal bandwidth, and absorption properties of the medium as noted by Ribay, de Rosny, and Fink [J. Acoust. Soc. Am. 117(5), 2866-2872 (2005)]. However, the effect of room size on TR focusing has not been explored. Using the image source method algorithm proposed by Allen and Berkley [J. Acoust. Soc. Am. 65(4), 943-950 (1979)], TR focusing was simulated in a variety of rooms with different absorption and volume properties. Experiments are also conducted in a couple rooms to verify the simulations. The peak focal amplitude, the temporal focus quality, and the spatial focus clarity are defined and calculated for each simulation. The results are used to determine the effects of absorption and room volume on TR. Less absorption increases the amplitude of the focusing and spatial clarity while decreasing temporal quality. Dissimilarly, larger volumes decrease focal amplitude and spatial clarity while increasing temporal quality.