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The lowermost portion of an explosive volcanic eruption column is considered a momentum-driven jet. Understanding volcanic jets is critical for determining eruption column dynamics and mitigating volcanic hazards; however, volcanic jets are inherently difficult to observe due to their violence and opacity. Infrasound from the 2011 eruption of Nabro Volcano, Eritrea has waveform features highly similar to the "crackle" phenomenon uniquely produced by man-made supersonic jet engines and rockets and is characterized by repeated asymmetric compressions followed by weaker, gradual rarefactions. This infrasonic crackle indicates that infrasound source mechanisms in sustained volcanic eruptions are strikingly similar to jet noise sources from heated, supersonic jet engines and rockets, suggesting that volcanologists can utilize the modeling and physical understandings of man-made jets to understand volcanic jets. The unique, distinctive infrasonic crackle from Nabro highlights the use of infrasound to remotely detect and characterize hazardous eruptions and its potential to determine volcanic jet parameters. Key Points Nabro Volcano produced sound similar to supersonic jet engines and rockets Volcanic and man-made jets have similar sound source mechanisms Infrasound can remotely detect and characterize volcanic eruptions and jets. © 2013. American Geophysical Union. All Rights Reserved.

When the SpaceX Falcon-9 rocket booster descends through the atmosphere after a launch, it produces a sonic boom with three shocks in the far field, rather than the usual two-shock N-wave. In this Letter, the additional shock's origin is explained using sonic boom theory, nonlinear propagation modeling, computational fluid dynamics, and photographic evidence. The extra central shock results from a forward-migrating compression wave caused by the grid fins merging with a rearward-migrating rarefaction wave caused by the lower portions of the booster, including the folded landing legs., (© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

This Letter analyzes launch noise from Starship Super Heavy's Flights 5 and 6. While Flight-5 data covered 9.7-35.5 km, the stations during Flight 6 spanned 1.0-35.5 km. A comparison of A-weighted and unweighted maximum and exposure levels is made between flights and with an updated environmental assessment (EA). Key findings include: (a) the two flights' noise levels diverge beyond 10 km, (b) EA models overestimate A-weighted metrics, and (c) the acoustic energy from a Starship launch is equivalent to 2.2 Space Launch System launches or ∼11 Falcon 9 launches. These measurements help predict Starship's noise levels around Kennedy Space Center., (© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

Far-field (9.7-35.5 km) noise measurements were made during the fifth flight test of SpaceX's Starship Super Heavy, which included the first-ever booster catch. Key results involving launch and flyback sonic boom sound levels include (a) A-weighted sound exposure levels during launch are 18 dB less than predicted at 35 km; (b) the flyback sonic boom exceeds 10 psf at 10 km; and (c) comparing Starship launch noise to Space Launch System and Falcon 9 shows that Starship is substantially louder; the far-field noise produced during a Starship launch is at least ten times that of Falcon 9., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).)

The National Transportation Noise Map predicts time-averaged road traffic noise across the continental United States (CONUS) based on annual average daily traffic counts. However, traffic noise can vary greatly with time. This paper outlines a method for predicting nationwide hourly varying source traffic sound emissions called the Vehicular Reduced-Order Observation-based Model (VROOM). The method incorporates three models that predict temporal variability of traffic volume, predict temporal variability of different traffic classes, and use Traffic Noise Model (TNM) 3.0 equations to give traffic noise emission levels based on vehicle numbers and class mix. Location-specific features are used to predict average class mix across CONUS. VROOM then incorporates dynamic traffic class mix data to obtain dynamic traffic class mix. TNM 3.0 equations then give estimated equivalent sound level emission spectra near roads with up to hourly resolution. Important temporal traffic noise characteristics are modeled, including diurnal traffic patterns, rush hours in urban locations, and weekly and yearly variation. Examples of the temporal variability are depicted and possible types of uncertainties are identified. Altogether, VROOM can be used to map national transportation noise with temporal and spectral variability., (© 2024 Acoustical Society of America.)

During NASA X-59 quiet supersonic aircraft community response tests, low-boom recordings will contain contaminating noise from instrumentation and ambient acoustical sources. This noise can inflate sonic boom perception metrics by several decibels. This paper discusses the development and comparison of robust lowpass filtering techniques for removing contaminating noise effects from low-boom recordings. The two filters are a time-domain Butterworth-magnitude filter and a frequency-domain Brick Wall filter. Both filters successfully reduce noise contamination in metric calculations for simulated data with real-world contaminating noise and demonstrate comparable performance to a modified ISO 11204 correction. The Brick Wall filter's success indicates that further attempts to match boom spectrum high-frequency roll-off beyond the contaminating noise floor are unnecessary and have marginal improvements on final metric calculations. Additionally, the Butterworth filter removes statistical correlation between ambient and boom levels for a real-world flight campaign, adding evidence that these techniques also work on other boom shapes. Overall, both filters can produce accurate metric calculations with only a few hundred hertz of positive signal-to-noise ratio. This work describes methods for accurate metric calculations in the presence of moderate noise contamination that should benefit X-59 and future low-boom supersonic aircraft testing., (© 2024 Acoustical Society of America.)

Separating crowd responses from raw acoustic signals at sporting events is challenging because recordings contain complex combinations of acoustic sources, including crowd noise, music, individual voices, and public address (PA) systems. This paper presents a data-driven decomposition of recordings of 30 collegiate sporting events. The decomposition uses machine-learning methods to find three principal spectral shapes that separate various acoustic sources. First, the distributions of recorded one-half-second equivalent continuous sound levels from men's and women's basketball and volleyball games are analyzed with regard to crowd size and venue. Using 24 one-third-octave bands between 50 Hz and 10 kHz, spectrograms from each type of game are then analyzed. Based on principal component analysis, 87.5% of the spectral variation in the signals can be represented with three principal components, regardless of sport, venue, or crowd composition. Using the resulting three-dimensional component coefficient representation, a Gaussian mixture model clustering analysis finds nine different clusters. These clusters separate audibly distinct signals and represent various combinations of acoustic sources, including crowd noise, music, individual voices, and the PA system., (© 2024 Acoustical Society of America.)

To improve acoustical models of super heavy-lift launch vehicles, this Letter reports Space Launch System's (SLS's) overall sound power level (OAPWL) and compares it to NASA's past lunar rocket, the Saturn V. Measurements made 1.4-1.8 km from the launchpad indicate that SLS produced an OAPWL of 202.4 (±0.5) dB re 1 pW and acoustic efficiency of about 0.33%. Adjustment of a static-fire sound power spectrum for launch conditions implies Saturn V was at least 2 dB louder than SLS with approximately twice the acoustic efficiency., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

The National Transportation Noise Map (NTNM) gives time-averaged traffic noise across the continental United States (CONUS) using annual average daily traffic. However, traffic noise varies significantly with time. This paper outlines the development and utility of a traffic volume model which is part of VROOM, the Vehicular Reduced-Order Observation-based model, which, using hourly traffic volume data from thousands of traffic monitoring stations across CONUS, predicts nationwide hourly varying traffic source noise. Fourier analysis finds daily, weekly, and yearly temporal traffic volume cycles at individual traffic monitoring stations. Then, principal component analysis uses denoised Fourier spectra to find the most widespread cyclic traffic patterns. VROOM uses nine principal components to represent hourly traffic characteristics for any location, encapsulating daily, weekly, and yearly variation. The principal component coefficients are predicted across CONUS using location-specific features. Expected traffic volume model sound level errors-obtained by comparing predicted traffic counts to measured traffic counts-and expected NTNM-like errors, are presented. VROOM errors are typically within a couple of decibels, whereas NTNM-like errors are often inaccurate, even exceeding 10 decibels. This work details the first steps towards creation of a temporally and spectrally variable national transportation noise map., (© 2023 Acoustical Society of America.)

The distinctive geometry and structural characteristics of Balinese gamelan gongs lead to the instrument's unique sound and musical style. This work presents high-resolution directivity measurements of two types of gamelan gongs to quantify and better understand their acoustic behavior. The measured instruments' structural modes clearly impact their far-field directivity patterns, with the number of directional lobes corresponding to the associated structural mode shapes. Many of the lowest modes produce dipole-like radiation, with the dipole moment determined by the positions of the nodal and antinodal regions. Higher modes exhibit more complex patterns with multiple lobes often correlated with the location and number of antinodal regions on the gong's edge. Directivity indices correspond to dipole radiation at low frequencies and quadrupole radiation at intermediate and higher frequencies. Symmetry analysis confirms that the gong's rim significantly impacts the resultant directivity., (© 2023 Acoustical Society of America.)

Modeling environmental sound levels over continental scales is difficult due to the variety of geospatial environments. Moreover, current continental-scale models depend upon machine learning and therefore face additional challenges due to limited acoustic training data. In previous work, an ensemble of machine learning models was used to predict environmental sound levels in the contiguous United States using a training set composed of 51 geospatial layers (downselected from 120) and acoustic data from 496 geographic sites from Pedersen, Transtrum, Gee, Lympany, James, and Salton [JASA Express Lett. 1(12), 122401 (2021)]. In this paper, the downselection process, which is based on factors such as data quality and inter-feature correlations, is described in further detail. To investigate additional dimensionality reduction, four different feature selection methods are applied to the 51 layers. Leave-one-out median absolute deviation cross-validation errors suggest that the number of geospatial features can be reduced to 15 without significant degradation of the model's predictive error. However, ensemble predictions demonstrate that feature selection results are sensitive to variations in details of the problem formulation and, therefore, should elicit some skepticism. These results suggest that more sophisticated dimensionality reduction techniques are necessary for problems with limited training data and different training and testing distributions., (© 2023 Acoustical Society of America.)

Classical jet noise theory indicates that radiated sound power is proportional to the jet velocity raised to the eighth and third powers for subsonic and supersonic jets, respectively. To connect full-scale measurements with classical jet noise theory, this letter presents sound power and acoustic efficiency values for an installed GE-F404 engine. When subsonic, the change in sound power follows the eighth-power law, and the sound power change approximately follows the third-power law at supersonic conditions, with an acoustic efficiency of ∼0.5-0.6%. However, the OAPWL increase from subsonic to supersonic jet velocities is greater than would be predicted., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

The nonlinear evolution of high-amplitude broadband noise is important to the psychoacoustic perception, usually annoyance, of high-speed jet noise. One method to characterize the nonlinear evolution of such noise is to consider a characteristic nonlinear waveform distortion length for the signal. A common length scale for this analysis is the shock formation distance of an initially sinusoidal signal. However, application of this length scale to broadband noise, even with the amplitude and source frequency replaced with characteristic values, may lead to underestimates of the overall nonlinear waveform distortion of the noise as indicated by the skewness of the time derivative of the acoustic pressure (or derivative skewness). This paper provides an alternative length scale derived directly from the evolution of the derivative skewness of Gaussian noise that may be more appropriate when analyzing the nonlinear evolution of broadband noise signals. This Gaussian-based length scale is shown to be a useful metric for its relative consistency and its physical interpretation. Various analytical predictions of the evolution of the derivative skewness for an ensemble of numerical simulations of noise propagation are used to highlight various aspects of this new length scale definition., (© 2023 U.S. Government.)

To improve understanding of super heavy-lift rocket acoustics, this letter documents initial findings from noise measurements during liftoff of the Space Launch System's Artemis-I mission. Overall sound pressure levels, waveform characteristics, and spectra are described at distances ranging from 1.5 to 5.2 km. Significant results include: (a) the solid rocket boosters' ignition overpressure is particularly intense in the direction of the pad flame trench exit; (b) post-liftoff maximum overall levels range from 127 to 136 dB, greater than pre-launch predictions; and (c) the average maximum one-third-octave spectral peak occurred at 20 Hz, causing significant deviation between flat and A-weighted levels.

High-fidelity measurement of sonic boom waveforms requires microphones and data acquisition hardware with flat frequency responses extending below 1 Hz. Hardware limitations can pose challenges meeting these requirements. This letter describes an engineering method involving digital pole-shift filtering that can be used in post-processing to extend effective hardware bandwidth. This approach is evaluated for sonic boom recordings from NASA's Quiet Supersonic Flights 2018 measurement campaign. Recordings of several booms at multiple measurement sites using different hardware/microphone combinations were used to design filters. Results demonstrate that the measurement-designed filters significantly reduce the mean square error between original and benchmark waveforms. Digital filter designs based on hardware manufacturer specifications also reduce error, but not as much. Residual errors after filtering, method limitations, and transferability to a launch vehicle reentry boom measurement are discussed.

Sonic boom measurements from recent flight tests have provided an opportunity to investigate effects of microphone installation on sonic boom waveforms, spectra, and metric levels in support of NASA X-59 flight test planning. While those flight tests used N-wave aircraft (F-18s), modeling studies were also conducted using source characteristics for a shaped low-boom aircraft. Of particular interest were the effects of receiver height on boom waveforms and metrics at elevated receiver positions, microphone installation, and local ground cover type. Reductions of more than 2 dB in A-weighted sound exposure level and perceived level were shown for 1.6 ft (0.48 m) microphone heights for 35º ray elevation angle. Measured and modeled results are described in this letter.

The Saturn V is a monument to one of mankind's greatest achievements: the human Moon landings. However, online claims about this vehicle's impressive acoustics by well-meaning individuals are often based on misunderstood or incorrect data. This article, intended for both educators and enthusiasts, discusses topics related to rocket acoustics and documents what is known about the Saturn V's levels: overall power, maximum overall sound pressure, and peak pressure. The overall power level was approximately 204 dB re 1 pW, whereas its lesser sound pressure levels were impacted by source size, directivity, and propagation effects. As this article is part of a special issue on Education in Acoustics in The Journal of the Acoustical Society of America, supplementary Saturn V-related homework problems are included.

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.

The 15 January 2022 climactic eruption of Hunga volcano, Tonga, produced an explosion in the atmosphere of a size that has not been documented in the modern geophysical record. The event generated a broad range of atmospheric waves observed globally by various ground-based and spaceborne instrumentation networks. Most prominent was the surface-guided Lamb wave (≲0.01 hertz), which we observed propagating for four (plus three antipodal) passages around Earth over 6 days. As measured by the Lamb wave amplitudes, the climactic Hunga explosion was comparable in size to that of the 1883 Krakatau eruption. The Hunga eruption produced remarkable globally detected infrasound (0.01 to 20 hertz), long-range (~10,000 kilometers) audible sound, and ionospheric perturbations. Seismometers worldwide recorded pure seismic and air-to-ground coupled waves. Air-to-sea coupling likely contributed to fast-arriving tsunamis. Here, we highlight exceptional observations of the atmospheric waves.

The phase and amplitude gradient estimator (PAGE) method [Thomas, Christensen, and Gee, J. Acoust. Soc. Am. 137, 3366-3376 (2015)] has been developed as an alternative to the traditional p-p method for calculating energy-based acoustic measures such as active acoustic intensity. While this method shows many marked improvements over the traditional method, such as a wider valid frequency bandwidth for broadband sources, contaminating noise can lead to inaccurate results. Contaminating noise degrades performance for both the traditional and PAGE methods and causes probe microphone pairs to exhibit low coherence. When coherence is low, better estimates of the pressure magnitude and gradient can be obtained by using a coherence-based approach, which yields a more accurate intensity estimate. This coherence-based approach to the PAGE method, known as the CPAGE method, employs two main coherence-based adjustments. The pressure magnitude adjustment mitigates the negative impact of uncorrelated contaminating noise and improves intensity magnitude calculation. The phase gradient adjustment uses coherence as a weighting to calculate the phase gradient for the probe and improves primarily the calculation of intensity direction. Though requiring a greater computation time than the PAGE method, the CPAGE method is shown to improve intensity calculations, both in magnitude and direction.

Although near-field acoustical holography (NAH) and acoustic intensity analysis have previously been used to investigate the apparent jet noise sources produced by military aircraft, explicit connections to supersonic jet characteristics cannot be made due to a lack of information about the exhaust plume. To begin to bridge this gap and better understand the source information yielded by NAH, the current study instead applies NAH to a virtual measurement of the near-field pressures of a highly heated laboratory-scale supersonic jet generated by large-eddy simulation (LES). The holographic reconstructions of the pressure, particle velocity, and acoustic intensity are found to match the LES-generated acoustic field well and are used to calculate the acoustic power of the jet. The jet's calculated overall acoustic power is compared to the free-stream mechanical power, resulting in an acoustic efficiency of 1.5%. Ray-tracing of the acoustic intensity to the jet centerline generates an axial distribution of the acoustic power origin, showing that almost all the power originates from the supersonic portion of the flow and with the distribution peak upstream of the potential core tip. Holographic reconstruction of the pressures along the nozzle lipline captures the general spectral shape of the LES-generated pressures, though it underestimates the amplitude.

In 1971, the U.S. National Aeronautics and Space Administration (NASA) published a seminal report-NASA SP-8072-which compiled the results of the early supersonic jet noise studies and provided methods to calculate the noise produced from launch vehicles. Fifty years later and despite known limitations, SP-8072 remains the foundation for much of the launch vehicle noise modeling today. This article reviews what has been learned about the physics of noise generation and radiation from free and impinging rocket plumes since the completion of SP-8072. State-of-the-art methods for the mitigation of launch vehicle noise are also reviewed. A discussion of launch vehicle noise modeling, from empirical to numerical and including reduced-order models of supersonic jets, points to promising approaches that can describe rocket noise characteristics not captured by SP-8072.

Modeling outdoor environmental sound levels is a challenging problem. This paper reports on a validation study of two continental-scale machine learning models using geospatial layers as inputs and the summer daytime A-weighted L 50 as a validation metric. The first model was developed by the National Park Service while the second was developed by the present authors. Validation errors greater than 20 dBA are observed. Large errors are attributed to limited acoustic training data. Validation environments are geospatially dissimilar to training sites, requiring models to extrapolate beyond their training sets. Results motivate further work in optimal data collection and uncertainty quantification.

This study investigates source-related noise characteristics of the Falcon 9, a modern launch vehicle with a high operational tempo. Empirical prediction of the noise characteristics of launched rockets has long been a topic of study; however, there are relatively few comparisons with high-fidelity, far-field data, and historical inconsistencies persist. Various quantities are considered: overall directivity, overall sound power, maximum overall sound pressure level (OASPL), and peak frequency. The noise directivity of the Falcon 9 vehicle is shown to be between two disparate ranges given in the historical literature, but the observed peak directivity angle is well represented using convective Mach number concepts. A comparison between mechanical and acoustic power yields a radiation efficiency is consistent with the literature. Two independent methods of predicting maximum OASPL produce results accurate within 2 dB, even at distances of several kilometers. Various scaling parameters are calculated for observed spectral peak frequency and connect these measurements with prior observations. Finally, the impact of terrain shielding on levels and spectra is assessed. These determined source characteristics of the Falcon 9 vehicle provide a connection to prior launch vehicle acoustics studies, which helps identify useful models and methods for understanding rocket noise.

Outdoor acoustic data often include non-acoustic pressures caused by atmospheric turbulence, particularly below a few hundred Hz in frequency, even when using microphone windscreens. This paper describes a method for automatic wind-noise classification and reduction in spectral data without requiring measured wind speeds. The method finds individual frequency bands matching the characteristic decreasing spectral slope of wind noise. Uncontaminated data from several short-timescale spectra can be used to obtain a decontaminated long-timescale spectrum. This method is validated with field-test data and can be applied to large datasets to efficiently find and reduce the negative impact of wind noise contamination.

Strategic control and eradication programs for wild pigs ( Sus scrofa ) are being developed to help curtail the expanding populations of this invasive, alien species. Drop nets and corral traps have a long history of capturing a multitude of wildlife species, so we evaluated the effectiveness and efficiency of these traps for controlling wild pigs in southern Oklahoma. We also developed and evaluated a suspended metal trap that provided real-time monitoring and deployment to capture animals. Effectiveness of each trap type was estimated as the proportion of pigs removed from the total population, whereas efficiency was calculated based on catch per unit effort (CPUE) (i.e., the number of person hours per pig removal). During 3 years of study (2010-2012), we removed 601 pigs, 296 using drop nets, 60 using corral traps, and 245 using suspended traps. Suspended traps removed 88.1% of the estimated population, whereas drop nets removed 85.7% and corral traps removed 48.5%. CPUE was 0.64 person hours/pig using suspended traps followed by 1.9 person hours/pig for drop nets and 2.3 person hours/pig for corral traps. Drop nets and suspended traps were more effective at removing a large proportion of the population (>85%), mainly through whole sounder removal, but the suspended trap with real-time notifications was the most efficient trap type, requiring fewer person hours to operate.

Skewness values for the pressure time derivative are greater at ground-based measurements near a tactical aircraft than they are at nearby off-ground locations. A possible explanation for this phenomenon is the occurrence of nonlinear, irregular shock reflections at the ground. Propagation angle, source location, and corresponding angle of incidence relative to the ground are estimated using a two-point cross correlation of windowed shock events. Nonlinear reflections are likely to occur based on the combination of angles of incidence and measured shock strengths and cause a pressure increase at the shock that is greater than twice the free-field pressure. The associated pressure increase at the shocks appears to enhance shock-related metrics at the ground compared to off-ground locations.

This letter describes how a landmark 1960s supersonic jet noise experiment influenced subsequent noise models. A discrepancy in other researchers' application of Potter and Jones's axial decomposition of the sound power generated from a laboratory-scale jet can be traced to an erroneous plot in the original report. Whereas most jet noise research indicates the dominant sound power is generated upstream of the supersonic core tip, propagation of this error in the ubiquitous NASA SP-8072 report has caused rocket noise modelers for five decades to disproportionately allocate sound power generation to the subsonic flow.

Since the Morfey-Howell Q/S was introduced as a single-point frequency-domain nonlinearity indicator for propagation of intense broadband noise [AIAA J. 19, 986-992 (1981)], there has been debate about its validity, utility, and interpretation. In this Letter, the generalized Burgers equation is recast in terms of specific acoustic impedance along with linear absorption and dispersion coefficients, normalized quadspectral density (Q/S), and newly proposed normalized cospectral density (C/S). The formulation leads to a rather straightforward interpretation in which Q/S and C/S, respectively, represent the additional absorption and dispersion at a locale, produced by the passage of a finite-amplitude wave.

The traditional method for intensity-based sound power estimates often used in engineering applications is limited in bandwidth by microphone phase mismatch at low frequencies and by microphone spacing at high frequencies. To overcome these limitations, the Phase and Amplitude Gradient Estimator (PAGE) method [Gee, Neilsen, Sommerfeldt, Akamine, and Okamoto, J. Acoust. Soc. Am. 141(4), EL357-EL362 (2017)] is applied to sound power for a reference sound source, a blender, and a vacuum cleaner. Sound power measurements taken according to ISO 3741:2010 (2010) are compared against traditional- and PAGE-processed intensity-based sound power estimates measured according to ANSI S12.12-1992 (R2017). While the traditional method underestimates the sound power at the spatial Nyquist frequency by 7-10 dB, the PAGE-based sound power is accurate up to the spatial Nyquist frequency, and above when phase unwrapping is successful.

Noise from a tactical aircraft can impact operations due to concerns regarding military personnel noise exposure and community annoyance and disturbance. The efficacy of mission planning can increase when the distinct, complex acoustic source mechanisms creating the noise are better understood. For each type of noise, equivalent acoustic source distributions are obtained from a tied-down F-35B operating at various engine conditions using the hybrid method for acoustic source imaging of Padois, Gauthier, and Berry [J. Sound Vib. 333, 6858-6868 (2014)]. The source distributions for the distinct noise types are obtained using different sections of a 71 element, ground-based linear array. Using a subarray close to the nozzle exit plane, source distributions are obtained for fine-scale turbulent mixing noise and broadband shock-associated noise, although grating lobes complicate interpretations at higher frequencies. Results for a subarray spanning the maximum sound region show that the multiple frequency peaks in tactical aircraft noise appear to originate from overlapping source regions. The observation of overlapping spatial extent of competing noise sources is supported by the coherence properties of the source distributions for the different subarrays.

A broadband equivalent acoustic source distribution can be used to model the sound field near a high-speed jet. Such models must account for the spatiospectral variation of the sound levels. This work presents a technique for obtaining such a model using a spectral decomposition method associated with large and fine-scale turbulent mixing noise to create broadband equivalent source distributions for each noise type. The large-scale turbulent mixing noise is represented by frequency-dependent wavepackets, while the fine-scale turbulent mixing noise is modeled as a frequency-dependent incoherent, extended source distribution. This technique is applied to acoustical measurements from an ideally expanded, unheated Mach 1.8 jet. The wavepackets model the sound field levels in the maximum radiation region, but the second incoherent source distribution is required to obtain the levels at the other locations. The combination of the incoherent source distribution and the wavepacket provides a broadband, equivalent acoustic source representation that adequately models the sound field for Strouhal numbers between 0.04 and 0.25. At higher Strouhal numbers, better agreement is obtained when accounting for a frequency-dependent shift in the apparent acoustic source region. This frequency-dependent source region is more important closer to the jet than in the far field.

An impulsive noise exposure model for outdoor military shooting ranges was created. The inputs to the model included spatial interpolation of noise exposure metrics measured from a single round of fire from a small-arms ballistic weapon. Energies from this single-shot model were spatially translated and summed to simulate multiple shooters firing multiple rounds based on the equal energy hypothesis for damage risk assessment. A validation measurement was performed, and the uncertainties associated with measurement and modeling were shown to be acceptably low. This model can predict and assess total exposures and protection measures for shooters, instructors, and other range personnel.

Application of phased-array algorithms to acoustic measurements in the vicinity of a high-performance military aircraft yields equivalent source reconstructions over a range of engine conditions. Beamforming techniques for aeroacoustics applications have undergone significant advances over the past decade to account for difficulties that arise when traditional methods are applied to distributed sources such as those found in jet noise. The hybrid method, an inverse method approached via beamforming, is applied to jet noise measured along a 50 element, 30 m linear array to obtain equivalent source distributions. The source distribution extent decreases with increasing frequency or with a decrease in engine condition. A source coherence analysis along the axial dimension of the jet plume reveals that the source coherence lengths scale inversely with increasing engine condition. In addition, a method for extending the array bandwidth to frequencies beyond the spatial Nyquist frequency limit is also implemented. A directivity analysis of the beamforming results reveals that sources near the nozzle radiate to the sideline from a relatively stationary point irrespective of frequency, while the noise source origin of downstream radiating noise varies significantly with frequency.

Calculation of acoustic intensity using the phase and amplitude gradient estimator (PAGE) method has been shown to increase the effective upper frequency limit beyond the traditional p-p method when the source of interest is broadband in frequency [Torrie, Whiting, Gee, Neilsen, and Sommerfeldt, Proc. Mtgs. Acoust. 23, 030005 (2015)]. PAGE processing calculates intensity for narrowband sources without bias error up to the spatial Nyquist frequency [Succo, Sommerfeldt, Gee, and Neilsen, Proc. Mtgs. Acoust. 30, 030015 (2018)]. The present work demonstrates that for narrowband sources with frequency content above the spatial Nyquist frequency, additive low-level broadband noise can improve intensity calculations. To be effective, the angular separation between the source and additive noise source should be less than 30°, while using phase unwrapping with a smaller angular separation will increase the usable bandwidth. The upper frequency limit for the bandwidth extension depends on angular separation, sound speed, and probe microphone spacing. Assuming the signal-to-additive-noise ratio (SNR a ) is larger than 10 dB, the maximum level and angular bias errors incurred by the additive broadband noise beneath the frequency limit-or up until probe scattering effects must be taken into account-are less than 0.5 dB and 2.5°, respectively. Smaller angular separation yields smaller bias errors.

Bias errors for two-dimensional active acoustic intensity using multi-microphone probes have been previously calculated for both the traditional cross-spectral and the Phase and Amplitude Gradient Estimator (PAGE) methods [Whiting, Lawrence, Gee, Neilsen, and Sommerfeldt, J. Acoust. Soc. Am. 142, 2208-2218 (2017)]. Here, these calculations are expanded to include errors due to contaminating noise, as well as probe orientation. The noise can either be uncorrelated at each microphone location or self-correlated; the self-correlated noise is modeled as a plane-wave with a varying angle of incidence. The intensity errors in both magnitude and direction are dependent on the signal-to-noise ratio (SNR), frequency, source properties, incidence angles, probe configuration, and processing method. The PAGE method is generally found to give more accurate results, especially in direction; however, uncorrelated noise with a low SNR (below 10-15 dB) and low frequency (wavelengths more than 1/4 the microphone spacing) can yield larger errors in magnitude than the traditional method-though a correction for this is possible. Additionally, contaminating noise does not necessarily impact the possibility of using the PAGE method for broadband signals beyond a probe's spatial Nyquist frequency.

Many methods of two-microphone directional sensing have limited bandwidth. For active intensity, finite-difference error can be removed by using the phase and amplitude gradient estimator method. Using similar principles, a directional pressure sensor based on the phase gradient is developed that is accurate up to the spatial Nyquist frequency, and beyond if phase unwrapping is applied. A highly directional frequency-independent array response of arbitrary order can be achieved with two microphones. The method is compared against beamforming and traditional gradient sensing for single and multiple sources and is found to have improved localization capabilities and increased bandwidth.

Broadband shock-associated noise (BBSAN) is a prominent noise component from nonideally expanded jets in the forward and sideline directions. BBSAN from laboratory-scale jets has been studied extensively, and spatial trends in BBSAN spectral peak characteristics-frequency, level, and width-have been established. These laboratory-scale trends are compared to those for BBSAN from a tied-down F-35B operated at four engine conditions. While the peak frequency varies as expected, both spatially and across engine condition, the peak level and width do not, pointing to the need for additional research into BBSAN for high-performance military aircraft.

Supersonic jet noise reduction efforts benefit from targeted source feature extraction and high-resolution acoustic imaging. Another useful tool for feature extraction is partial field decomposition of sources into independent contributors. Since such decomposition processes are nonunique, care must be taken in the physical interpretation of decomposed partially coherent aeroacoustic fields. The optimized-location virtual reference method (OLVR) is a partial field decomposition designed to extract physically meaningful source and field information through the strategic placement of virtual references within a reconstructed field. The OLVR method is applied here to obtain spatially distinct and ordered partial sources at multiple frequencies of a full-scale, high-performance supersonic jet engine operating at 100% engine power. Partial sources are shown to mimic behaviors of the total source distributions including monotonic growth and decay. Because of finite spatial coherence, multiple partial sources are used to reproduce far-field radiation away from the main lobe, and the number of required sources increases with increasing frequency. An analytical multiwavepacket model is fitted to the partial sources to demonstrate how OLVR partial fields can be leveraged to produce reduced-order models.

Results of the first formal perceptual study of jet crackle are presented. Prior studies examined noise waveform properties believed to be linked to the jet crackle percept from a physics perspective or using signal processing and informal subjective evaluation. This investigation involves 31 listeners that rated 15 jet noise waveforms with a category subdivision scaling test. Results reveal a strong log-linear correlation between the pressure waveform time derivative's skewness and crackle rating. A regression analysis establishes practical derivative skewness bounds for a five-point categorical crackle scale and results in the suggested definition of the crepit as the unit of crackliness.

A single-point, frequency-domain nonlinearity indicator is calculated and analyzed for noise from a model-scale jet at Mach 0.85, Mach 1.8, and Mach 2.0. The nonlinearity indicator, ν N , has been previously derived from an ensemble-averaged, frequency-domain version of the generalized Burgers equation (GBE) from Reichman, Gee, Neilsen, and Miller [J. Acoust. Soc. Am. 139, 2505-2513 (2016)]. The indicator gives the spatial rate of change due to nonlinear processes in sound pressure level (SPL) spectrum, and two other indicators from the GBE-ν S and ν α -give the same quantity due to geometric spreading and absorption, respectively. Trends with frequency, angle, distance, and jet condition-supported both by spectral analysis and by calculation of the GBE-derived indicators-reveal a concentration of nonlinear effects along radials close to the plume with large overall SPLs. The calculated indicators for nonlinearity and absorption effects far from the source combine to give the same decay predicted by nonlinear theory for monofrequency sources. Trends in the ν N indicator are compared with trends observed for other indicators such as pressure-derivative skewness and bicoherence, revealing both the qualitative and quantitative advantages of the ν N indicator.

Acoustic shocks have been previously documented in high-amplitude jet noise, including both the near and far fields of military jet aircraft. However, previous investigations into the nature and formation of shocks have historically concentrated on stationary, ground run-up measurements, and previous attempts to connect full-scale ground run-up and flyover measurements have omitted the effect of nonlinear propagation. This paper shows evidence for nonlinear propagation and the presence of acoustic shocks in acoustical measurements of F-35 flyover operations. Pressure waveforms, derivatives, and statistics indicate nonlinear propagation, and the resulting shock formation is significant at high engine powers. Variations due to microphone size, microphone height, and sampling rate are considered, and recommendations for future measurements are made. Metrics indicating nonlinear propagation are shown to be influenced by changes in sampling rate and microphone size, and exhibit less variation due to microphone height.

In acoustic intensity estimation, adding a microphone at the probe center removes errors associated with pressure averaging. Analytical bias errors are presented for a one-dimensional, three-microphone probe for active intensity, reactive intensity, and specific acoustic impedance in a monopole field. Traditional estimation is compared with the Phase and Amplitude Gradient Estimator (PAGE) method; the PAGE method shows an increased bandwidth for all three quantities. The two- and three-microphone methods are compared experimentally, showing reduced bias errors with three-microphone PAGE for active and reactive intensity, whereas using two microphones is preferred for specific acoustic impedance.

Sound quality metrics help improve the psychoacoustic acceptability of devices and environments by modeling and thus enabling deliberate improvement of perceptual attributes. Sharpness as defined in DIN 45692 [(2009). Deutsches Institut für Normung, Berlin] requires inputs from Zwicker's loudness metric [ISO 532-1 (2017). International Organization for Standardization, Geneva]. This letter demonstrates that sharpness can be formulated to accept specific loudness values from Moore and Glasberg's loudness metric [ISO 532-2 (2017). International Organization for Standardization, Geneva; ANSI S3.4 (2007). American National Standards Institute, Inc., Washington, DC]. Sharpness calculations using the two loudness metrics produce similar results. This method thus enables evaluation of sharpness as a straightforward add-on to standard loudness calculations using Moore and Glasberg's metric, for which sharpness calculations were not previously available.

Sound intensity measurements using two microphones have traditionally been processed using a cross-spectral method with inherent error in the finite-sum and finite-difference formulas. The phase and amplitude gradient estimator method (PAGE) has been seen experimentally to extend the bandwidth of broadband active intensity estimates by an order of magnitude. To provide an analytical foundation for the method, bias errors in active intensity and specific acoustic impedance are presented and compared to those of the traditional method. Bias errors are reported for a plane-wave field and sound radiated from a monopole and a dipole. Additionally, bias errors are reported for reactive intensity, the estimation of which is unchanged by the PAGE method for the two-microphone case.

The jet sound quality "crackle" has historically been studied and quantified using the statistics of the pressure waveform. Some investigators have suggested crackle, and its associated shock content, may be better quantified using the statistics of the time derivative of the waveform. Modified waveforms are used to evaluate crackle prediction criteria based on the skewness of each variable. The resultant waveforms are provided as direct evidence that the pressure distribution does not directly predict or quantify a crackling sound quality while the statistics of the derivative appear to do so.

A method is presented to suppress grating lobes in beamforming using phase unwrapping and array interpolation. When the phase of each cross spectrum is successfully unwrapped, the magnitude and phase of the cross spectral matrix may be interpolated; for cases where these quantities vary smoothly, interpolation is straightforward, even above the spatial Nyquist frequency. Two applications are presented: localization of a broadband source and characterization of a source with frequency-dependent location. In both cases, grating lobes are suppressed and the source is localized at frequencies up to at least 8 times the spatial Nyquist frequency.

The phase and amplitude gradient estimator (PAGE) method for active acoustic intensity uses pairwise microphone transfer functions to obtain the phase gradient, which improves the calculation bandwidth over the traditional weighted quadspectral method. Additionally, for broadband sources, the PAGE theory indicates that the transfer function phase can be unwrapped to further extend the usable frequency range to beyond the spatial Nyquist frequency. Here, two experiments demonstrate intensity bandwidth extension by more than an order of magnitude using phase unwrapping. First, plane-wave tube results show accurate one-dimensional intensity calculations with the microphones separated by five wavelengths, 30 times the traditional limit. Second, two-dimensional measurements of a laboratory-scale jet with a four-microphone probe yield physically reasonable calculations at frequencies 15 times the traditional limit.