## Selected Publications

BYU Authors: K. L. Gee, published in

*AIAA J.*The role of nonlinearity in the propagation of noise radiated from high-performance jet aircraft is currently not well understood, despite past studies such as those by Blackstock and Howell and Morfey (see Refs. 2 and 3). More recently, Norum et al. found that F-15 flyover data exhibited anomalously high spectral levels above 1.5kHz; although nonlinear effects were mentioned as a possible cause for the High levels, the issue was not pursued further. As a finite amplitude noise waveform propagates, it undergoes amplitude-dependent steepening, which results in a transfer of spectral energy from mid- to higher frequencies. If competing processes, such as atmospheric absorption and geometrical spreading, are not sufficient to prevent shock formation, coalescence of shocks will also transfer energy to lower frequencies. Significant nonlinear spectral broadening, if present in high-speed jet noise, would cause perceived levles to vary from those predicted via linear methods.

BYU Authors: Kent L. Gee, published in

*11th AIAA/CEAS Aeroacoustics Conference*(Monteray, CA, May 2005). AIAA paper 2005-2937.The overall sound pressure levels of noise radiated by military jet aircraft along certain

angles are such that nonlinearity is likely to influence the propagation. Bispectral analysis of

noise data from the F/A-18E Super Hornet has been carried out in order to provide further

evidence that nonlinear effects are indeed present. The bicoherence, which is a normalized

form of the bispectral density, has been previously used in a variety of applications to detect

quadratic phase coupling (QPC) in a signal. In this case, the results of the bicoherence

calculations indicate that QPC is indeed present at high-thrust conditions along the peak

radiation angles, which means that nonlinearity does play a role. However, additional

investigations are still needed to more fully understand the physical interpretation of the

bispectral results for a random noise signal, which will also help better quantify the role of

nonlinearity in jet noise propagation.

angles are such that nonlinearity is likely to influence the propagation. Bispectral analysis of

noise data from the F/A-18E Super Hornet has been carried out in order to provide further

evidence that nonlinear effects are indeed present. The bicoherence, which is a normalized

form of the bispectral density, has been previously used in a variety of applications to detect

quadratic phase coupling (QPC) in a signal. In this case, the results of the bicoherence

calculations indicate that QPC is indeed present at high-thrust conditions along the peak

radiation angles, which means that nonlinearity does play a role. However, additional

investigations are still needed to more fully understand the physical interpretation of the

bispectral results for a random noise signal, which will also help better quantify the role of

nonlinearity in jet noise propagation.

BYU Authors: Kent L. Gee, published in

*11th AIAA/CEAS Aeroacoustics Conference*(Monteray, CA, May 2005). AIAA paper 2005-3089.An algorithm has been developed to study the nonlinear propagation of high-amplitude

jet noise. The hybrid time-frequency domain algorithm employs a split-step solution to a Mendousse-Burgers equation that includes the effects of quadratic nonlinearity, atmospheric absorption and dispersion, and geometrical spreading. Spectral predictions generated using the algorithm are compared to recent F/A-18E engine run-up noise measurements made at afterburner and military thrust conditions at distances of 74 and 150 m from the engine nozzles. The agreement between the predicted and measured spectra is such that the results help confirm that energy transfer is occurring to higher frequencies. However, the differences between the model and the measurement raise important issues regarding some of the physical phenomena likely associated with the measurement but not accounted for in the model. Among these are the substantial multipath interference effects in the measured spectra and the finite extent of the aeroacoustic sources within the jet.

jet noise. The hybrid time-frequency domain algorithm employs a split-step solution to a Mendousse-Burgers equation that includes the effects of quadratic nonlinearity, atmospheric absorption and dispersion, and geometrical spreading. Spectral predictions generated using the algorithm are compared to recent F/A-18E engine run-up noise measurements made at afterburner and military thrust conditions at distances of 74 and 150 m from the engine nozzles. The agreement between the predicted and measured spectra is such that the results help confirm that energy transfer is occurring to higher frequencies. However, the differences between the model and the measurement raise important issues regarding some of the physical phenomena likely associated with the measurement but not accounted for in the model. Among these are the substantial multipath interference effects in the measured spectra and the finite extent of the aeroacoustic sources within the jet.

BYU Authors: Kent L. Gee, published in

*10th AIAA/CEAS Aeroacoustics Conference*, (Manchester, Great Britain, May 2004).Analyses of recent F/A-18E/F military power and afterburner measurements suggest that the noise propagation is nonlinear in the far field. Spectral broadening takes place as the radiated noise propagates from 18 to 150 m, the limits of the measurement range. This broadening phenomenon cannot be readily explained in terms of linear propagation effects. Calculation of a nonlinearity indicator derived by Howell and Morfey supports the assertion that nonlinear propagation effects are present. Furthermore, skewness and kurtosis calculations indicate that the noise data distributions are non-Gaussian over the propagation range at these engine settings. Finally, the measured spectra have been compared against predictions obtained with existing nonlinear spectral evolution methods. Even though the prediction results compare poorly with the actual measurements, this is attributable to limitations of the spectral evolution methods themselves.

BYU Authors: Kent L. Gee, published in

*INTER-NOISE and NOISE-CON Congress and Conference Proceedings, NoiseCon04*, pp. 725-733 (Baltimore MD, July 2004).Multichannel active control has been applied to the global reduction of tonal noise from a cooling fan. In order to achieve consistent far-field attenuation of multiple harmonics of the blade passage frequency (BPF) of the fan, an analytical model has been applied to the control system in order to determine appropriate transducer configurations. The results of the modeling show that the additional global reduction possible by locating acoustically compact secondary sources coplanar with a compact primary source rapidly lessens as the number of symmetrically placed sources is increased beyond three. Furthermore, the model suggests that there are locations in the extreme near field of the sources that can be considered ideal for the minimization of far-field radiated power. Experiments carried out show that a four-channel control system is more effective than a two-channel system at achieving far-field attenuations, especially at the higher harmonics of the BPF for the fan tested. In addition, greater far-field mean-square pressure attenuations are achieved with the error microphones located along the calculated ideal regions than for nonideal placement. (C) 2004 Acoustical Society of America.

## Theses, Captstones, and Dissertations

Recent experimental achievements in active noise control (ANC) for cooling fans have used near-field error sensors whose locations are determined according to a theoretical condition of minimized sound power. A theoretical point source model, based on the condition previously stated, reveals the location of near-field pressure nulls that may be used to optimize error sensor placement. The actual locations of these near-field pressure nulls for both an axial cooling fan and a monopole loudspeaker were measured over a two-dimensional grid with a linear array of microphones. The achieved global attenuation for each case is measured over a hemisphere located in the acoustic far field of the ANC system. The experimental results are compared to the theoretical pressure null locations in order to determine the efficacy of the point source model. The results closely matched the point source model with a loudspeaker as the primary source, and the sound power reduction was greatly reduced when error sensors were placed in non-ideal locations. A weakness of the current near-field modeling process is that a point monopole source is used to characterize the acoustic noise from an axial cooling fan, which may have multipole characteristics. A more complete characterization of fan noise may be obtained using a procedure based on the work of Martin and Roure [J. Sound Vib. 201 (5), 577–593 (1997)]. Pressure values are obtained over a hemisphere in the far field of a primary source and the contributions from point source distributions up to the second order, centered at the primary source, may be calculated using a multipole expansion. The source information is then used in the aforementioned theoretical near-field calculation of pressure. The error sensors are positioned using the complete fan characterization. The global far-field attenuation for the multipole expansion model of fan noise is compared to that of previous experiments. Results show that the multipole expansion model yields a more accurate representation the near field, but is not successful in achieving greater sound power reductions in the far field.

Near-field acoustical holography (NAH) has been used extensively for acoustical imaging of infinitesimal-amplitude (or small-amplitude) sources. However, recent interests are in the application of NAH to image finite-amplitude (or high-amplitude) sources such as jets and rockets. Since NAH is based on linear equations and finite-amplitude sources imply nonlinear effects, which cause shock formation and consequently an altered spectral shape, a feasibility study is carried out to determine the effect of nonlinear propagation on NAH. Jet and rocket sources typically have a distinct spectral shape resembling a ‘haystack’ and center frequencies varying from 30 to 300 Hz. To test the effect of nonlinear propagation on jet or rocket noise, several waveforms with varying spectral shapes and center frequencies were created and numerically propagated in one dimension using a nonlinear propagation algorithm. Bispectral methods were used to determine the amount and effect of nonlinearity, showing that higher center frequencies lead to more nonlinearities for a given amplitude. Also, higher-order statistical analysis of the time derivative of the waveforms was used to determine information about the relative amount of waveform steepening and shock coalescence occurring. NAH was then used to reconstruct the original waveform magnitude and the errors were determined. It was found that the ‘haystack’ spectral shape can be preserved by the nonlinear effects leading to low amplitude-reconstruction errors, whereas a narrow-band spectral shape will become altered and reconstruct very poorly. However, if nonlinear effects become strong due to higher center frequencies, longer propagation distances or higher amplitudes, even the ‘haystack’ shape will become altered enough to cause poor reconstruction. Two-dimensional propagation studies were also performed from two point sources, showing differences between linear and nonlinear propagation.

A balloon filled with a gas that has a different sound speed than that of air has been used by science teachers in the past as an ”acoustic lens.” One purpose of the lens is to show refraction of sound waves as an analogy to geometric optics [H. Kruglak and C. C. Kruse, Am. J. Phys. 8, 260-261 (1940)]. This paper discusses the physics involved with the balloon lens demonstration. In order to determine the validity of a gas-filled balloon as a classroom demonstration of an acoustic lens and to understand the corresponding phenomena, the problem is considered analytically, numerically, and experimentally. The results show that although a geometric analogy is a valid first order approximation, scattering theory is often required to fully understand the observed phenomena. Thus, this demonstration can be adapted to a wide range of students, from those learning basic principles of refraction to mathematically advanced students studying scattering.

The Rubens flame tube is a teaching demonstration that is over 100 years old that allows observers to visualize acoustic standing wave behavior [H. Rubens and O. Krigar-Menzel, Ann. Phys. (Leipzig) 17, 149 (1905)]. Flammable gas inside the tube flows through holes drilled along the top, and flames are then lit above. The tube is closed at one end and is driven with a loudspeaker at the other end. When the tube is driven at one of its resonance frequencies, the flames form a visual standing wave pattern as they vary in height according to the pressure amplitude in the tube. Although the basic performance of the tube has been explained [G. Ficken and C. Stephenson, Phys. Teach., 17, 306-310 (1979)], this paper discusses the previously unreported characteristic of the tube’s resonance frequency shifts. This study observed that this phenomenon involves an upward shift of the natural frequencies of the lower modes from what would ordinarily be expected in a closed-closed tube. Results from a numerical model suggest that the shift is primarily due to a Helmholtz resonance effect created by the drilled holes. The numerical model is explained and the numerical results are compared to experimental findings and discussed.

I have constructed a device that demonstrates the spectral decomposition of waves according to spatial location along a surface analogous to the function of the basilar membrane of the mammalian cochlea. The design is based on previous work done by Robert Keolian at Pennsylvania State University.1 I have modified Keolian’s design to incorporate variable mass as well as stiffness and an electronically driven shaker, which allows the device to be driven with complex waveforms. The model can be used to demonstrate beating, masking, and other psychoacoustical phenomena that occur on the basilar membrane.

Interest in predicting the community impact of flyover noise from high-performance aircraft has stimulated research into metrics that accurately represent human perception of the loudness of the noise thus created. This problem is complicated by both human factors involved in the perception of the noise waveforms, and physical ones, particularly the nonlinear process that underlies the transmission of high-amplitude noise through the atmosphere. An introduction will be given to the process of nonlinear propagation and how it is modeled to give our simulated nonlinear waveform. The processes underlying loudness perception in the hearing system and the methods used in this project to model them will be discussed. The reaction of the time-varying loudness metric, as described by Moore and Glasberg, to simulated linearly and nonlinearly propagated signals will be discussed and compared to its reaction to a “rephased” signal, in which the power spectrum of the nonlinearly propagated signal is maintained but the Fourier phase randomized to eliminate the shocks. Qualitative perceived reactions to the waveforms will be compared the quantitative reaction of the metric. These will be considered in the light of recent research into the phenomenon of “crackle” and the importance of the first derivative of the wave form in the qualitative experience of crackle.

In the active control of tonal noise from cooling fans, one factor that can limit the achievable attenuation is fluctuation of the blade passage frequency in time. Large fluctuations in a short time can hinder the algorithm from converging to the optimal solution. Some fans have steadier speeds than others, which can be due to unsteady driving mechanisms or the physical structure of the fan. Environmental effects such as back pressure and unsteady blade loading can also cause the fan speed to fluctuate. The shifting in the blade passage frequency will be measured using a zero-crossing technique to track the frequency of each cycle. Blade passage frequency fluctuations will be presented for various driving mechanisms and environmental conditions. Techniques to minimize frequency shifting will also be discussed.

This study investigates the source characteristics of the Falcon 9 rocket from a series of measurements and evaluates models for maximum overall level, directivity, and radiated sound power. These models are based on a handful of rocket parameters and provide a basic description these rocket source characteristics. The models for maximum level and sound power perform well, while the angle of maximum radiation falls between historic predictions for static and launched vehicles.

An improved microphone configuration for making outdoor sound measurements has been studied. This configuration, nicknamed the Compact Outdoor Unit for Ground-based Acoustical Recordings (COUGAR), consists of an inverted microphone placed above a circular plastic plate and covered with a dome wind screen. The second generation of COUGAR, known as COUGARxt, follows the same general design but with a thinner plastic plate and a thicker wind screen. These two configurations, COUGAR and COUGARxt, along with an Elevated microphone configuration, have been tested in the BYU large anechoic chamber at various elevation and rotation angles relative to a noise source. The COUGAR and COUGARxt configurations have been tested on field tests involving rocket motor noise. Results indicate that both configurations record reliable acoustic data. Compared to COUGAR, COUGARxt is shown to vary less with rotation relative to the sound source and to reduce more low-frequency wind noise. As expected, the Elevated microphone configuration is shown to experience multi-path interference at all tested elevation angles when placed on a hard reflecting surface.

Crackle is a perceptual feature of supersonic jet noise that is related to the presence of acoustic shocks. The skewness of the time-derivative of the pressure waveform, or derivative skewness, is used as a metric indicative of crackle perception. The three main objectives of this work are: 1) Determine the potential spatial origin of crackle-related events in the near field of a high-performance military aircraft via an event-based beamforming method. 2) Investigate the potential for nonlinear, irregular shock reflections occurring along the near-field ground array and their implications on derivative skewness. 3) Relate the near-field, crackle-related events to far-field crackle perception by comparing nonlinearly propagated waveforms with measured far-field data. The event-based beamforming method used to determine source and far-field relationship of shock-like events utilizes the cross correlation between adjacent microphone waveform segments to determine the angle of propagation for an ensemble of crackle-related events within the waveform. The angle of propagation is traced towards the source for each event to find its apparent origin along the jet lipline. Beamforming results indicate that crackle-related events appear to originate anywhere from 2 to 14.5 m downstream along the jet lipline, with distributions that shift downstream and broaden with increasing engine power. The shock reflection classification method builds on the event-based beamforming method to calculate angle of incidence relative to the ground for an ensemble of shock events. The combination of angles of incidence and the measured shock strengths of the events reveal that irregular reflections are likely to occur over the majority of the array, which likely elevates the derivative skewness values due to steeper shocks with greater peak-to-peak pressures relative to off-ground measurements. Near-field, crackle-related events are extrapolated to the far field using a nonlinear propagation model to determine their prevalence in the far field. Cross-correlation coefficients of waveform segments centered about the propagated events indicates that for farther aft angles, near-field events are more related to far-field measurements. Waveform observations show that shock-like events in the near field that are more spiked in nature tend not propagate into the far field. However, near-field, large-derivative events with broader, high-pressure peaks nonlinearly steepen and form shocks in the far field that are likely contribute to crackle perception.

In community noise measurements, two standard setups require elevated or ground-based microphones. This study compares elevated and ground-based microphone measurements, particularly for low-frequency wind-induced microphone self-noise. To understand wind-related microphone noise, simultaneous sound level and wind speed measurements were employed using both elevated and ground-based approaches. The elevated setup utilized a commercial outdoor windscreen, whereas the ground setup included an acoustically reflective plate and was surrounded by a larger windscreen. Measurements were taken at several locations of varying geography in Juab County, UT; Utah County, UT; and Tooele County, UT. The results show the ground plate setup is preferable for outdoor noise measurements for two reasons. First, the wind speed is lower near the ground. Second, the larger windscreen yields superior wind noise rejection. These observations are quantified to expand the noise database for a predictive machine-learning soundscape model.

Because direct flow measurements of tactical aircraft jet engines are not currently possible, acoustic source characteristics are instead inferred from array processing methods. Models obtained through these methods are then used to reconstruct the surrounding sound field. This thesis compares two such methods using acoustical measurements made near a high-performance military aircraft. Hybrid beamforming (HBF) and multisource statistically-optimized near-field acoustical holography (M-SONAH) have both been used previously for jet noise sound field reconstruction but are compared here for the same input data--namely, the complex pressures across a 71-element linear array of equally spaced microphones covering 32 meters, placed approximately 8 to 10 m from and parallel to the shear layer. From the input data, M-SONAH and HBF produce an equivalent wave model (EWM) and an equivalent source model (ESM), respectively, and these models are used to predict sound field levels in the vicinity of the jet. Comparing the methods' results with measured sound field data showed favorable agreement at mid frequencies with varying results for low and high frequencies. The M-SONAH method produced sound field levels with lower errors at low frequencies while the HBF method outperformed M-SONAH at high frequencies. While the methods continue to have their relative strengths and reasons for use, this favorable agreement indicates that a consistent representation of the acoustic radiation for military jet noise has been achieved.

Coherence, which gives the similarity of signals received at two microphone locations, can be a powerful tool for calculating acoustic quantities, particularly active acoustic intensity. To calculate active acoustic intensity, a multi-microphone probe is often used, and therefore coherence between all microphone pairs on the probe can be obtained. The phase and amplitude gradient estimator (PAGE) method can be used to calculate intensity, and is well suited for many situations. There are limitations to this method—such as multiple sources or contaminating noise in the sound field—which can cause significant error. When there are multiple sources or contaminating noise present, the coherence between microphone pairs will be reduced. A coherence-based approach to the PAGE method, called the CPAGE method, is advantageous.Coherence is useful in phase unwrapping. For the PAGE method to be used at frequencies where the probe microphone spacing is larger than half a wavelength (above the spatial Nyquist frequency), the phase of transfer functions between microphone pairs must be unwrapped. Phase differences are limited to a 2π radian interval, so unwrapping—adding integer multiples of 2π radians to create a continuous phase relation across frequency—is necessary to allow computation of phase gradients. Using coherence in phase unwrapping can improve phase gradient calculation, which in turn leads to improved intensity calculation.Because phase unwrapping is necessary above the spatial Nyquist frequency, the PAGE method is best suited to dealing with broadband signals. For narrowband signals, which lack coherent phase information at many frequencies, the PAGE method can give erroneous intensity results. One way to improve calculation is with low-level additive broadband noise, which provides coherent phase information that can improve phase unwrapping, and thereby improve intensity calculation. There are limitations to this approach, as additive noise can have a negative impact on intensity calculation with the PAGE method. The CPAGE method, fortunately, can account for contaminating noise in some situations. A magnitude adjustment—which arises naturally from investigation of the bias errors of the PAGE method—can account for the additional pressure amplitude caused by the contaminating noise, improving pressure magnitude calculations. A phase gradient adjustment—using a coherence-weighted least squares algorithm—can likewise improve phase gradient calculations. Both adjustments depend upon probe microphone coherence values. Though not immune to contaminating noise, this method can better account for contaminating noise. Further experimental work can verify the effectiveness of the CPAGE method.

Energy-based acoustic quantities provide vital information about acoustic fields and the characterization of acoustic sources. Recently, the phase and amplitude gradient estimator (PAGE) method has been developed to reduce error and extend bandwidth of energy-based quantity estimates. To inform uses and applications of the method, analytical and experimental characterizations of the method are presented. Analytical PAGE method bias errors are compared with those of traditional estimation for two- and three-microphone one-dimensional probes. For a monopole field when phase unwrapping is possible, zero bias error is achieved for active intensity using three-microphone PAGE and for specific acoustic impedance using two-microphone PAGE. A method for higher-order estimation in reactive fields is developed, and it is shown that a higher-order traditional method outperforms higher-order PAGE for reactive intensity in a standing wave field. Extending the applications of PAGE, the unwrapped phase gradient is used to develop a method for directional sensing with improved bandwidth and arbitrary array response.

For a Marine in training, he or she will spend many hours on the firing range expending ammunition. This can cause lasting hearing damage for marines. Although previous weapons measurements have been done, the standards require further testing. To address this problem a team composed of members from Brigham Young University (BYU), Air Force Research Laboratory (AFRL), and the National Institute for Occupational Safety and Health (NIOSH) performed a test of M16A4 rifles measured at Quantico Marine Base in July 2017. In this thesis measurement techniques are presented for measuring rifle noise as well as data verification. A 113-microphone array was used to acquire the data with microphone heights selected to mirror shooters’ ear positions in the standing, kneeling, and prone configurations. It was found that peak levels (Lpk) exceeded 162 dB near the muzzle blast of the rifle, and within a 20 m radius Lpk exceeded 140 dB. These levels are known to cause hearing damage. Measurements clearly show specific events, such as the muzzle blast, sonic boom, and ground reflections, as well as effects of shielding. This thesis proposes that the quality of data acquisition promotes further use of the protocol employed here.

Acoustical room characterization typically involves a lot of high end and expensive equipment for measuring, modeling, and finding solutions to problems. Recently, Room EQ Wizard (REW) was introduced to BYU as a less costly option. This paper will evaluate REW's effectiveness through the metrics of mapping sound coverage, reverberation time and clarity calculations, while providing the Missionary Training Center with acoustical consulting for their auditorium. REW proved to be efficient and effective in all metrics and helped narrow the problem down to an unforeseen interaction between the loudspeakers and podium microphone.

Data acquisition for machine learning training data sets can be an expensive and time consuming process. For the BYU Acousitics Research Group and the Blue Ridge Research Company, the acquisition of outdoor ambient acoustic data for a single location can take up to a week to measure accurately. Since the purpose of our research is to create an accurate model for predicting ambient acoustic noise levels across the continental United States area, we would like to maximize the benefit of new data added to our existing training data set while minimizing the amount of new data needed. A joint K-means Clustering analysis was used to measure the statistical similarity between the geospatial feature values of our training and input data set for the North Carolina region. Using this analysis we were able to identify which kinds of geographic locations are under-sampled in the NC area. We can conclude from our analysis that our current training set does not fully represent the geographical area over which we are trying to make predictions. Additionally, targeted sampling of locations based on cluster assignment will improve the statistical similarity of our training and input data sets.

Sound generation and radiation properties are studied of full-scale tactical jet engine noise. This is motivated by the high sound exposure levels from jet noise, particularly for tactical engines. Acoustic source reconstruction methods are implemented computationally on existing jet noise data. A comparative study is performed using numerical simulations to understand the capabilities of more advanced beamforming methods to successfully estimate the source properties of a distributed, partially correlated source distribution. The properties and limitations of each beamforming method are described. Having validated the methods, beamforming with regularization—via the Hybrid Method—is implemented on linear array measurements near an installed tactical engine. A detailed analysis of the correlation and coherence properties associated with the phased array measurements guides the implementation of the beamforming. When the measurements are used as inputs to the beamforming, they produce partially correlated, distributed sources in a full-order model representation. A processing technique is also implemented that increases the usable bandwidth of the array measurements to almost an order of magnitude above the array design frequency. To more appropriately study the equivalent sources, a decomposition technique is designed and implemented to create a reduced-order wavepacket model of the jet noise. The wavepacket model is modular and scalable to allow for the efficient characterization of similar jet noise measurements. It is also appropriate for its physical significance, as wavepackets are attributed to the turbulent flow as well as the hydrodynamic and acoustic properties of the radiation. The reduced order model can estimate the levels and coherence properties of the acoustic radiation and represents a significant step towards a complete jet noise prediction model.

Acoustic intensity measurements traditionally use cross spectral processing methods with multi-microphone probes to estimate pressure and particle velocity. In 2015, Thomas showed that the phase and gradient estimator (PAGE) method increases probe bandwidth without modifying microphone spacing as compared to the traditional cross spectral method. In this study, acoustic intensity is estimated by both the PAGE method and the traditional method across two commercially built 3D intensity probes and three in-house built 2D intensity probes. Probe performance is compared in a broadband, white noise, anechoic sound field radiated from a loudspeaker. Probe orientation is considered by rotating each probe over a 360 degree horizontal plane at 2.5 degree increments. Results show increased frequency bandwidth using the PAGE method across all probe designs. 3D intensity level estimates suffered the least amount of error with the spherical probe. 2D intensity level and direction estimates suffered the least error with the 2D triangular probe with ½” microphones spaced at 2”. Measurement limitations concerning the 2D triangular probes with ¼” microphones are discussed

Energy quantities, which are calculated from pressure and particle velocity, yield a great deal of information about acoustic fields. Errors in pressure or particle velocity estimation lead to bias errors the estimation of energy quantities. The bias errors arise from different probe configurations and processing methods. Two processing methods are examined: the traditional method and the recently developed Phase and Amplitude Gradient Estimation (PAGE) method. These two methods are compared to investigate how each estimates pressure and particle velocity and the subsequent bias errors in a plane wave, standing wave, and spherical spreading wave field. Analytical expressions are derived for the energy quantity estimation using ideal one-dimensional probes. A simulation of the field from a baffled circular piston and measurements using ideal two-dimensional probes is computed. Compared to the traditional method, the PAGE method significantly extends the range of frequencies for which the results are accurate. It is found that a probe with a center microphone significantly reduces the estimation error and extends the usable range of frequencies. The PAGE method with unwrapping, perfectly matches the analytical results for plane waves, while the traditional method is only good at wavelengths that are large compared to the probe size. Furthermore, the PAGE method has a constant bias error in spherical wave fields due to the 1/r decrease in pressure. The traditional method has a frequency dependent bias error that is much worse at higher frequencies. Lastly, the PAGE method has the same or worse error for the standing wave. As an application of energy quantities, acoustic intensity is used to develop an equivalent source model for jet noise from an F-22 at military and afterburner engine conditions. An optimization is used to find the best-matching wavepacket model for measured intensity vectors. The results are compared to another intensity method of estimating the source region and source directivity, and the two methods have good agreement.

Understanding the impact of jet noise and other high-amplitude sound sources can be improved by quantifying the nonlinearity in a signal with a single-microphone measurement. An ensemble-averaged, frequency-domain version of the generalized Burgers equation has been used to derive a quantitative expression for the change in spectral levels (in decibels) over distance due to geometric spreading, thermoviscous absorption, and nonlinearity, respectively. The nonlinearity indicator, called νN, is based on the quadspectral Morfey-Howell indicator, which has been used in the past to characterize nonlinearity in noise waveforms. Unlike the Morfey-Howell indicator, the νN indicator has direct physical significance, giving a change in decibels per meter of the sound pressure level spectrum specifically due to nonlinearity. However, a detailed characterization of the expected behavior and potential issues for the nonlinearity indicator has been lacking. The quadspectral nonlinearity indicator is first calculated for well-known solutions to several basic acoustical scenarios to determine its expected behavior in both the near field and far field. Next, the accuracy of νN is examined as a function of measurement parameters such as sampling frequency, signal bandwidth, scattering, and noise. Recommendations for conducting experiments are given based on the findings. Finally, the indicator is calculated for model-scale and military jet noise waveforms. These tests reveal the utility and accuracy of the νN indicator for characterizing broadband noise; the indicator gives frequency-dependent information about the waveform from a single-point measurement.

A recently developed phase and amplitude gradient estimator (PAGE) method for calculating acoustic intensity from multiple pressure measurements [Thomas et al., J. Acoust. Soc. Am. 134, 4058 (2013)] has been tested via anechoic laboratory measurements of the radiation from broadband sources. The measurements determine that the effective frequency bandwidth of valid acoustic intensity calculations can be substantially increased when using the PAGE method over the traditional cross-spectral approaches. Preliminary results are shown for two probe sizes and multiple broadband source configurations.

Mach stem formation in acoustic shocks is investigated using oxyacetylene balloon explosions conducted a short distance above pavement. As the shock wave propagates away from the blast site it transitions from a regular reflection to irregular reflection. The location of this transition point, as well as the path of the triple point, are experimentally resolved using microphone arrays and a high-speed camera. The measured transition point falls between that predicted from derivations based on weak shock waves and an empirical relationship derived from large-scale explosions. It also agrees well with predicted values based on von Neumann’s three shock theory.

The scientific community has employed multiple methods to analyze and describe the jet noise emanating from the turbulent exhaust flow from modern military aircraft engines, with the goal that better characterization of the sound radiation will improve noise reduction efforts. This thesis utilizes three different approaches to characterize the noise source region from a static F-22A Raptor. First, the energy flow field along planes near the aircraft and along an arc is measured using a multidimensional vector intensity probe. The resulting vector intensity maps give a clear indication of the directionality of the noise as a function of frequency at different engine conditions. A straightforward ray-tracing method show the utility of vector intensity measurements in source characterization by estimating the region from which the loudest portions of sound are emanating. Second, intensity reconstructions from near-field acoustical holography (NAH) provide an estimate of the three-dimensional radiated energy flow field. The sound field is shown to be dominated by mutually incoherent radiation lobes, which can be partially isolated by a partial decomposition method. Lastly, a wavepacket source model is optimized in light of amplitude-based NAH reconstructions near the jet axis. The wavepacket model successfully fits the NAH-reconstructed partial fields, especially at frequencies above 50 Hz, indicating that the source may be modeled by multiple wave packets at each frequency.

Most everyone is familiar with the loud crashing sound of a musical cymbal, but very few people are familiar with how a cymbal sounds close up. Through initial observation, it appears that cymbals have evanescent effects in low frequencies. This project quantifies how much the cymbal evanesces and at what frequencies. The stated properties of a cymbal are proven through detailed acoustical analysis, including far-field directivity analyses and near field versus far-field acoustical measurements. The harmonic modes of the cymbal are analyzed through Scanning Laser Doppler Vibrometry.

Nonlinear propagation effects in rocket noise have been previously shown to be significant [M. B. Muhlestein et al. Proc. Mtgs. Acoust, (2013)]. This paper explores the influence of source level, peak frequency, and ambient atmospheric conditions on predictions of nonlinear propagation. An acoustic pressure waveform measured during a full-scale solid rocket motor firing is numerically propagated via generalized Burgers equation model for atmospheric conditions representative of plausible spaceport locations. Cases are explored where the overall sound pressure level and peak frequency has been scaled to model engines of different scale or thrust. The predicted power spectral densities and overall sound pressure levels, both flat and A-weighted, are compared for nonlinear and linear propagation for distances up to 30 km. Differences in A-weighted overall sound pressure levels of up to 8 dBA are found for one of the cases explored. The differences in overall level suggest that further research to appropriately include nonlinear effects in launch vehicle noise models is worthwhile.

In high-amplitude noise propagation, as is the case with a military jet, nonlinear effects have to be taken into account. This paper will highlight and compare these nonlinear effects with those of geometric spreading and atmospheric absorption. Extensive measurements were taken, in April 2009, at Holloman Air Force Base, New Mexico during which one engine was cycled through four power settings while the other engine was set to idle. Measurements were conducted over five days during which atmospheric conditions changed significantly. Changes in temperature, humidity, ambient pressure, and wind speed affect absorption and other important acoustic variables, such as air density and the speed of sound. Although the changes were drastic over the course of a day, within a measurement period (typically thirty minutes), the changes are small enough that these variables can be treated as constants. This phenomenon allows researchers to successfully analyze the nonlinear characteristics of jet noise.

This thesis is a direct continuation of work done by Kuhn et al. [J. Acoust. Soc. Am. 63, S1, S84 (1978)] and Bodon et al. [J. Acoust. Soc. Am. 133, 5, 3507 (2013)] concerning propagation of finite-amplitude, or nonlinear, waves from a baffled pipe. Band-limited Gaussian noise and 1 kHz, 1.5 kHz, and 2 kHz sinusoidal acoustic waves were driven with initial peak pressure amplitudes ranging from 98 dB to 163 dB through a 6.1 m long circular cylindrical PVC pipe with a 5.1 cm inner diameter and baffled end. The pipe end was open, allowing the driven sound to propagate from the pipe. The waveform was measured along its propagation path, including near the driver, inside the pipe, at the pipe’s face, and at radial distances outside the pipe as far as 1.3 m from the pipe opening. This thesis examines characteristics of the waveform and its changes along its propagating path through and outside the pipe. Characteristics discussed include shock wave formation inside the pipe, reflection near the pipe opening, amplitude at the pipe face, amplitude of its positive impulse and nonlinear asymmetry at distances outside the pipe, and the rate of amplitude decay of the propagated wave as it travels away from the pipe.

An alternative pressure-sensor based method for estimating the acoustic intensity, the phase and amplitude gradient estimation (PAGE) method, is presented. This method is similar to the finite-difference p-p (FD) method, in which the intensity is estimated from pressure measurements made using an array of closely spaced microphones. The PAGE method uses the same hardware as the FD method, but does not suffer from the frequency-dependent bias inherent to the FD method. Detailed derivations of the new method and the traditional FD method are presented. Both methods are then compared using two acoustic fields: a plane wave and a three monopole system. The ability to unwrap the phase component of the PAGE method is discussed, which leads to accurate intensity estimates above previous frequency limits. The uncertainties associated with both methods of estimation are presented. It is shown that the PAGE method provides more accurate intensity estimates over a larger frequency bandwidth. The possibility of using a higher-order least-squares estimation with both methods is briefly demonstrated. A laboratory experiment designed to validate the PAGE method was conducted. The preliminary results from this experiment are presented and compared to analytical predictions. Finally, the application of the PAGE method to a static rocket test firing is presented. The PAGE method is shown to provide accurate intensity estimates at frequencies that are higher than possible with just the FD method.

In scan-based array measurements, stationary reference sensors are needed to temporally correlate the different measurement scans and produce coherent complex pressure fields that can be used to perform near-field acoustical holography (NAH). Because the number of references required increases with the number of subsources contributing to the sound field, an extended, partially correlated source (e.g., a turbulent jet) comprising many ill-defined sources can result in significantly increased measurement complexity and expense. Demonstrated here a is a new approach to creating spatiotemporally coherent pressures using self-referencing between overlapping measurement positions instead of separate reference channels. A laboratory experiment was designed and the data have been used to explore "stitching" together a complex pressure field. This experiment is described and the “stitching” method is detailed. To successfully execute the technique, unwrapping of intrascan phases is first accomplished with a two-dimensional phase unwrapping algorithm. Individual scan positions are then stitched together using median phase differences between multiple adjacent scans to create coherent planes of data. Amplitude-stitching is done by averaging across scans and preserving the integrated squared pressure across the overall aperture. The validity of this method is shown by showing that a consistent local coherence maintained through the stitching process. The technique is applied to jet noise, and the possibility of applying it to NAH is discussed. This technique provides direction for efficient experimental design for scan-based array measurements of extended sources.

Correlation analysis is useful in extracting spatiotemporal relationships between signals and can be used to examine features of jet noise for source properties. When applied to F-22 jet noise, maximum correlation coefficients show noticeable distinctions between near-field and downstream microphones; these distinctions become increasingly apparent in the spatial variation between short and long correlation lengths. Waveform width analysis complements the meaningfulness of our results. Finally, the calculation of phase speed clearly defines the relevant regions: a fine-scale upstream region, a large-scale downstream region, and a midway region that shares properties of fine-scale and large-scale noise. [Work supported by the Office of Naval Research.]

Acoustic intensity measurements of the F-22A Raptor are analyzed as part of ongoing efforts to characterize the noise radiation from military jet aircraft. Data were recorded from a rig of microphones and an attached tetrahedral intensity probe at various locations to the sideline and aft of the aircraft. Numerical analysis of the intensity at one-third octave band center frequencies along various measurement planes and at a 23 m radius arc reveals the magnitude and directionality of the vector acoustic intensity. Differences in the trends for low-frequency and high-frequency data are discussed and, via a simple ray tracing method from maximum intensity regions, interpreted in terms of far-field behavior and source location. In particular, the extended source region contracts and moves upstream with increasing frequency, and vector directionalities point farther toward the sideline.

The radiation of finite-amplitude waves from the open end of a baffled, circular pipe is considered as a direct continuation of work begun by Kuhn, Blackstock, and Wright more than three decades ago [Kuhn et al., J. Acoust. Soc. Am. 63, S1, S84 (1978)]. Band-limited Gaussian noise, as well as 1 kHz, 1.5 kHz, and 2kHz sinusoidal pulses, with initial peak pressure amplitudes ranging from 0.5 – 1.2 kPa, have been propagated down a 6.1 m pipe, whose open end (5.1 cm inner diameter) has been placed off-center in a large rectangular baffle. As the steepened or shock-like waves exit the pipe, the measured waveforms are comprised of sharp impulses that are delta function-like in nature, particularly on axis. Although linear piston theory predicts similar waveform shapes, there is also evidence that nonlinear propagation of these impulses, which can exceed peak pressure amplitudes of 1.5 kPa near the pipe opening, is occurring.

Military aircraft generate high-amplitude noise which can cause injury to attending personnel. Efforts to mitigate the effects of this noise require a detailed understanding of the propagation of the noise, which was shown previously to be nonlinear. This thesis presents an analysis of highamplitude noise propagation, emphasizing measures used to quantify the importance of considering nonlinearity. Two measures of the importance of nonlinearity are compared. These measures are the wave steepening factor and a skewness estimate. The wave steepening factor is a measure of how much nonlinear waveform steepening has occurred in a waveform. The skewness estimate is the skewness of the first time-derivatives of the pressure amplitudes, and can be considered a measure of the shock content in a waveform. These two measures are analyzed analytically in terms of the Earnshaw, Fubini, Fay, and Khokhlov solutions to the Burgers equation. In addition, an analysis of how discrete sampling affects the estimation of these quantities is also presented. It is determined that the wave steepening factor is robust with respect to low sampling rates, but the skewness of the first time-derivatives of the pressure amplitudes is not robust, and requires very large sampling rates to be adequately estimated. Using numerical and experimental techniques, the two nonlinearity measures are applied to more complicated waveforms, such as Gaussian noise and noise with jet noise-like statistics. It is found that the evolution of the two nonlinearity measures discussed above for noise signals is distinctive in various ways. In particular, the skewness of the first time derivative of the pressure amplitudes suggest that noise waveforms experience nonlinear phenomena faster than initially sinusoidal signals, while the wave steepening factor suggests that they occur at approximately the same rate. The measures are then applied to full-scale military aircraft. By comparing these nonlinearity metrics with the results of the analytical, numerical, and experimental results found in this thesis, it is determined that nonlinearity is likely to be significant in the near field of a military aircraft at military and afterburner engine conditions.

The noise emissions of jets from full-scale engines installed on military aircraft pose a significant hearing loss risk to military personnel. Noise reduction technologies and the development of operational procedures that minimize noise exposure to personnel are enhanced by the accurate characterization of noise sources within a jet. Hence, more than six decades of research have gone into jet noise measurement and prediction. In the past decade, the noise-source visualization tool near-field acoustical holography (NAH) has been applied to jets. NAH fits a weighted set of expansion wave functions, typically planar, cylindrical, or spherical, t measured sound pressure sin the field. NAH measurements were made of a jet from an installed engine on a military aircraft. In the present study, the algorithm of statistically optimized NAH (SONAH) is modified to account for the presence of acoustic reflections from the concrete surface over which the jet was measured. The three dimensional field in the jet vicinity is reconstructed, and information about sources is inferred from reconstruction at the boundary of the turbulent jet flow. Then, a partial field decomposition (PFD) is performed, which represents the total field as the superposition of multiple, independent partial fields. This is the most direct attempt to equate partial fields with independent sources in a jet to date.

Aircraft maintenance workers can be exposed to high noise levels while working around military aircraft. Near-field measurements of an F-22 Raptor at different engine conditions provide information regarding the noise dosage experienced in the vicinity of the aircraft. Level weighting curves, which account for different aspects of hearing perception, have been applied to the overall sound pressure level data from locations where personnel might stand. Hearing protection attenuations are applied to the A-weighted overall sound pressure levels to determine the exposure levels while wearing properly inserted ear plugs and muffs. It is found that significant reduction is achieved by the required dual hearing protection used for this project. The dual hearing protection can provide around 40 dB of attenuation in the overall exposure level. These results can be used by the military to make informed decisions regarding acceptable exposure times for maintenance personnel.

Microphone arrays are useful for measuring acoustic energy quantities (e.g. acoustic intensity) in the near-field of a full-scale solid rocket motor. Proper characterization of a rocket plume as a noise source will allow for more accurate predictions in engineering models that design for protection of structures, payloads and personnel near the rockets. Acoustic intensity and energy density quantities were measured in three rocket noise fields and have shown that the apparent source region of the rocket becomes smaller and moves upstream as frequency increases. Theoretical results accounting for some scattering and finite-difference errors arising in these types of energy-based measurements have been previously discussed by other authors. This thesis includes results from laboratory experiments which confirm some of this previous theoretical work as well as gives insight into the physical limitation of specific microphone array designs. Also, calibrations for both magnitude and directional response of the microphones are demonstrated. Of particular interest is the efficacy of phase calibration of array microphones for the low-frequency regime below 200 Hz.

For years, the effects of sound pressure level measurements upon human hearing and psychology have been studied, and only in recent years scientists have seen a link between these measurements and headphones connected to portable listening devices. The Brigham Young University Educational Acoustics Research Study (E.A.R.S) is an interactive demonstration devoted to acquiring samples of the student body that connect findings between the use of headphones with portable listening devices, such as mp3 players, and educating individuals in the process. This report will highlight the reasoning for conducting the study, describe the proper background in acoustics needed to understand the material, and analyze the results from the study, while concluding observations. The study will evaluate the overall sound pressure level due to a one second Leq, safe listening time according to non-occupational noise criterion, and demographics that define the individual, such as age, gender, listening preference, and mp3 player. Also, the study will ask the individual about their listening habits and if they will change based around the feedback received from the E.A.R.S. This study will ultimately benefit science with information to understand connections between listening habits and safe practices of listener protection.

Referee whistles output high-level short duration noise that has not been thoroughly studied. Damage risk criteria (DRC) exist to quantify the overall risk of sound exposure for continuous noise (OSHA, 1981; NIOSH, 1998) and other DRCs are intended for use with impulse noise (MIL-STD-1474D, 1991; Price, 2007). The noise from whistles is similar to impulse noise and the impulse DRC of equivalent A-weighted 8-hour energy (LeqA8), MIL-STD-1474D, Pfander, Smoorenburg, and the AHAAH model are used to analyze recordings of whistle-blows from a trained referee in a controlled environment. Recording locations were at the ear and one meter in front of the referee. Computational analysis shows that using some of the DRC, allowable exposures for referees during a sports match range from 18 to 118 exposures. Hearing protection is recommended for officials, especially for those who are exposed to other loud situations on the same day.

BYU Acoustics has a collection of almost 100 microphone sets, each including a microphone and a preamplifier. It is important to have accurate calibration of these to ensure accurate experimentation results. In the past, field calibration has been the only option. This project looks at the benefits of the GRAS 90CA calibration system and includes development of a MATLAB program to provide a database of all information gathered from the calibrator.

A statistical analysis of noise data from various-sized solid propellant rocket motors is presented. Time waveform data sampled at 204.8kHz using 6.35mm and 3.18mm microphones were collected near motors with nozzle exit diameters ranging from 0.13m to 1.22m. Non-Gaussian features of the data are explored by calculating estimates of the probability density functions of the data, its standard deviation, its skewness, and its kurtosis. This is carried out for both the pressure waveform and its first order time difference to reveal the formation of acoustic shocks within the noise. The analysis shows greater similarity between different rocket statistics for the pressure than for the time derivative.

The contributions of cavity and structural resonances to the sound radiation from a hammered dulcimer have been investigated. Results indicate that the sound quality of the lowest notes is affected by a relatively weak structural resonance in that frequency range. Additionally, near-field acoustical holography indicates significant sound radiation from front and back sound holes at frequencies of importance, contradicting the commonly held notion that the dulcimer’s sound holes serve no acoustical purpose.

Since the 1950s the jet aeroacoustics community has been involved in predicting and measuring the noise distribution in jets. In this work, cylindrical and planar Fourier near-field acoustical holography are used to investigate radiation from a full-scale, installed jet engine. Practical problems involving measurement aperture and the highly directional nature of the source are addressed. Insights from numerical simulations reveal usable reconstruction regions. A comparison of cylindrical and planar NAH for the respective measurement apertures shows cylindrical NAH outperforms planar NAH on reconstructions both towards and away from the source.

Exploding hydrogen-oxygen balloons are a popular demonstration in introductory chemistry and physical science courses. Initial research quantified potential hearing risk from exploding hydrogen-oxygen balloon demonstrations. Further time waveform and spectral analysis was conducted to characterize hydrogen-oxygen balloons as impulsive noise sources. Pure hydrogen balloons produce low levels (less than 140 dB) and inconsistent reactions. Balloons filled the stoichiometric ratio of hydrogen to oxygen produce very consistent results between trials. Hydrogen-oxygen balloons are also nearly omnidirectional, with little variation over angles. Levels for hydrogen-oxygen balloons increase as a function of balloon size and oxygen content. Comparison is provided with other impulsive noise sources, including various firearms, other explosive chemistry demonstrations, and firecrackers. Consideration is given to characteristics such as A-duration, rise time, and peak level. It is concluded that the hydrogen-oxygen balloons are less impulsive than other sources of similar amplitude, with longer A-durations and rise times. As such, the balloons have lower characteristic frequencies than other impulsive noise sources considered.

Exploding gas-filled balloons are common chemistry demonstrations. They provide an entertaining and educational means to experimentally verify nonlinear acoustical theory as described by the Earnshaw solution to the lossless Burgers equation and weak-shock theory. This paper describes the theory, the demonstration, and the results of a propagation experiment carried out to provide typical results. Data analysis shows that an acetylene-oxygen balloon produces an acoustic shock whose evolution agrees well with weak-shock theory. On the other hand, the pressure wave generated by a hydrogen-oxygen balloon also propagates nonlinearly, but does not approach N-wave-like, weak-shock formation over the propagation distance. High-speed video of these explosions provide discussion material on directionality of propagating acoustic shocks. Overall, the experiment shows that popular demonstrations of chemical reactions can be extended from chemistry classrooms to a pedagogical tool for the student of advanced physical acoustics.

A method of measuring angular dependence of acoustic transmission through supercritical plates in air is discussed. The coincidence effect occurs in a supercritical plate when the component of the acoustic wave number parallel to the plate matches the bending wave number in the plate. The transmission of sound is a maximum at the angle where this trace wave number matching occurs. The theory of the coincidence effect is well-defined for unbounded thin plates using plane-wave excitation. However, experimental results for finite plates are known to diverge from theory, especially near grazing angles. An experimental setup has been developed in order to observe the coincidence effect using continuous-wave excitation and phased-array methods. Experimental results through a 0.5 mm thick aluminum bar exhibit strong maxima at the predicted coincidence angles, showing that coincidence is observable using continuous waves. Also, transmission near grazing angles is seen to diverge from infinite plate theory. Further work is suggested to improve the measurement setup and explore the source of the divergence.

The acoustic field near large-scale solid rocket motors represents a harsh, high-amplitude noise environment rich with high-bandwidth acoustic shocks. Type-1 prepolarized microphones may be used in these environments with the benefit of reduced cost and measurement because they require only a constant-current supply available in many data acquisition systems. However, there are potential issues related to microphone response that should be considered. The main issue discussed here has to do with temporary failure of the constant-current supply due to an insufficiently fast response time in representing rapid voltage changes at shocks, which results in spurious, capacitive-like effects in the waveform data that are also manifest as a low-frequency roll-up in the spectrum noise floor. An experiment was conducted to identify under what circumstances these waveform effects arise. Data were measured from a solid rocket motor using several combinations of transducer, cable type, cable length and constant current supply. Results and mitigation methods found from the experiment are discussed. These include increasing the supply current, using low-impedance cables, and choosing the correct orientation for the transducers.

This study explores an alternative approach using a semi-empirical equivalent simple-source model to analyze and characterize the turbulence-induced aeroacoustic sources from military jet aircraft. Initially the model is a single point source located above a hard plane such that the locations of destructive interference from its mirror image matched the measured interference nulls. This provides useful information about the location of the dominant noise source region from the jet. The model then develops into a superposition of Rayleigh-distributed line arrays of uncorrelated and correlated monopoles. The model is tested on an extensive set of acoustic data taken on an F-22 Raptor. Although the model's line source characteristics are developed using data from only one measurement plane, it is able to accurately reproduce the radiation at other measurement planes. This equivalent line source matches the current prevailing theory that the sideline radiation is largely due to uncorrelated noise, whereas the correlated sources dominate downstream. In addition, the semi-empirical, simple-source model results corroborate the theory that the peak source location moves upstream with increasing frequency and lower engine conditions.

The Endevco 8510B-5 piezo-resistive pressure transducer is often used for acoustical measurements in high-intensity, harsh aerospace engineering situations. A series of laboratory tests have been created to categorize the response of these sensors and compare it to GRAS 40BH and 40BD microphones. Environmental factors native to the testing of large solid rocket motors (such as the ARES DM-1 RSRM tested in September, 2009) have been considered and recreated in the laboratory setting. These factors include high amplitude acoustic levels, raised temperatures, and sensor vibrations. The purpose of this thesis is to determine which, if any, of these factors affect the response of the Endevco sensors and to what degree. Also, the effects on response of vent tube extensions will be tested and compared with theory for venting of condenser microphones. To this extent, data have shown that venting the Endevco sensor into the acoustic field being measured attenuates low frequency signals.

Scan-based near-field acoustical holography (NAH) is applied to partially correlated sources. Partial field decomposition via the virtual coherence method is used to implement the scan-based NAH. The background and theory of these methods are developed. Multiple stationary reference microphones are required for the partial field decomposition. Guidelines for reference microphone placement in the literature thus far have been limited. Improved guidelines for reference microphones are given after the results of two sets of experiments. The first set involves discrete, partially correlated sources, both physical and numerical. The second set of experiments is strictly numerical and involves continuous sources. Fewer microphones are required for partially correlated sources as compared to completely uncorrelated sources. Reference microphone number is found to be more critical to reducing holography reconstruction errors than is placement or location. For the continuous results, an appropriate figure of merit is created: reference microphones per coherence length. Based upon the definition of coherence length, two reference microphones per coherence length are required to minimize reconstruction error. Further practical reference microphone guidelines are given. These guidelines are to assist in preparing for a full-scale application of scanbased near-field acoustical holography to a military aircraft jet.

The United States Army Engineer District in Sacramento, California, selected HHI Corporation, a design-build construction and engineering firm of Farmington, Utah, to design and build an indoor test facility for the GAU-8 Avenger at Hill Air Force Base, Ogden, Utah. The blast pressures from this 30-mm Gatling gun, however, are large enough to cause spallation of the concrete walls over time. The facility is being designed and constructed to last for over 20 years, requiring several acoustical treatments. The pressures from the gun were measured outdoors, with maximum pressures exceeding 3000 Pa (163 dB) at a distance of 30 ft (9.1 m). A computer model of the room was designed using EASE, and impulse responses were generated at several positions. These impulse responses were convolved with an ideal blast wave pulse train to mimic the sound of the gun in the room. From these data and results collected from preliminary tests in the range, recommendations have been provided as to placement and types of necessary treatments. Final data confirm that the test facility meets all acoustical and occupational safety requirements.

A one-micron diameter platinum wire resistance thermometer measures temperature fluctuations generated by propagating noise produced by a horizontally-fired, static GEM-60 solid rocket motor. A relationship between small amplitude acoustic pressure and acoustic temperature is derived and the data are compared with those calculated from pressure data recorded by a nearby 3.18 mm condenser microphone. The validity of taking acoustic temperature measurements in a rocket field is discussed, particularly the role of turbulence induced temperature fluctuations.

A large Balinese gamelan gong, the gong ageng wadon, is similar to other Indonesian gongs in that it is tonal. A previously undocumented phenomenon is the distinct acoustic beating this gong produces. In this study of the Brigham Young University's gong ageng wadon, acoustical and vibrometry measurements were performed. Scanning laser Doppler vibrometer results show a beat frequency of about 3 Hz is produced near 150 Hz and 160 Hz by closely spaced structural modes. A slightly slower beat frequency (around 2.5 Hz) is also produced at about 120 Hz. The difference in this case is that there is only one structural mode measured near this frequency. The acoustic radiation from this mode beats with a harmonic of the radiation from a lower structural mode, which harmonic is caused by nonlinear structural phenomena.

In order to facilitate the acquisition and accurate interpretation of intensity and energy density data in high-amplitude pressure fields, the expressions for intensity and energy density are examined to ascertain the impact of nonlinear processes on the standard expressions. Measurement techniques for estimating acoustic particle velocity are presented. The finite-difference method is developed in an alternate manner and presented along with bias and confidence estimates. Additionally, two new methods for estimating the local particle velocity are presented. These methods appears to eliminate the errors and bias associated with the finite-difference technique for certain cases.

The implementation of an automated positioning and measurement system in the fully anechoic chamber at Brigham Young University is described. The system is employed to study the frequency generation of a hypersonic speaker. The general positioning system design consists of suspended rails for planar motion which are moved using stepper motors controlled by a computer. Con- siderations for mounting, acoustically absorptive insulation, system error han- dling, and automated measurement techniques are addressed. Software design and necessary functionality is outlined in detail. This system is useful for high-resolution measurements in stationary sound fields that could not be car- ried out with a reasonable number of channels or in a reasonable amount of time. The system is used to measure hypersonic speaker frequency generation of using driving signals of 500 Hz, 3 kHz, 10 kHz and all of those frequencies combined. The speaker is also studied using a white noise input signal.