Plane Wave Tube Research Articles

Au–Au Bonding-Associated Lapping and Polishing Technique for Sapphire-Based Fabry–Perot Acoustic Sensor Applied for Harsh Environment

This article presents a sapphire-based Fabry–Perot acoustic sensor with potential for application in harsh environment acoustic sensing. The key component of the sensor is a thin sapphire diaphragm with a diameter of 20 mm and thickness down to 10 proposed Au–Au bonding-associated lapping and polishing technique. Microfabrication characterizations have corroborated the availability of realizing wafer-class thin sapphire diaphragm fabrication by employing the Au–Au bonding-associated lapping and polishing technique, and the diaphragm can be then easily transferred and assembled as a sensor. The strategy for optimizing the stripping phenomenon during lapping is also proposed. Acoustic calibration experiment through a plane wave tube indicates the sensitivity of 13.58 mV/Pa at 10 kHz and the frequency response range of 100250 kHz. The temperature tolerance experiment through the muffle furnace shows that no structural damage or optical spectrum invalidity occurs even if the environmental temperature reaches 800°, which indicates a high working temperature of the sensor up to 80°. Major findings and future application directions of this article are concluded as: 1) realization of an innovative sapphire-based Fabry–Perot acoustic sensor that shows significant potential in applications of numerous key industrial domains, such as aerospace engineering, and 2) a novel approach for achieving wafer-class sapphire ultrathin diaphragm fabrication, which might offer innovative methods for the optimization of sapphire-based harsh environment sensors and give reference to the sapphire lapping process as demanded in the gallium nitride (GaN)-based light-emitting diodes (LED) industry.

From mechanics to acoustics: Critical assessment of a robust metamaterial for acoustic insulation application

The increasing popularity of sandwich and composite double panel structures stems from their better sound insulation properties over a wide frequency range with respect to their single panel counterparts. However, in the design of such multi-layer panels particular attention must be paid to the resonance dominated region of the Sound Transmission Loss (STL), where the Mass-Spring-Mass resonance causes a frequency region of poor acoustic performance. In the present contribution, a metamaterial unit cell endowed with an ultra-wide band gap is integrated with faceplates to create a novel acoustic insulation sandwich panel. The panel is realized with a single material and with a properly designed mechanical stiffness that does not affect results in terms of acoustic wave attenuation over a wide frequency range, making at the same time the internal core self-sustained. The STL of the panel is numerically evaluated through a plane wave tube model. The solid-air interaction in terms of resonance frequencies is critically assessed and accurately described by the proposed lumped-parameter model. The model represents a simple tool to predict and optimize the behaviour of the panel in the resonance dominated region of the STL. The acoustic performances of the panel are validated through an experimental campaign on a Nylon prototype, which is 3D printed through Selective Laser Sintering technique.

Characterization of MEMS Acoustic Sensors and Amplifiers in Cryogenic Fluids for Quench Detection Applications in HTS CICC

An acoustic quench detection method utilizing MEMS (Micro Electro-Mechanical System) acoustic sensors is proposed. To investigate this method, a commercially available MEMS piezoelectric microphone, the Vesper VM1000, and two types of second stage amplifiers, using either an OPA344 or a LMH6629 based amplifier circuit, were characterized at cryogenic temperatures in helium gas. The MEMS microphones were in their original package with an integrated preamplifier. The tests were performed inside a two-stage Gifford-McMahon cryocooler from room temperature down to 60 K, at static pressures between 1.2 and 1.4 bar in gaseous helium, over the frequency band from 100 Hz to 10 kHz. Second stage amplifiers were needed to achieve signal to noise ratios approaching the manufacturer specified operating levels. The OPA344 based amplifier reduced in gain by >55 dB below 230 K, while the LMH6629 based amplifier performed well down to 60 K. The MEMS microphones appear to perform acoustic measurements down to 165 K but with some reduction in sensitivity down to 60 K. An acoustic model of the cryocooler plane wave tube calibration setup is developed and used to calibrate the microphone despite the presence of a significant thermal gradients down the plane wave tube.

Experimental extraction of loudspeaker parameters from sound transmission measurements in a plane wave tube for moving-coil drivers and passive radiators

Moving-coil loudspeaker parameters are typically derived from electrical impedance measurements. Leishman and Anderson previously provided the theoretical foundations for extracting these parameters from sound transmission measurements conducted in a plane wave tube. This presentation will discuss experimental results of using this idea to extract the parameters of moving-coil drivers and those of passive radiators, the latter of which cannot be derived from electrical impedance measurements. The two-load method is used to account for the non-anechoic behavior of the tube to better enable accurate extraction of the sound transmission. Mechanical parameters are extracted from an open-circuit sound transmission measurement, and the electrical parameters are extracted by placing a wire across the loudspeaker’s terminals to provide a closed-circuit sound transmission measurement. Parameters extracted from measurements of electrical impedance, sound transmission, and destructive analysis of diaphragm assemblies will be compared.

Acoustical characteristics of ultralight polylactic acid foams fabricated via solution phase inversion

The acoustic properties of highly porous polylactic acid (PLA) foams with very low densities (as low as 0.12 g/cm3) are evaluated using an impedance tube. PLA foams with a mesoporous or a combined meso/macroporous morphology exhibiting different mechanical and physical properties, are produced via nonsolvent induced phase separation (NIPS). The resulting foams exhibit an interesting resonance-like acoustic absorption behavior providing the opportunity to design acoustic materials to target specific frequency bands by controlling their microstructure. Despite very low densities, plane wave tube measurements suggest that these PLA foams may have the potential for sound barrier applications. Using the transfer matrix approach on multilayer configurations, we showed that the combined meso/macroporous morphology has the most significant impact on the absorption and transmission capacity of the foams. The knowledge produced from this study helps to understand the correlation between the characteristics of highly porous NIPS-derived foams and their acoustic properties.

Extension of the phase and amplitude gradient estimator method for acoustic intensity to multiple tones

The phase and amplitude gradient estimator (PAGE) method [Thomas etal., J. Acoust. Soc. Am. 137, 3366–3376 (2015)] has proven successful in improving the accuracy of measured energy quantities over the traditional p-p method in several applications. One advantage of the PAGE method is the use of phase unwrapping, which allows for increased measurement bandwidth. However, phase unwrapping works best for broadband sources and fields with high coherence. Narrowband sources often do not have coherent phase information over a sufficient bandwidth for a phase unwrapping algorithm to unwrap properly. Even for narrowband signals, the PAGE method has been shown to provide correct intensity measurements for frequencies up to the spatial Nyquist frequency. This is improved bandwidth over the p-p method. Previous work with sawtooth waves in a plane wave tube shows that in cases with multiple tones, the PAGE method with a few additional steps of processing accurately calculates intensity above the spatial Nyquist frequency provided one tone is below it. A variety of further experiments with multiple tones are explored to determine if any extra steps in processing or ingenuity in data acquisition can reasonably be used to achieve comparable results in a free-field environment. [Work supported by NSF.]

Microphone and microphone array characterization utilizing the plane wave tube method

Microelectromechanical Systems (MEMS) Microphone arrays are becoming ubiquitous in consumer electronics. Large and expensive anechoic chambers are commonly used to characterize these arrays. Individual MEMS microphones, on the other hand, are typically tested using one of three methods: a free field calibration in an anechoic chamber, a pressure field calibration in a pressure chamber, or a pressure field calibration in a plane wave tube (PWT). In this work, we present a PWT system for testing a single microphone as well as a second PWT system for testing an array of four MEMS microphones. Both systems utilize a 3D printed portion of the tube that is designed to minimize reflections and standing waves while allowing the sound pressure to reach a calibrated instrumentation microphone and the MEMS microphone(s) under test. With these PWT systems, we characterize individual microphones up to 30 kHz and microphone arrays up to 3 kHz. Further, the array test system is used to measure the polar pattern of the microphone array at several frequencies and measure the impact of microphone mismatch on array performance. This PWT test methodology is a size and cost effective way to characterize MEMS microphone arrays.

Bias error comparison for plane-wave acoustic intensity using cross-spectral and phase-and-amplitude-gradient-estimator methods

Acoustic vector intensity relies on the product of the acoustic pressure and particle velocity. The particle velocity is typically approximated via Euler’s equation using the gradient of the complex pressure across closely spaced microphones, which is traditionally found using the cross-spectral density. In contrast, the phase-and-amplitude-gradient-estimator (PAGE) method [Thomas et al., J. Acoust. Soc. Am., 137, 3366-3376 (2015)] relies on gradients of pressure magnitude and phase. For a broadband source this allows for the phase to be unwrapped, which extends the usable bandwidth of the intensity calculation well above the spatial Nyquist frequency. The benefits of the PAGE method are evident in plane wave tube measurements in which microphones spaced 90 cm apart yield accurate intensity values at frequencies at least ten times the spatial Nyquist frequency. This represents an increase in bandwidth of 30 times over the traditional method. The bias errors for the traditional method for calculating acoustic intensity are reviewed and compared with the bias errors for the PAGE method for the case of both two and three microphone intensity probes in a plane-wave tube environment. [Work supported by the National Science Foundation.]

Experimental validation of acoustic intensity bandwidth extension by phase unwrapping.

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.

High-Bandwidth and Sensitive Air Flow Sensing Based on Resonance Properties of CNT-on-Fiber Hairs

Artificial hair flow sensors were fabricated using piezoresistive, radially grown carbon nanotube arrays on glass fibers and investigated for their dynamic aerodynamic response as measured within an instrumented plane-wave tube. The sensors were experimentally observed to provide both a large bandwidth of operation below first resonance and a strong resonance response at selected frequencies above first resonance. The frequency of first resonance was easily tunable by adjusting the length of the exposed hair and could be made to vary from a few hundred hertz to over 13 kHz. Higher frequency bands were accessible for a given hair length using higher-order resonance modes, up to five of which were observed. All of the responses were understood and modeled using a vibrating Euler-Bernoulli beam analysis.

Transfer matrix modeling of a recessed microphone for unsteady surface pressure measurements

Recessed microphones are commonly used for unsteady surface pressure measurements, either due to space limitations or to satisfy performance requirements. A technique is developed using transfer matrices to design a configuration by modeling its frequency response. This technique is beneficial since it provides guidance to optimize the recessed configuration prior to fabrication. The recessed nature also allows for utilization of closely-spaced pressure ports on a surface, thus providing an inexpensive means for measuring unsteady surface pressures with high spatial resolution. A tube-branch design capable of achieving a 10-kHz bandwidth is presented and validated experimentally using an acoustic plane wave tube.

Sound transmission measurements through porous screens

The two microphone transfer function technique is used to measure sound transmission properties of porous screens or membranes in a plane wave tube. This presentation will compare sound transmission of porous screens from several manufacturers. Measurements are made with two different plane wave tubes, one of diameter 10.2 cm to measure frequencies between 100 Hz and 2 kHz, and the other of diameter 1.3 cm to measure frequencies between 2 kHz and 16 kHz. Special considerations are made to account for the intrinsic losses in the smaller diameter tube.

Evolution of the temporal slope density function for waves propagating according to the inviscid Burgers equation.

An exact formulation for the evolution of the probability density function of the time derivative of a waveform (slope density) propagating according to the one-dimensional inviscid Burgers equation is given. The formulation relies on the implicit Earnshaw solution and therefore is only valid prior to shock formation. As explicit examples, the slope density evolution of an initially sinusoidal plane wave, initially Gaussian-distributed planar noise, and an initially triangular wave are presented. The triangular wave is used to examine weak-shock limits without violating the theoretical assumptions. It is also shown that the moments of the slope density function as a function of distance may be written as an expansion in terms of the moments of the source slope density function. From this expansion, approximate expressions are presented for the above cases as well as a specific non-Gaussian noise case intended to mimic features of jet noise. Finally, analytical predictions of the propagation of initially Gaussian-distributed noise are compared favorably with plane-wave tube measurements.

An impedance-mobility model of stacked membrane-type acoustic metamaterials

Membrane-type acoustic metamaterials have been proven to exhibit high low-frequency transmission loss despite their small thickness and light weight. To date, analysis has focused primarily on experimental studies in plane-wave tubes and numerical modeling using finite element methods. These methods are inefficient when used for applications that require iterative changes to the structure of the material. In addition, high sound transmission loss with a single layer of such metamaterial only occurs in a narrow frequency range. To facilitate design and optimization of stacked membrane-type acoustic metamaterials, a computationally efficient dynamic model based on the impedance-mobility approach is proposed. Results are verified against a finite element model. Single and double layer transmission loss characteristics are compared. Wide-band high-transmission-loss acoustic metamaterials can be achieved by double layer membranes and using the proposed approach for optimization. The impedance-mobility approach is shown to be very efficient for modeling and optimization of such materials, compared against the conventional finite element approach.

High sensitivity Polyvinylidene Fluoride (PVDF) microphone based on area ratio amplification and minimal capacitance

This paper presents an inexpensive high-sensitivity microphone based on polyvinylidene fluoride (PVDF) film. High sensitivity is achieved through pressure amplification created by the area ratio between the rigid surface exposed to acoustic waves and a crosshair-shaped PVDF film, in combination with the reduced capacitance created by a similarly shaped top electrode. The crosshair shape is obtained through simple chemical etching from commercial PVDF film. Finite-element simulations including static structure analysis, modal analysis, and harmonic response are performed to design the microphone. Peak coalescence of the first three adjacent natural frequencies caused by the structure damping ratio is observed. Static and dynamic stress analyses ensure that the design meets the mechanical constraints imposed by PVDF. A plane wave tube experiment and signal conditioning electronics are developed. Measurements include benchmarking against a commercial microphone and show that the PVDF microphone exhibits a linear response up to a sound pressure level of 140 dB and overall fluctuations of less than ±4 dB over the frequency range of 10 to 20000 Hz. The sensitivity of the microphone alone, without a conditioning circuit, is measured as 27.8 μV/Pa, which is 3.01 times the sensitivity of commercial PVDF film operating in 3-3 mode. This sensitivity gain is close to the physical area ratio of 3.2. We experimentally characterize the directivity of the sensor and measure a decay of -10.5 dB at ±90° from the microphone's axis.

Evolution of the wave steepening factor for high-amplitude sound propagation

One suggested metric to quantify nonlinear noise propagation is the wave steepening factor (WSF) [J. Gallagher, AIAA-82-0416 (1982)], defined as the absolute value of the mean negative slope of an entire waveform over the mean positive slope. Qualitatively, the WSF describes a waveform's average distortion, but a quantitative analysis has not been performed previously. To aid in the interpretation of the WSF, its evolution is presented in analytical fashion for the Earnshaw and Khokhlov solutions to the Burgers equation. Furthermore, the results of an analysis of the effects of finite sampling rates on the estimation of the wave steepening factor for these ideal cases are presented. A generalized Burgers equation-based model has been used to analyze the numerical evolution of the WSF for atmospheric and boundary layer absorption and dispersion and compare with plane wave tube experiments. From the numerical simulations, it is found that the WSF is dominated by initial level and frequency and is relatively less affected by absorption, bandwidth, and initial statistics for noise signals. Furthermore, the WSF is shown to be relatively insensitive to reduced sampling rates.

Evaluation of moving-coil loudspeaker and passive radiator parameters using normal-incidence sound transmission measurements: Theoretical developments

The parameters of moving-coil loudspeaker drivers are typically determined using direct electrical excitation and measurement. However, as electro-mechano-acoustical devices, their parameters should also follow from suitable mechanical or acoustical evaluations. This paper presents the theory of an acoustical method of excitation and measurement using normal-incidence sound transmission through a baffled driver as a plane-wave tube partition. Analogous circuits enable key parameters to be extracted from measurement results in terms of open and closed-circuit driver conditions. Associated tools are presented that facilitate adjacent field decompositions and derivations of sound transmission coefficients (in terms of driver parameters) directly from the circuits. The paper also clarifies the impact of nonanechoic receiving tube terminations and the specific benefits of downstream field decompositions.

Statistical analysis of a characteristic shock formation distance for high-amplitude noise

Previous research involved investigating a characteristic shock formation distance for Gaussian, finite-amplitude noise propagating in a cylindrical plane wave tube [Muhlestein and Gee, POMA 12, (in press)]. In particular, the evolution of the probability density function of the pressure and the first-order time derivative of pressure along with the skewness of the pressure derivative were experimentally studied. It was concluded that a constant-factor modification to the nonlinear distortion length defined by Gurbatov and Rudenko may yield a suitable characteristic shock formation distance in a statistical sense. Additional Gaussian noise data with a broader frequency range have now been taken, and the effects of boundary layer dispersion considered. Furthermore, noise with other statistical distributions and pressure statistics mimicking high velocity jet noise have been examined. These data are analyzed statistically as before using probability density function estimates and the skewness of the pressur...

Analyzing acoustic response of orifices using transfer matrix method.

The impedance of an orifice is critical in many applications such as sound absorption, fluidic actuation, and stability prediction of hydraulic piping systems. In this work, a transfer matrix analysis of orifices (circular orifice, slit, and perforated plate) is presented, which provides physical insights into the acoustic behavior of orifices under unsteady excitation. Specifically, the acoustic transfer matrix (TM) for an orifice in the presence or absence of mean flow is developed and compared to a lumped element model (LEM). An experimental investigation is conducted in a plane wave tube (PWT) for circular and slit orifices in the absence of mean flow for a variety of frequencies and sound pressure levels. The experimental results are compared with TM and LEM predictions. The TM predictions for circular orifices in the presence of mean flow are also compared with other available experimental data.

Experimental characterization of shock formation distance in broadband noise propagation.

Unlike initially sinusoidal waveforms, the definition of the “shock formation distance” for broadband noise is complicated by the fact that not all shocks form at the same rate. Examination of the concept of a “characteristic” shock formation distance for broadband noise raises some questions: Is there some generalization of the shock formation distance for sinusoidal signals or narrowband noise that can be applied to broadband noise? If so, is it inversely proportional to amplitude and frequency, as the pure tone and narrowband noise distances are? Possible methods to investigate these questions, such as statistical analyzes and examining spectral slopes and time waveform derivatives, are discussed. These techniques have been studied using experimental data acquired from finite-amplitude broadband noise propagation in an anechoically terminated plane-wave tube. Preliminary results from these experiments are discussed.