Reverberant Acoustic Field Research Articles

Model based spectral feature analysis in reverberant acoustic fields

The spectral features of a reverberant acoustic field that can lead to improved source localization methods are investigated. Of particular interest are identification of deterministic and probabilistic features that characterize the environment and models of the acoustic transfer function that generate such features. For example, models that predict Schroeder’s invariant standard deviation in the pressure response at source-receiver distances where the direct sound approaches the reverberant field energy are proposed. Models examined include non-stationary Gaussian processes for the acoustic reverberant components and all-pass parametric models of the acoustic impulse response.

The Acoustic Environment of York Minster’s Chapter House

York Minster is the largest medieval Gothic cathedral in Northern Europe, renowned for its magnificent architecture and its stained glass windows. Both acoustic measurements and simulation techniques have been used to analyse the acoustic environment of its Chapter House, which dates from the 13th-century and features an octagonal geometry with Gothic Decorated stone walls replete of geometric patterns and enormous stained glass windows, covered by a decorated wooden vault. Measured and simulated room impulse responses served to better understand how their architectural features work together to create its highly reverberant acoustic field. The authors start by analysing its acoustic characteristics in relation to its original purpose as a meeting place of the cathedral’s Chapter, and end by reflecting on its modern use for a variety of cultural events, such as concerts and exhibitions. This work is part of the “Cathedral Acoustics” project, funded by the EC through the Marie-Sklodowska-Curie scheme.

Strains/Stresses in Plates Subjected to Reverberant Acoustic Excitation Using Statistical Energy Analysis

Objective of the present work is to theoretically estimate the strains generated in a plate by a reverberant acoustic excitation, in SEA frame work. An expression for determining the strains due to the trace wave generated in the plate is derived, which is an essential component of vibration caused due to the acoustic excitation. Strains developed in a plate when subjected to reverberant acoustic field are obtained experimentally and the results are compared with the theoretically estimated results and they are in good agreement.

The Calculation Method and the Test for Radiated Sound Power of Impulsive Noise in a Reverberant Tank

A method for calculating the radiated sound power of impulsive noise in a reverberant acoustic field is proposed in this paper, and the computing results of the time-frequency domain characteristic are verified in the tank at ASTL (Acoustic Science and Technology Laboratory). In the frequency domain analysis, the power spectrum of the impulsive noise is processed by the Welch way. In the time domain analysis, the total sound power of the impulsive noise is calculated by the autocorrelated processing, and by which the radiated sound power is reduced. In order to verify the proposed method, the radiated sound power of the impulsive noise is successfully tested in a reverberant tank. The experiment result shows that the radiated sound power of the 10 kHz CW impulsive noise signals in the testing tank is almost as same as that in the anechoic pool, which the testing deviation is less than 1 dB both in time and frequency domain. The work of this paper provides a useful calculation method for measuring the characteristic of the transient noise in a reverberant tank.

Modeling translation of a pulsating spherical bubble between viscoelastic layers

A model was developed previously that enables calculation of the translational force exerted on a pulsating bubble between parallel viscoelastic layers [Hay et al., J. Acoust. Soc. Am. 128, 2441 (2010)]. Here the translational motion of the bubble is taken into account. Force on the bubble is calculated with a Green’s function for the reverberant acoustic field in the channel. The Green’s function takes into account not only elastic waves in the channel walls but also viscous boundary layers at the interfaces with the liquid. The dynamical response of the bubble is modeled by an equation of Rayleigh-Plesset form for pulsation, coupled to a momentum equation for translation. The dynamical equations are coupled to the Green’s function providing the reverberant pressure field and its gradient acting on the bubble. Calculation of the time-dependent Green’s function requires integration over both wavenumber and frequency space at each location along the trajectory of the bubble. Different numerical implementations were considered based on accuracy and efficiency. Simulations will be presented for several combinations of bubble radius, standoff distance, and viscous boundary layer thickness. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and NIH DK070618.]

Removal of Electrostatically Deposited Powders Using High Intensity Low Frequency Sound Part 1: Experimental Deposition and Removal

This paper describes the controlled removal of powder layers using high intensity low frequency sound. The research has an industrial application, the cleaning of electrostatic precipitator filters in coal-fired power stations. The aim of the work is to quantify the sound pressure level and frequency content required to overcome adhesive and cohesive bonding forces formed when powder is electrostatically deposited onto a metal surface. In this, the first of two papers, a repeatable method for electrostatically depositing powder layers on to a metal surface is described. The design, construction and calibration of a high intensity wave tube also are described. The measured sound pressure level required for removal is compared with prediction. Measurements in a reverberant acoustic field using commercially available acoustic cleaning systems also are reported.

Spatial correlation and coherence in reverberant acoustic fields: Extension to microphones with arbitrary first-order directivity

Spatial correlation and coherence functions in reverberant sound fields are relevant to the acoustics of enclosed spaces and related areas. Theoretical expressions for the spatial correlation and coherence functions between signals representing the pressure and/or the components of the particle velocity vector in a reverberant sound field are established in the literature and most of these have also been corroborated with measurements [F. Jacobsen, J. Acoust. Soc. Am. 108, 204-210 (2000)]. In the present paper, these expressions are generalized to microphones of first-order directivity, whereby the directivity can be expressed in terms of pressure and pressure gradient. It is shown that the resulting spatial correlation and coherence functions can be expressed in terms of the established spatial correlation and coherence functions. The derived theoretical expression for the spatial coherence function is validated with a modeled diffuse sound field. Further, it is compared with the experimental coherence obtained from the reverberant tails of room impulse responses measured with two common surround sound microphone setups in a concert and a lecture hall.

DISTRIBUTION OF SPATIAL VARIABILITY IN VIBRATION RESPONSE

Understanding the distribution of dynamic response is important in setting random vibration test levels for equipment. This paper describes how the probability distribution of a set of data could be tested. The Kolmogorov-Smirnov test statistic indicates that the third octave average PSD vibration responses on a set of components are spatially log-normal when excited by a reverberant acoustic field. Two procedures for estimating the P95/50 level are demonstrated to agree well for the component attachment sensors: one calculates the mean and standard deviation of log-transformed PSD, while the other uses a warping function with PSD mean and standard deviation calculated directly.

Modeling of the Acoustic Reverberation Special Research Program deep ocean seafloor scattering experiments using a hybrid wave propagation simulation technique

Quantitative modeling of bottom‐interacting ocean acoustic waves is complicated by the long propagation ranges and by the complexity of the scattering targets. We employ a two‐dimensional (2‐D) hybrid technique combining Gaussian beam, finite difference, and Kirchhoff integral solutions of the wave equation to simulate ocean acoustic experiments within half of a convergence zone in the SOFAR channel. The 2‐D modeling approach is reasonable due to the one‐dimensional (1‐D) velocity distribution in the water column and the strong lineation of the seafloor morphology parallel to the mid‐ocean ridges. Full‐waveform modeling of ocean acoustic data requires that the topography and the material properties of the seafloor are available at scales that are several orders of magnitude smaller than typical bathymetric sampling rates. We have therefore investigated the effects on the ocean acoustic response of a stochastic interpolation scheme used to generate seafloor models. For typical grazing angles of the incident wave field (approximately 5°–20°), we found that different stochastic realizations of the same seafloor segment (sampled at 200 m) yield an intrinsic uncertainty of the order of 3–8 dB in amplitude and 0.1–0.3 s in time for individual prominent events in the reverberant acoustic field. Hybrid simulations are compared to beam‐formed ocean acoustic data collected during the Acoustic Reverberation Special Research Program (ARSRP) cruises. Side lobe noise in the observed acoustic data is simulated by adding band‐limited white noise at −30 dB relative to the maximum intensity in the synthetic data. Numerical simulations can be limited to the response of only one of the mirror azimuth beams provided that the experimental geometry is suitably chosen. For the 2‐D approximation to be valid, the cross‐range resolution of the observed data must be smaller than the characteristic scale of seafloor lineations, and the beams of interest must be approximately perpendicular to the dominant structural grain. Under these premises, the arrival time and maximum intensity of the observed backscattered acoustic events can be modeled within 0.3 s and 5–10 dB, respectively. The mismatch in arrival time is interpreted to be due predominantly to intrinsic uncertainties in the stochastic interpolation of the seafloor profiles, whereas the fact that the intensity of the backscattered events is systematically overestimated is attributed to 3‐D effects within the “footprint” of the beam and/or to underestimated noise levels.

Panel dynamic response to a reverberant acoustic field

A novel semianalytical approach based on the integral equation method has been developed to predict the structural response of a panel located in a rigid-walled cavity. This problem is related to the study of the acoustic response of satellite panels with electronic equipment. The main difficulty lies in the treatment of the response of an unbaffled panel, strongly coupled to a high modal density pressure field. A two-indices empty cavity Green's function is used, inspired from electromagnetism. The plate contribution to the sound pressure is obtained by expanding the pressure jump and Green's function on the same basis functions. This approach presents two main advantages : it reduces the size of the linear system to be solved and avoids ill-conditioning problems. This method is found to be quite efficient (10 s per frequency point on a 10 Mflops machine). Results show that the panel responds better at acoustical eigenfrequencies than at its in vacuo modes. The values at which the diffraction phenomena governs the structural and acoustic responses are pointed out in terms of density and flexural rigidity. Finally, the formulation allows the quantification of differences between light and heavy fluid environments.

The application of a biologically inspired controller to control sound transmission

A biologically inspired control approach for reducing sound transmission through a distributed elastic system has been theoretically and experimentally verified for narrow-band excitation. The control paradigm approximates natural biological systems for initiating movement, in that a low number of signals are sent from an advanced, centralized controller (analogous to the brain) and are then distributed by local rules and actions to multiple actuators (analogous to muscle fiber). A local learning rule that was developed from linear quadratic optimal control theory and solved apriori was implemented. The investigation considered a plate excited by normal plane wave, oblique plane wave, and reverberant acoustic fields. Radiated sound power was the defined cost function and therefore used as the controller error signal. Four control inputs in the form of piezoelectric actuators were mounted on the plate in a two-by-two array. Results indicate that increases in transmission loss of approximately 18 dB are attainable for off-resonance excitation. In general, comparisons of theoretical and experimental data show good agreement. This investigation has demonstrated that the biological control approach has the potential to control multimodal response in distributed elastic systems using an array of many actuators with a reduced order main controller. Thus significant reductions in control system computational complexity have been realized by this approach. [Work supported by NASA Langley.]

Determination of sound power of coupled machines

Several procedures are available for the determination of the sound power level of machines in normal environments. Most of these give adequate results for single medium-sized equipment, but difficulties arise in extending the concepts to large coupled machines. [“Evaluation of Proposed ASME PTC 36 Code for Sound Power Level Determination of Large Steam Turbine Generators,” S.E. Grabkowski, J. MacDonald, and T. Van Schaick (General Electric Company), to be presented at Fall 1975 ASME meeting.] Much of the problem is because the direct acoustic field of a component machine may not extend to as much as one foot from its surface due to reverberation from other components. A procedure is suggested in which all acoustic measurements are confined to surfaces near each component machine. Correction is made for the reverberant acoustic field of the entire environment. The correction procedure utilizes reverberation time determinations from impulsive noise tests; and applies a Monte Carlo approach to the problem of correcting for nearfield effects in the evaluation of sound power. An iterative computation is employed. Comparisons with free-field sound power determinations are shown.

Energetics of Resonant Structures and Reverberant Acoustic Fields

Energetics of Resonant Structures and Reverberant Acoustic Fields

On the Transmission of Sound through Finite Closed Shells: Statistical Energy Analysis, Modal Coupling, and Nonresonant Transmission

An investigation of sound transmission into small enclosures considers the effects of acoustically induced coupling between shell modes. The level of cavity reactance is examined. The noise reductions for a closed cylinder and a rectangular parallelopiped enclosure (with a single flexible panel) placed in reverberant acoustic fields are computed and experimentally checked. The transmission by resonant and nonresonant shell modes is examined, especially in relation to the statistical-energy-analysis approach. The nature of the predominance of one type of transmission over the other is considered in relation to shell and cavity configurations and structural damping levels.

On the Transmission of Sound Through Finite, Closed Shells: Statistical Energy Analysis, Modal Coupling, and Non-resonant Transmission

An investigation of sound transmission into small enclosures considers the effects of acoustically induced coupling between shell modes. The level of cavity reactance is examined. The noise reductions for a closed cylinder and a rectangular parallelopiped enclosure (with a single flexible panel) placed in reverberant acoustic fields are computed and experimentally checked. The transmission by resonant and nonresonant shell modes is examined, especially in relation to the statistical‐energy‐analysis approach. The nature of the predominance of one type of transmission over the other is considered in relation to shell and cavity configurations and structural damping levels.

On the Transmission of Sound into Finite, Closed Shells: Statistical Energy Analysis, Modal Coupling, and Nonresonant Transmission

An investigation of sound transmission into small enclosures considers the effects of acoustically induced coupling between shell modes. Using an integral equation approach, the transmission loss into a small rectangular box is computed and the level of cavity reactance examined. The noise reduction for a closed cylinder sitting in a reverberant acoustic field is computed. The transmission by resonant and nonresonant shell modes is examined, especially in relation to the statistical energy analysis approach. The nature of the predominance of one type of transmission over the other is considered in relation to shell and cavity configurations and structural damping levels.

Diffraction about a Rigid Cylinder in a Reverberant Acoustic Field

The existence of an interference pattern about a cylinder exposed to a randomly incident acoustic field has been established analytically. [R. V. Waterhouse, J. Acoust. Soc. Amer. 35, 1610–1628 (1963)]. A series of experiments has been performed to investigate this phenomenon for the case where the wavelength of the incident waves is much smaller than the circumference of the cylinder. The experiments were performed in a reverberant acoustic field using a hard-walled cylindrical surface. The measured relationship between cylindrical radius, wavelength of excitation, and sound pressure level at varying radial distances is presented. The results are qualitatively compared with a calculation based on Waterhouse's solution for the diffraction around a cylinder in a two-dimensional field.

Response of Uniform Beams to Homogeneous, Random Pressure Fields

A study of the expression for the response power spectral density of linear systems to random pressures shows that the response problem essentially reduces to evaluating the joint acceptance of the system with the pressure field. A novel method using a coordinate transformation is presented. This method enables one to determine very simply the joint acceptance of a beam that has arbitrary end constraints with a pressure field that has a spatial-pressure correlation function that is easily described mathematically. The joint acceptance of a simply supported beam with a reverberant acoustic field as a function of mode number and nondimensionalized frequency parameter (beam length/acoustic wavelength) has been computed for the first 16 modes. An engineering approximation for the joint acceptance of a simply supported flat plate with a reverberant acoustic field is obtained from the beam results. The method is also used to determine very simply beam and flat-plate joint acceptance with a turbulent-boundary-layer pressure field and with an acoustic plane wave.

The response of a supersonic transport fuselage to boundary layer and to reverberant noise

The responses of part of the fuselage of a typical supersonic transport to turbulent boundary layer noise for two flight speeds, and to reverberant noise, are computed by the classical modal approach. These responses are used to compute equivalent reverberant acoustic fields which would produce essentially the same response in the structure as would turbulent boundary layer pressure fluctuations of given overall levels, spectra and correlation patterns. The equivalent reverberant acoustic fields may be used for cabin noise calculations, laboratory boundary layer simulation tests, or sonic fatigue studies.

Noise Reduction and Response of Two Concentric Cylinders

The equations for the noise reduction and response of two concentric cylinders subjected to a reverberant acoustic field were derived based on the statistical-energy approach. Using the derived equations, the noise reduction and response of two concentric cylinders were calculated and compared with experimental data. To verify the analytical results, two cylinders with the physical properties described above were placed inside an acoustic reverberant room. The ends of the cylinders were sealed with plywood. Microphones were placed outside, between, and inside the cylinders. Accelerometers were placed at random on both the cylinders. The resulting study can be applied to the prediction of the acoustic and vibration enironoments of a typical space vehicle enclosed within a shroud.