Sound field visualization for primary reflection using equivalent sources and image source methods

The Green’s function (GF) directly eases the efficient computation for acoustic radiation problems in shallow water with the use of the Helmholtz integral equation. The difficulty in solving the GF in shallow water lies in the need to consider the boundary effects. In this paper, a rigorous theoretical model of interactions between the spherical wave and the liquid boundary is established by Fourier transform. The accurate and adaptive GF for the acoustic problems in the Pekeris waveguide with lossy seabed is derived, which is based on the image source method (ISM) and wave acoustics. First, the spherical wave is decomposed into plane waves in different incident angles. Second, each plane wave is multiplied by the corresponding reflection coefficient to obtain the reflected sound field, and the field is superposed to obtain the reflected sound field of the spherical wave. Then, the sound field of all image sources and the physical source are summed to obtain the GF in the Pekeris waveguide. The results computed by this method are compared with the standard wavenumber integration method, which verifies the accuracy of the GF for the near- and far-field acoustic problems. The influence of seabed attenuation on modal interference patterns is analyzed.

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Reconstruction of semi-free transient sound field under different reflection conditions using an extended interpolated time-domain equivalent source method

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214542035 ◽

2014 ◽

Vol 229 (5) ◽

pp. 895-905 ◽

Cited By ~ 1

Author(s):

Siwei Pan ◽

Weikang Jiang ◽

Shang Xiang

Keyword(s):

Time Domain ◽

Free Field ◽

Sound Field ◽

Sound Sources ◽

Equivalent Source ◽

Source Method ◽

Equivalent Sources ◽

The Time Domain ◽

Reflecting Surface ◽

Equivalent Source Method

Transient acoustic field can be rebuilt directly in the time-domain via the interpolated time-domain equivalent source method (ITDESM). However, this method requires that the reconstruction should be addressed in the free-field only, which can hardly be met in the engineering noise problems. To circumvent this difficulty, an extended ITDESM procedure is developed by extending the ITDESM from the free-field to the semi-free-field. In this approach, the time-domain equivalent sources are placed not only near the actual sound sources but also around their image sources with respect to the planar reflecting surface. The solving procedure of the equivalent source strengths is improved to decrease the computing load. The reflection conditions treated here can be arbitrary, i.e. both perfectly rigid and impedance-effected. Reconstruction results of the transient sound field radiated from three monopoles under different reflection conditions demonstrate the validity and applicability of the proposed method.

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Prediction of Sound Level in Rooms and Experimental Validation

Building Acoustics ◽

10.1177/1351010x9700400204 ◽

1997 ◽

Vol 4 (2) ◽

pp. 117-135

Author(s):

Mauricy Cesar R. de Souza ◽

Samir N.Y. Gerges

Keyword(s):

Ray Tracing ◽

Input Data ◽

Sound Propagation ◽

Power Level ◽

Computing Time ◽

Sound Field ◽

Sound Level ◽

Image Source ◽

Geometric Acoustics ◽

Ray Tracing Model

Traditional Sabine equations still are used for factories or offices where diffuse sound fields rarely occur and prediction can be inaccurate. More recently, methods based on geometric acoustics have been developed which require large computing time and which demand better defined input data. A problem, often encountered, is how to include input data which is appropriate, accurate and relatively easy to obtain. Three acoustic models of a furnished room were created: a diffuse field, an image source and a ray tracing model. The initial values of absorption coefficient and sound power level were obtained by standard measurements and the sound propagation SP was predicted and compared with measurement for each model. Then, the models were calibrated by altering the input parameters in order to minimise the difference between predicted and measured values. Sound pressure level due to two sources was also predicted and compared with measurement. For the room studied, the precision of the predictions, after calibration, is similar for the three models considered, with an average difference between simulated and measured values of less than 2 dB. Without the calibration procedure, the ray-tracing model gave the most precise first estimate. The diffuse and image source models needed significant modification of the input data to obtain a similar precision. The sound field in the room chosen for this study was nearly diffuse and simulation, based on geometric acoustics, did not offer clear advantages. However, this will not be the case for rooms with more complicated geometrical and acoustic characteristics such as in factories and offices. In addition, the image source model will not be appropriate for internal fittings which are much more complex than in the present study and an appropriate estimate of the scattering cross-section is problematical. In the ray tracing model, this problem is circumvented by incorporating the fittings as part of the geometry of the room.

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Coherent Image Source Modeling of Sound Fields in Long Spaces with a Sound-Absorbing Ceiling

Applied Sciences ◽

10.3390/app11156743 ◽

2021 ◽

Vol 11 (15) ◽

pp. 6743

Author(s):

Hequn Min ◽

Ke Xu

Keyword(s):

Sound Field ◽

Wave Theory ◽

Source Model ◽

Scale Model ◽

Source Modeling ◽

Image Source ◽

Sound Fields ◽

Absorbing Boundaries ◽

Proposed Model ◽

Coherent Image

Sound-absorbing boundaries can attenuate noise propagation in practical long spaces, but fast and accurate sound field modeling in this situation is still difficult. This paper presents a coherent image source model for simple yet accurate prediction of the sound field in long enclosures with a sound absorbing ceiling. In the proposed model, the reflections on the absorbent boundary are separated from those on reflective ones during evaluating reflection coefficients. The model is compared with the classic wave theory, an existing coherent image source model and a scale-model experiment. The results show that the proposed model provides remarkable accuracy advantage over the existing models yet is fast for sound prediction in long spaces.

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Optimization of the Equivalent Source Configuration for the Equivalent Source Method

Journal of Marine Science and Engineering ◽

10.3390/jmse9080807 ◽

2021 ◽

Vol 9 (8) ◽

pp. 807

Author(s):

Lanyue Zhang ◽

Jia Wang ◽

Desen Yang ◽

Bo Hu ◽

Di Wu

Keyword(s):

Acoustic Radiation ◽

Optimal Solution ◽

Sound Field ◽

Optimization Method ◽

Field Calculation ◽

Equivalent Source ◽

Source Method ◽

Calculation Results ◽

Equivalent Sources ◽

Equivalent Source Method

The equivalent source method is widely applied to study structural acoustic radiation in an underwater environment. However, there is still uncertainty in arranging the equivalent source, and the current mainstream configuration method needs a large number of equivalent sources, limiting its practical applicability. In this paper, an equivalent source configuration method that is simple, effective, and easy to implement, and which based on a tradeoff between the ill condition of the transfer matrix and the adequacy of the simulated structure’s radiated sound field, is proposed. The optimization method can derive the appropriate positions and quantity of monopole equivalent sources simultaneously. The method does not yield an optimal solution in a strict mathematical sense but provides satisfactory results compared with those obtained by uniformly distributed equivalent sources. Numerical simulation results showed that the optimization method derives accurate sound field calculation results with a relatively small number of equivalent sources, significantly reducing the number of subsequent calculations needed. Finally, the experiments conducted with a cylindrical shell structure verified the validity and practicality of the proposed method.

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Optimization of Equivalent Source Configuration for an Independent-Equivalent Source Method in Half-Space Sound Field

Shock and Vibration ◽

10.1155/2020/6029393 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Wen-Qian Jing ◽

Huawei Wu ◽

Jin-Quan Nie

Keyword(s):

Numerical Simulations ◽

Half Space ◽

Sound Field ◽

Reconstruction Accuracy ◽

Equivalent Source ◽

Source Method ◽

Equivalent Sources ◽

Optimal Configurations ◽

Measured Pressure ◽

Equivalent Source Method

In the situation that vibrating objects are located above a reflecting plane, an independent-equivalent source method (I-ESM) regards the reflections due to the plane as being radiated by equivalent sources placed under the plane and then the half-space sound field is reconstructed by matching the measured pressure with the equivalent sources distributed within the vibrating object and those substituting for reflections. But, this method heavily depends on the equivalent source configuration and may obtain bad reconstruction results if the equivalent sources are arranged incorrectly. This paper deals with the optimization of the equivalent source configuration to ensure I-ESM always perform well. Through numerical simulations and experiments, the influence of equivalent source configurations on the reconstruction accuracy was studied and optimal configurations were acquired and confirmed.

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Sound production at the edge of a steady flow

Journal of Fluid Mechanics ◽

10.1017/s0022112074000516 ◽

1974 ◽

Vol 66 (4) ◽

pp. 791-816 ◽

Cited By ~ 35

Author(s):

J. E. Ffowcs Williams

Keyword(s):

Shear Layer ◽

Sound Production ◽

Jet Noise ◽

Sound Field ◽

Vortex Sheet ◽

Sound Waves ◽

Plane Shear ◽

Distinct Structure ◽

Amplifying Effect ◽

Equivalent Sources

The theory initiated by Lighthill (1952) to describe the sound radiated by turbulence embedded in an uniform fluid at rest is here extended to the case where the turbulence exists on the edge of a uniformly moving stream. An exact analogy is developed between the distant real sound field and that which would be radiated by a particular quadrupole distribution adjacent to a vortex sheet positioned in the linearly disturbed flow. The equivalent sources in this analogy are quadrupoles identical in strength with those in Lighthill's model, but the quadrupoles are now shown to convect with the fluid-particle velocity. There is no amplifying effect of shear. The particular case of a plane shear layer is worked out in detail for sound waves of scale large in comparison with the shear-layer thickness.A downstream zone of silence is predicted as is the formation of highly directional beams associated with the interference of sound radiated directly and sound reflected from the fluid interface. A distinct structure results in which the variation of sound with flow velocity, density and angle is not easily accounted for by simple power-law scaling. Finally a comparison is made with some features of jet noise; the modelling of the high frequency jet noise problem by a single shear layer yields some features consistent with experiment.

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Spatial extrapolation of early room impulse responses in local area using sparse equivalent sources and image source method

Applied Acoustics ◽

10.1016/j.apacoust.2021.108027 ◽

2021 ◽

Vol 179 ◽

pp. 108027

Author(s):

Izumi Tsunokuni ◽

Kakeru Kurokawa ◽

Haruka Matsuhashi ◽

Yusuke Ikeda ◽

Naotoshi Osaka

Keyword(s):

Local Area ◽

Impulse Responses ◽

Image Source ◽

Source Method ◽

Equivalent Sources

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Decay of Temporary Threshold Shift in Noise

Journal of Speech and Hearing Research ◽

10.1044/jshr.1602.267 ◽

1973 ◽

Vol 16 (2) ◽

pp. 267-270 ◽

Cited By ~ 5

Author(s):

John H. Mills ◽

Seija A. Talo ◽

Gloria S. Gordon

Keyword(s):

Sound Field ◽

Threshold Shift ◽

Temporary Threshold Shift ◽

Octave Band ◽

Band Noise ◽

Lower Asymptote

Groups of monaural chinchillas trained in behavioral audiometry were exposed in a diffuse sound field to an octave-band noise centered at 4.0 k Hz. The growth of temporary threshold shift (TTS) at 5.7 k Hz from zero to an asymptote (TTS ∞ ) required about 24 hours, and the growth of TTS at 5.7 k Hz from an asymptote to a higher asymptote, about 12–24 hours. TTS ∞ can be described by the equation TTS ∞ = 1.6(SPL-A) where A = 47. These results are consistent with those previously reported in this journal by Carder and Miller and Mills and Talo. Whereas the decay of TTS ∞ to zero required about three days, the decay of TTS ∞ to a lower TTS ∞ required about three to seven days. The decay of TTS ∞ in noise, therefore, appears to require slightly more time than the decay of TTS ∞ in the quiet. However, for a given level of noise, the magnitude of TTS ∞ is the same regardless of whether the TTS asymptote is approached from zero, from a lower asymptote, or from a higher asymptote.

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Modified Earpieces and CROS for High Frequency Hearing Losses

Journal of Speech and Hearing Research ◽

10.1044/jshr.1101.204 ◽

1968 ◽

Vol 11 (1) ◽

pp. 204-218 ◽

Cited By ~ 9

Author(s):

Elizabeth Dodds ◽

Earl Harford

Keyword(s):

Hearing Loss ◽

Hearing Aids ◽

High Frequency ◽

Hearing Aid ◽

Sound Field ◽

Intensity Level ◽

Test Results ◽

High Frequency Hearing Loss ◽

Increased Sensitivity ◽

Difficult Cases

Persons with a high frequency hearing loss are difficult cases for whom to find suitable amplification. We have experienced some success with this problem in our Hearing Clinics using a specially designed earmold with a hearing aid. Thirty-five cases with high frequency hearing losses were selected from our clinical files for analysis of test results using standard, vented, and open earpieces. A statistical analysis of test results revealed that PB scores in sound field, using an average conversational intensity level (70 dB SPL), were enhanced when utilizing any one of the three earmolds. This result was due undoubtedly to increased sensitivity provided by the hearing aid. Only the open earmold used with a CROS hearing aid resulted in a significant improvement in discrimination when compared with the group’s unaided PB score under earphones or when comparing inter-earmold scores. These findings suggest that the inclusion of the open earmold with a CROS aid in the audiologist’s armamentarium should increase his flexibility in selecting hearing aids for persons with a high frequency hearing loss.

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