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a Directivity diagram obtained increasing the angular resolution by interpolation of the data of Fig. 2. b Obtained radiated sound field simulated in a FDTD mesh.
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Discrete-time domain methods provide a simple and flexible way to solve initial boundary value problems. With regard to the sources in such methods, only monopoles or dipoles can be considered. However, in many problems such as room acoustics, the radiation of realistic sources is directional-dependent and their directivity patterns have a clear in...
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... It leads to our initial assumption that the top plate is solely considered a sound source and we attempt to simulate the radiation patterns from the mode shapes of the plate. This can be achieved by considering each node on the top plate as a point source and combining [23] the resulting monopoles of different phases and amplitudes to calculate the overall sound pressure at a point, ...
... The sound pressure emitted from the nodal point source, for a modal frequency, is calculated as [23]: ...
The large wooden resonator of the Sarasvati Veena amplifies and radiates the sound in almost all directions. The directional and spatial dependence of this radiation is studied in conjunction with the mode shapes of the top plate of the resonator. Sound radiation patterns are simulated theoretically using the nodal displacement data obtained from the numerical modal analysis of the resonator. The experimental analysis involves the manual plucking of the Veena string. The radiated sound is recorded by placing microphones around the resonator in circular arrays of different radii in the different planes. These combinations of arrays at different distances and planes provide a thorough knowledge of sound radiating out of the resonator. The intensities of different frequencies in the recorded spectral data as functions of direction and distance from the approximate center of the top plate of the resonator are studied. Experimentally measured patterns show the importance of the top plate over the body of the resonator. Theoretical and experimental radiation patterns for different harmonics of the plucked string are compared and a good match is observed. The behavior of the radiating sound in the different planes at different radial distances from the assumed center is discussed.
... By assuming an array of point sources, the source strength (also known as the driving function) for each source is obtained via fitting against a predefined or measured directivity. 15,16 The multipole-based methods express the sound field radiated by a directional source using the cylindrical 4 and spherical 8 harmonic representations in two-dimensional (2D) and three-dimensional (3D) models, respectively. The concept is that the cylindrical or spherical harmonics form an orthogonal and complete basis for any well-behaved functions defined on a circle and a sphere, respectively, so that the directivity can be represented using either basis. ...
The prediction of reverberant sound fields generated by a directional source is of great interest because practical sound sources are not omnidirectional, especially at high frequencies. For an arbitrary directional source described by cylindrical and spherical harmonics, this paper developed a modal expansion method for calculating the reverberant sound field generated by such a source in both two-dimensional and three-dimensional rectangular enclosures with finite impedance walls. The key is to express the modal source density using the cylindrical or spherical harmonic expansion coefficients of the directional source. A method based on the fast Fourier transform is proposed to enable the fast computation of the summation of enclosure modes when walls are lightly damped or rigid. This makes it possible to obtain accurate reverberant sound fields even in a large room and/or at high frequencies with a relatively low computational load. Numerical results with several typical directional sources are presented. The efficiency and the accuracy of the proposed method are validated by the comparison to the results obtained using the finite element method.
... 26 Such models are often more convenient for numerical simulations using directivities. 29 Figure 2 illustrates the locations and amplitudes of a seven-point-source model that reconstructs the pressure field for kR << 1 with high accuracy provided that kϵ << 1, where ϵ is the separation distance of opposing point sources. The single point source at the origin represents the monopole field, whereas the three orthogonal opposite-polarity pairs represent the dipole field. ...
The structural modes of gamelan gongs often have clear impacts on their far-field directivity patterns with the number of directional lobes corresponding to the associated structural mode shapes. Many of the lowest modes produce dipole-like radiation with the dipole moment determined by the positions of the nodal and antinodal regions. Spherical harmonic and multipole expansions facilitate further understanding of the gongs’ low-frequency directional characteristics. The expansions also yield practical simplifications to model their radiation.
... The most basic method is to introduce a simple directivity such as a dipole [3,4] or cardioid [5,6]. Furthermore, various methods such as spatial distribution of multipole sources or receivers with amplitude weightings [3,7,8], and more recently, the spherical harmonic functions method have been proposed [9,10]. However, there are only limited studies on a moving source or receiver with directivity. ...
This paper reports on the implementation of a moving sound source and receiver with directivity in the two-dimensional finite-difference time-domain (FDTD) method. A two-dimensional fundamental solution of a moving monopole source is theoretically derived. Then, a fundamental solution of a moving dipole source is obtained by differentiating the fundamental solution of a monopole source in space. Finally, the directivity of moving monopole, dipole, and cardioid sources is theoretically derived. Numerical experiments performed on the two-dimensional sound field showed that the effect of moving velocity on amplitude differs for the monopole and dipole sources. Furthermore, it was found that directivity characteristics of dipole and cardioid sources vary depending on the beam steering angle and moving direction. The present method can be accurately applied to the moving sound source and receiver with directivity.
... For example, the source directivity affects how strongly individual room modes are excited. This phenomenon becomes evident when decomposing a source with arbitrary directivity into monopoles with different amplitudes and phases [36], [37]. Each monopole excites the same room modes, but with different amplitudes. ...
The decaying sound field in rooms is typically described by energy decay functions (EDFs). Late reverberation can deviate considerably from the ideal diffuse field, for example, in multiple connected rooms or non-uniform absorption material distributions. This paper proposes the common-slope model of late reverberation. The model describes spatial and directional late reverberation as linear combinations of exponential decays called common slopes. Its fundamental idea is that common slopes have decay times that are invariant across space and direction, while their amplitudes vary across both. We explore different approaches for determining the common slopes for large EDF sets describing different source-receiver configurations of the same environment. Among the presented approaches, the k-means clustering of decay times is the most general. Our evaluation shows that the common-slope model introduces only a small error between the modeled and the true EDF, while being considerably more compact than the traditional multi-exponential model. The amplitude variations of the common slopes yield interpretable room acoustic analyses. The common-slope model has potential applications in all fields relying on late reverberation models, such as source separation, dereverberation, echo cancellation, and parametric spatial audio rendering.
... For example, the source directivity affects how strongly individual room modes are excited. This phenomenon becomes evident when decomposing a source with arbitrary directivity into monopoles with different amplitudes and phases [44], [45]. Each monopole excites the same room modes, but with different amplitudes. ...
The decaying sound field in rooms is typically described in terms of energy decay functions (EDFs). Late reverberation can deviate considerably from the ideal diffuse field, for example, in scenes with multiple connected rooms or non-uniform absorption material distributions. This paper proposes the common-slope model of late reverberation. The model can be used to describe spatial and directional late reverberation variations as linear combinations of exponential decays with fixed decay times. Its fundamental idea is to determine a set of common decay times that is representative of multiple EDFs. Consequently, all spatial and directional EDF variations are described solely with amplitude changes of the respective decaying exponentials. After deriving the common-slope model, we explore different approaches for determining the common decay times for large EDF sets, whose EDFs describe different source-receiver configurations of the same environment. Among the presented approaches, the k-means clustering of decay times is the most general. Our evaluation shows that the common-slope model introduces only a small error between the modeled and the true EDF, although the common-slope model is considerably more compact than the traditional multi-exponential model. Due to its compactness, the common-slope model yields interpretable room acoustic analysis results. The common-slope model has potential applications in all fields relying on late reverberation models, such as source separation, dereverberation, echo cancellation, and parametric spatial audio rendering.
... For example, the source directivity affects how strongly individual room modes are excited. This phenomenon becomes evident when decomposing a source with arbitrary directivity into monopoles with different amplitudes and phases [44], [45]. Each monopole excites the same room modes, but with different amplitudes. ...
p>The decaying sound field in rooms is typically described in terms of energy decay functions (EDFs). Late reverberation can deviate considerably from the ideal diffuse field, for example, in scenes with multiple connected rooms or non-uniform absorption material distributions. This paper proposes the common-slope model of late reverberation. The model can be used to describe spatial and directional late reverberation variations as linear combinations of exponential decays with fixed decay times. Its fundamental idea is to determine a set of common decay times that is representative of multiple EDFs. Consequently, all spatial and directional EDF variations are described solely with amplitude changes of the respective decaying exponentials. After deriving the common-slope model, we explore different approaches for determining the common decay times for large EDF sets, whose EDFs describe different source-receiver configurations of the same environment. Among the presented approaches, the k-means clustering of decay times is the most general. Our evaluation shows that the common-slope model introduces only a small error between the modeled and the true EDF, although the common-slope model is considerably more compact than the traditional multi-exponential model. Due to its compactness, the common-slope model yields interpretable room acoustic analysis results. The common-slope model has potential applications in all fields relying on late reverberation models, such as source separation, dereverberation, echo cancellation, and parametric spatial audio rendering.</p
... One approach involves combinations of a small number of basic sources, usually in alignment with a Cartesian grid, in order to generate simple directivity patterns 12,17 . Larger collections of simple monopole sources have been used as the basis for fitting against measured source directivities [18][19][20] . Source directivity modeling using spherical harmonic representations has been also been employed in wave-based methods, using pseudospectral time domain methods 7 , and using FDTD 21 , leading to a very sparse representation of the source in terms of a canonical set of spherical harmonic difference operators and low order finite impulse response filters. ...
All acoustic sources are of finite spatial extent. In volumetric wave-based simulation approaches (including, e.g., the finite difference time domain method among many others), a direct approach is to represent such continuous source distributions in terms of a collection of point like sources at grid locations. Such a representation requires interpolation over the grid, and leads to common staircasing effects, particularly under rotation or translation of the distribution. In this article, a different representation is shown, based on a spherical harmonic representation of a given distribution. The source itself is decoupled from any particular arrangement of grid points, and is compactly represented as a series of filter responses used to drive a canonical set of source terms, each activating a given spherical harmonic directivity pattern. Such filter responses are derived for a variety of commonly-encountered distributions. Simulation results are presented, illustrating various features of such a representation, including convergence, behaviour under rotation, the extension to the time varying case and differences in computational cost relative to standard grid-based source representations.
... Alternatively, grid-based least-squares problems of source synthesis can be based on a finite-difference timedomain (FDTD) method and solved in the time domain, for example, by determining a minimum eigenvector with an Arnoldi type algorithm (Takeuchi et al., 2019) or by obtaining a least-square fit by calculating a Moore-Penrose pseudo-inverse (Bilbao et al., 2019;Escolano et al., 2007). Other comparable finite-differences sound source modeling techniques are the pseudospectral time-domain method (Georgiou and Hornikx, 2016). ...
An adjoint-based approach for synthesizing complex sound sources by discrete, grid-based monopoles in finite-difference time-domain simulations is presented. Previously, Stein, Straube, Sesterhenn, Weinzierl, and Lemke [(2019). J. Acoust. Soc. Am. 146(3), 1774-1785] demonstrated that the approach allows one to consider unsteady and non-uniform ambient conditions such as wind flow and thermal gradient in contrast to standard methods of numerical sound field simulation. In this work, it is proven that not only ideal monopoles but also realistic sound sources with complex directivity characteristics can be synthesized. In detail, an oscillating circular piston and a real two-way near-field monitor are modeled. The required number of monopoles in terms of the sound pressure level deviation between the directivity of the original and the synthesized source is analyzed. Since the computational effort is independent of the number of monopoles used for the synthesis, also more complex sources can be reproduced by increasing the number of monopoles utilized. In contrast to classical least-square problem solvers, this does not increase the computational effort, which makes the method attractive for predicting the effect of sound reinforcement systems with highly directional sources under difficult acoustic boundary conditions.
... Geometric acoustics algorithms are able to incorporate SHbased sound source directivity data, even when incomplete (sparse and available over selected bands) [7], [6], [8], [3]. Wave-based methods such as, e.g., the finite difference time domain (FDTD) method [44], [45], [46], require more care in the incorporation of source directivity [47], [48], [49]. See, e.g., recent work allowing for the incorporation of measured directivity into an FDTD method, assuming a complete set of directivity data [12]. ...
The measurement of directivity for sound sources that are not electroacoustic transducers is fundamentally limited because the source cannot be driven with arbitrary signals. A consequence is that directivity can only be measured at a sparse set of frequencies—for example, at the stable partial oscillations of a steady tone played by a musical instrument or from the human voice. This limitation prevents the data from being used in certain applications such as time-domain room acoustic simulations where the directivity needs to be available at all frequencies in the frequency range of interest. We demonstrate in this article that imposing the signature of the directivity that is obtained at a given distance on a spherical wave allows for all interpolation that is required for obtaining a complete spherical harmonic representation of the source’s directivity, i.e., a representation that is viable at any frequency, in any direction, and at any distance. Our approach is inspired by the far-field signature of exterior sound fields. It is not capable of incorporating the phase of the directivity directly. We argue based on directivity measurement data of musical instruments that the phase of such measurement data is too unreliable or too ambiguous to be useful. We incorporate numerically-derived directivity into the example application of finite difference time domain simulation of the acoustic field, which has not been possible previously.
