Abstract
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.
Highlights
Accurate modeling of the directivity of complex sound sources is a prerequisite for many applications in technical acoustics, sound reinforcement, sound field synthesis, and auralization
We demonstrate that our source synthesis method can model the directivity of a Genelec 8020c 2-way near-field monitor as an example for real-life sources
The impulse response of the Genelec 8020c monitor was measured in the semi-anechoic chamber at RWTH Aachen on a 2 Â 2 equi-angular sampling grid using an exponential sweep of order 14 and a G.R.A.S. 40AF half-inch free-field microphone placed at a distance of 2 m from the speaker
Summary
Accurate modeling of the directivity of complex sound sources is a prerequisite for many applications in technical acoustics, sound reinforcement, sound field synthesis, and auralization. Grid-based approaches, on the other hand, do not require any a priori knowledge of the source but try to fit the coefficients of a synthetic source such that the resulting sound field optimally reproduces a given reference This can be considered as an inverse optimization approach, where, typically, some kind of least-squares problem needs to be solved. In contrast to previous approaches of grid-based source synthesis, the present method is based on the Euler equation as a more general form of the wave equation This generalized form allows one to model the behavior of acoustic sources in situations with complex background flow and thermal stratification, relevant for applications such as ventilation systems with thermal gradients, sound reinforcement in open spaces such as train stations or sports stadiums, or noise pollution in urban environments.
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