Abstract
The equations of acoustics are based on the general equations of fluid dynamics: conservation of mass, momentum, energy and closed by the appropriate constitutive equation defining the thermodynamic state. The use of a perturbation ansatz, which decomposes the physical quantities density, pressure and velocity into mean, incompressible fluctuating and compressible fluctuating ones, allows to derive linearized acoustic conservation equations and its state equation. Thereby, we derive acoustic wave equations both for homogeneous and inhomogeneous media, and the equations model both vibrational- and flow-induced sound generation and its propagation.
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Notes
- 1.
In the following, we will use both vector and index notation; for the main operations see Appendix.
- 2.
For a detailed derivation of perturbation equations both for compressible as well as incompressible flows, we refer to Hüppe (2013).
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Acknowledgements
The author wishes to acknowledge his former Ph.D. student Andreas Hüppe for main contributions towards the derivations of the different aeroacoustic equations. Furthermore, many thanks to Stefan Schoder for proof reading and his usefull suggestions.
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Kaltenbacher, M. (2018). Fundamental Equations of Acoustics. In: Kaltenbacher, M. (eds) Computational Acoustics. CISM International Centre for Mechanical Sciences, vol 579. Springer, Cham. https://doi.org/10.1007/978-3-319-59038-7_1
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DOI: https://doi.org/10.1007/978-3-319-59038-7_1
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