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One-Way Wave Equation Derived from Impedance Theorem

1
Aeroakustik Stuttgart, D-81679 Munich, Germany
2
Independent Researcher, D-42799 Leichlingen, Germany
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Author to whom correspondence should be addressed.
Acoustics 2020, 2(1), 164-170; https://doi.org/10.3390/acoustics2010012
Received: 15 December 2019 / Revised: 14 February 2020 / Accepted: 18 February 2020 / Published: 10 March 2020
The wave equations for longitudinal and transverse waves being used in seismic calculations are based on the classical force/moment balance. Mathematically, these equations are 2nd order partial differential equations (PDE) and contain two solutions with a forward and a backward propagating wave, therefore also called “Two-way wave equation”. In order to solve this inherent ambiguity many auxiliary equations were developed being summarized under “One-way wave equation”. In this article the impedance theorem is interpreted as a wave equation with a unique solution. This 1st order PDE is mathematically more convenient than the 2nd order PDE. Furthermore the 1st order wave equation being valid for three-dimensional wave propagation in an inhomogeneous continuum is derived. View Full-Text
Keywords: one-way wave equation; 1st order wave equation; two-way wave equation; 2nd order wave equation; impedance theorem; longitudinal wave propagation; inhomogeneous continuum one-way wave equation; 1st order wave equation; two-way wave equation; 2nd order wave equation; impedance theorem; longitudinal wave propagation; inhomogeneous continuum
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Bschorr, O.; Raida, H.-J. One-Way Wave Equation Derived from Impedance Theorem. Acoustics 2020, 2, 164-170.

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