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The Wave Equation for the Moving Source and the Moving Receiver
Version 1
: Received: 16 March 2024 / Approved: 17 March 2024 / Online: 18 March 2024 (10:08:28 CET)
How to cite: Dodig, H. The Wave Equation for the Moving Source and the Moving Receiver. Preprints 2024, 2024030977. https://doi.org/10.20944/preprints202403.0977.v1 Dodig, H. The Wave Equation for the Moving Source and the Moving Receiver. Preprints 2024, 2024030977. https://doi.org/10.20944/preprints202403.0977.v1
Abstract
The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but it does not admit solutions where the receiver is allowed to move. To overcome this limitation, the new wave equation is derived, permitting both the receiver and the source to move. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by the stationary point source. From this purely mathematical definition, the wave equation for the stationary source and the moving receiver is derived together with the corresponding free-space Green's function. Utilizing the derived Green's function, it was shown that this new wave equation also permits the solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for the moving source and the moving receiver governs the waves emitted by the moving point sources and received by the moving receivers.
Keywords
Standard wave equation; Wave propagation; Moving receiver; Moving source
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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