Determination of the green function of a pulsed acoustic source in a uniform homogeneous flow with an arbitrary Mach number

Keywords: Fourier expansion, Cauchy problem, causality principle, properties of the δ-function, delay, wavefront, Mach number

Abstract

The wave field created by a pulsed point source of sound in a uniform homogeneous flow with an arbitrary value of the Mach number is theoretically studied. The aim of research is to obtain an analytical dependence of the sound field on physical parameters.

The space-waveguide Fourier expansion of the sound field is used to solve the Cauchy problem for the wave equation in a reference frame moving together with the medium. It is only necessary to transform the spatiotemporal dependence of the source, given in a fixed frame of reference, to a dependence in a moving frame of reference.

The transition to the description of the solution in the frame of reference, relative to which the medium moves at a constant velocity, is made taking into account the main properties of the generalized Dirac δ-function.

Analytical dependences of the sound field on physical parameters are obtained for both subsonic and supersonic flows. A comparison is made with the results of calculations for the case of a pulsed point source moving in a medium at rest. The solution obtained in this work for the case of an impulsive source moving in a medium at rest made it possible to trace its connection with the Green's function for a stationary source in a moving medium. The analytical dependence of the obtained solution for the Green's function makes it possible to write down the explicit form of the "characteristic solution surface", that is, the "wave front". It is shown that the difference between the solutions for subsonic and supersonic motion is characterized by the position of the source relative to the moving wavefront.

The calculation results can be used to describe the sound field created by an arbitrary spatiotemporal distribution of sound sources

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Author Biographies

Anatoliy Bryukhovetski, O. Ya. Usikov Institute for Radio Physics and Electronics of the National Academy of Sciences of Ukraine

Department of Radiosignal Processing

Aleksey Vichkan', O. Ya. Usikov Institute for Radio Physics and Electronics of the National Academy of Sciences of Ukraine

Department of Radiosignal Processing

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Determination of the green function of a pulsed acoustic source in a homogeneous flow with an arbitrary Mach number

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Published
2023-01-19
How to Cite
Bryukhovetski, A., & Vichkan’, A. (2023). Determination of the green function of a pulsed acoustic source in a uniform homogeneous flow with an arbitrary Mach number. EUREKA: Physics and Engineering, (1), 165-176. https://doi.org/10.21303/2461-4262.2023.002743
Section
Mathematics