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NUMERICAL SIMULATIONS OF SOUND WAVE GENERATION IN A RANDOM MEDIUM

K. Murawski, M. Selwa

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Abstract

Abstract: In turbulent media, both sound wave sources and the speed of sound can be stochastic variables. By means of numerical simulations of one-dimensional Euler equations with random source terms we have studied two cases in a homogeneous stochastic random medium for which the speed of sound and sound sources are: (1) correlated and (2) uncorrelated. The numerical simulations indicate that, if the source and the speed of sound fluctuations are uncorrelated, the acoustic field is incoherent, with a zero expectation value. The mean field is non-zero in the correlated case. The correlated and uncorrelated cases are clearly distinguishable by the mean field, but also – to some extent – in the power spectrum, which displays a modified Lorentzian profile with a shift in frequency.

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What this paper is about

Abstract: In turbulent media, both sound wave sources and the speed of sound can be stochastic variables. By means of numerical simulations of one-dimensional Euler equations with random source terms we have studied two cases in a homogeneous stochastic random medium for which the speed of sound and sound sources are: (1) correlated and (2) uncorrelated. The numerical simulations indicate that, if the source and the speed of sound fluctuations are uncorrelated, the acoustic field is incoherent, with a zero expectation value. The mean field is non-zero in the correlated case. The correlated and uncorrelated cases are clearly distinguishable by the mean field, but also – to some extent – in the power spectrum, which displays a modified Lorentzian profile with a shift in frequency.

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Available abstract

Abstract: In turbulent media, both sound wave sources and the speed of sound can be stochastic variables. By means of numerical simulations of one-dimensional Euler equations with random source terms we have studied two cases in a homogeneous stochastic random medium for which the speed of sound and sound sources are: (1) correlated and (2) uncorrelated. The numerical simulations indicate that, if the source and the speed of sound fluctuations are uncorrelated, the acoustic field is incoherent, with a zero expectation value. The mean field is non-zero in the correlated case. The correlated and uncorrelated cases are clearly distinguishable by the mean field, but also – to some extent – in the power spectrum, which displays a modified Lorentzian profile with a shift in frequency.

Key concepts: Uncorrelated, Statistical physics, Mathematics, Acoustic source localization, Critical distance, Acoustics, Speed of sound, Spectral density

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