Abstract
This paper presents a mathematical model of linear acoustic wave propagation in fluids. The benefits of a mathematical model over a normal mode analysis are first discussed, then the mathematical model for acoustic propagation in the test medium is developed using computer simulations. The approach is based on a analytical solution to the homogeneous wave equation for fluid medium. A good agreement between the computational presented results with published data.
Highlights
In recent years, physical acoustic wave modeling has become a successful tool in diagnostic and therapeutic ultrasound application
This paper presents a mathematical model of linear acoustic wave propagation in fluids
The approach is based on a analytical solution to the homogeneous wave equation for fluid medium
Summary
Physical acoustic wave modeling has become a successful tool in diagnostic and therapeutic ultrasound application. Discrete-time simulation algorithms for wave propagation can be derived by numerically solving a acoustic wave equation in terms of the variables for sound pressure and particle velocity. Initial conditions for time derivatives and boundary conditions for space derivatives are necessary to provide a complete set of solutions of the wave equation. These equations are most commonly solved by propagation in time. The normal mode method analysis gives exact solutions without any assumed restrictions on pressure and velocity components distributions. It can be applied to boundary-layer problems, which are described by the linearized Navier-stokes equations in electrohydrodynamic (Othman [13]). The normal mode analysis can be employed to solve linear acoustic wave equation analytically. The propagation of acoustic pressure wave by the normal mood analysis in a medium with two-dimensional spatially-variable acoustic properties has been explained
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