ABSTRACT
AFIT-the Acoustic Finite Integration Technique-is the acronym for a numerical code to calculate the radiation, propagation, and scattering of acoustic waves (Wolter 1995; Marklein 1997): The propagation physics of acoustic waves, mathematically formulated with the acoustic governing equations, is literally visualized that way. Here, we calculate the pulsed wave field of an acoustic aperture radiator on the acoustically rigid surface of a half-space (infinitely rigid baffled transducer) using AFIT and display the field in terms of pulsed wavefronts (Figure 14.1). Afterward, we know what the respective analytical calculation should deliver, and we will see what it can deliver. Figure 14.1 (top) displays the pulsed wavefront of the pressure for a line dilatation rate source with RC2(t)-time dependence [more precisely: the time derivative of a dilatation rate source in order to account for the factor jω in (14.23)]; in the terminology of the next section, this is the RC2(ω)-bandlimited two-dimensional Green function satisfying a Neumann boundary condition: GN(x, z, t) ∗ RC2(t). The result meets our expectations: We observe a (twodimensional) semicircular wavefront that, according to our assumption, satisfies a Neumann boundary condition on the rigid surface, i.e., the normal component of the particle velocity vanishes. Figure 14.1 (bottom) shows the respective pulsed wavefronts of the pressure radiated from a strip-like dilatation rate aperture with constant amplitude: According to the scalar Huygens principle, each aperture point radiates semicircular wavefronts forming a plane pressure wavefront as envelope that is tangential to the semicircular wavefronts emanating from the aperture edges, it has the same lateral dimension as the aperture itself. Note: With increasing travel time, the radius of the aperture edge pulses increases, they nestle more and more against the aperture
K12611 Chapter: 14 page: 501 date: January 18, 2012
K12611 Chapter: 14 page: 502 date: January 18, 2012
FIGURE 14.1 AFIT-wavefronts of the line and strip-like infinitely rigid baffled aperture radiator (acoustic pressure with pressure prescribed within the aperture).
