Model equation for strongly focused finite-amplitude sound beams

A model equation that describes the propagation of sound beams in a fluid i s developed using the oblate spheroidal coordinate system. This spheroidal beam equation (SBE) is a parabolic equation and has a specific application to a theoretical prediction on focused, high-frequency beams from a circula r aperture. The aperture angle does not have to be small. The theoretical b ackground is basically along the same analytical lines as the composite met hod (CM) reported previously [B. Ystad and J. Berntsen, Acustica 82, 698-70 6 (1996)]. Numerical examples are displayed for the amplitudes of sound pre ssure along and across the beam axis when sinusoidal waves are radiated fro m the source with uniform amplitude distribution. The primitive approach to linear field analysis is readily extended to the case where harmonic gener ation in finite-amplitude sound beams becomes significant due to the inhere nt nonlinearity of the medium. The theory provides the propagation and beam pattern profiles that differ from the CM solution for each harmonic compon ent. (C) 2000 Acoustical Society of America. [S0001-4966(00)03706-1].