Contemporary aspects of the theory and application of nonlinear acoustics

Abstract

The foundations of nonlinear acoustics may be traced nearly 250 years back in time, but only the last 50 years have shown an increasing number of attempts to exploit the research results in nonlinear acoustics. Based upon the fundamental equations of fluid dynamics, the second-order acoustic equations may be derived which can be reduced to a compound equation describing several of the most important and fast developing areas of research in nonlinear acoustics. The relations between this compound equation and Burgers' equation, Korteweg-DeVries equation, the K-Z-K equation, Westervelt's equation and the general second-order wave equation are discussed in depth. Finally, it is shown how the derivatives of the compound equation can be applied to nonlinear acoustic research related to materials characterisation by use of the B/A-ratio, to underwater acoustics by use of the parametric acoustic array and to focused, high-power ultrasonic fields.