Bridging shock: Blackstock’s general solution for propagation of finite-amplitude sound waves

Abstract

Reflections are offered on D. T. Blackstock [“Connection between the Fay and Fubini solutions for plane sound waves of finite amplitude,” J. Acoust. Soc. Am. 39, 1019–1026 (1966)]. This work treats the propagation of planar finite-amplitude sound waves. It nominally links the Fourier-series-based solution of Fubini for the pre-shock condition, and the distant, post-shock solution of Fay. However, addressing the transition region between these two required solving the entire problem, which Blackstock did with aplomb. This additionally enabled specification of undetermined factors in the Fay solution, statement of an explicit bound on the applicability of the solution, and generalization to cylindrical and spherical waves. Hallmarks of Blackstock’s work are evident: scholarly mindfulness of historical precedent, meticulous analysis that inevitably advanced understanding of nonlinear acoustic phenomena, and elegance in presentation, which was, moreover, pedagogically convincing.