Victor W. Sparrow
Graduate Prog. in Acoust., Penn State Univ., 157 Hammond Bldg., University Park, PA 16802
A finite difference numerical approach to studying two-dimensional nonlinear wave propagation was recently developed [V. W. Sparrow and R. Raspet, J. Acoust. Soc. Am. 90, 2683--2691 (1991)]. In this talk the approach is modified and applied to a one-dimensional finite amplitude standing wave in a rigid tube. The numerical method can solve for lossless, weakly nonlinear waves in the tube including all second-order nonlinearities from the continuity equation, momentum equation, and the equation of state. The acoustic pressure in the time, space, and frequency domains and the time-averaged acoustic pressure distribution are all determined. Generation of harmonics of the fundamental frequency along with the development of a nonzero, time-averaged pressure are seen from discrete Fourier transforms of the numerical results. The results for the time-averaged pressure distribution are compared to recent analytical predictions [C. P. Lee and T. G. Wang, J. Acoust. Soc. Am. 94, 1099--1109 (1993)]. The results show agreement between the present work and that of Lee and Wang when the nonlinearities from both the momentum equation and equation of state are included. A slightly different result is obtained when one also includes nonlinearity from the continuity equation.