1pPA5. Perturbation and physics: A question raised in standing wave study.

Session: Monday Afternoon, December 2

Time: 3:00

Author: Dah-You Maa
Location: Inst. of Acoust., Academia Sinica, P.O. Box 2712, Beijing 100080, PROC


The perturbation method is a powerful tool in the treatment of nonlinear problems in physics. In the history of nonlinear acoustics, however, it was found unsuccessful when a standing wave was treated. In the Laplacian system of coordinates, the second-order approximate differential equation, after the first-order particle velocity u[sup (1)] is substituted, yields an ever-increasing solution for the second-order quantity u[sup (2)]. The result is certainly mistaken; how can an unstable solution come out of a stable system like the standing wave? From the physical considerations, the second spatial derivative of u[sup (2)] should not be preserved in the differential equation. The reason is that u[sup (2)] is merely the modification of u[sup (1)] at different points on the waveform due to nonlinearity, and its distribution is completely determined and accounted for by that of u[sup (1)] through the nonlinear term in the equation. The solution thus obtained is stable and agrees well with the exact solution. On the other hand, the Laplacian sound pressure derived from the particle velocity does not convert to the Eulerian one by the transformation of coordinates, the variable air density and sound velocity must be taken into account. Physics must be kept in mind when the perturbation method is applied. [Work supported by NNSF, PROC.]

ASA 132nd meeting - Hawaii, December 1996