## 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**

**Abstract:**

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