### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4pPAa9. Prediction of the time-averaged pressure distribution for finite
amplitude standing waves.

**Reh-lin Chen
**

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Victor W. Sparrow
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**
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*Graduate Prog. in Acoust., Penn State Univ., 157 Hammond Bldg., University
Park, PA 16802
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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.