Measurement and prediction of sound propagation over an absorbing plane

Ziqiang Hu, Purdue University

Abstract

In this thesis, a two-dimensional Hankel transform technique is described that makes it possible to predict multipole sound propagation over a finite impedance surface. The prediction procedure is based on representing the direct field of a source as a two-dimensional wavenumber spectrum in cylindrical coordinates. The transform procedure is illustrated here by using a number of examples and conclusions are drawn regarding ways of ensuring accurate predictions. The results of the transform procedure have also been found to be in excellent agreement with measurements of sound propagation over a finite impedance surface from a small, unbaffled loudspeaker. In principle, the Discrete Hankel Transform (DHT) approach described here may be used to predict the sound radiation from arbitrarily directional sources. However, owing to the time required to evaluate the inverse Hankel transform directly in discrete form, the calculation of a spatial sound pressure distribution can be time consuming. Here the use of a Fast Hankel Transform (FHT) has been investigated. The FHT in its original form was found to introduce significant computational noise. It has been found that a modification to the FHT algorithm results in improved prediction accuracy without a substantial increase in computation time. It is concluded that of the use of the FHT rather than the DHT can usually yield a significant reduction in the computation time required to make propagation predictions to a specified level of accuracy. The theory of reflection coefficient measurement in cylindrical coordinates is also described in this thesis. That theory allows for sound fields that are not cylindrically symmetric and thus allows a wide variety of sources to be used in practical measurement procedures. The principal benefit in using a two-dimensional Hankel transform approach is that it allows the use of a relatively high spatial sampling rate in the radial direction while permitting the use of a relatively low sampling rate in the azimuthal direction. The technique as presented here is source-independent, and can be used to estimate the reflection coefficient for both propagating and evanescent plane waves. In addition, the theory developed here makes it possible to measure the acoustic plane wave reflection coefficient of an azimuthally inhomogeneous reflecting surface. Another potential use of the present technique is to decompose a reverberant or semi-reverberant sound field into waves propagating in opposite directions, thus permitting the reconstruction of sources lying both above and below an enclosed region.

Degree

Ph.D.

Advisors

Bolton, Purdue University.

Subject Area

Mechanical engineering|Acoustics

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