The influence of scattering and diffraction on the performance of sound intensity probes has been examined using a boundary element model of an axisymmetric two-microphone probe with the microphones in the usual face-to-face arrangement. On the basis of calculations for a variety of sound field conditions and probe geometries it is concluded that the optimum length of the spacer between the microphones is about one microphone diameter; with this geometry the effect of diffraction and the finite difference error almost counterbalance each other up to about an octave above the frequency limit determined by the finite difference approximation. This seems to be valid under virtually any sound field condition that could be of practical importance in sound power determination. The upper frequency limit corresponds to about 10 kHz for an intensity probe with 12-in. microphones, which means that it should be possible to cover most of the audible frequency range, say, from 50 Hz to 10 kHz, with a single probe configuration. The numerical results have been confirmed by a series of experiments.
Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin. This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both problems give rise to the same kind of degeneracy in the method, and modified formulations have been proposed to overcome this difficulty. However, such techniques are better suited for the so-called thin-body problem than for the reciprocal narrow-gap problem, and only the first is usually dealt with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers like sound intensity probes and condenser microphones has motivated this work, although the proposed technique has a wider range of applications.
The recent introduction of hand-held intensity measurement equipment has created a growing need for verification of the measurement equipment in the field. The key feature for easy field use is the possibility of calibrating the two-microphone intensity probe without dismounting the spacer. Working models were built, but none of them worked to more than approximately 3 kHz. Compliance with IEC 61043 requires the calibrator to work up to 7.1 kHz. A lot of modifications on these models were tried, but none of them worked. The development project was close to being stopped. A boundary-element model of the sound intensity calibrator was built. It verified the measured result from the working models. Based on the boundary-element model the best type and position of the sound source and the optimum dimensions of the calibrator cavity were found. Measurements on a final model verified the simulation results. The calibrations could now be made without dismounting the spacer.
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