Estimating sound power from discrete measurements of sound intensity on a hemisphere

Abstract

In theory, total sound power radiated from a noise source can be determined by integrating the normal component of sound intensity over an arbitrary enclosing surface S. In practice, one must settle for approximation, taking the sound power integral to be a weighted sum of intensity measurements at certain strategically located nodes, or meshpoints, on S. What are the strategic locations, what are the weights, and what level of accuracy can be expected? The present paper attempts to answer these questions for the particular experimental setup described in a recent publication [R. Hickling and L. N. Bolen, “Indoor system for efficient measurement of the sound power of light vehicles,” NCPA Rep. RH-01-88]. Here, S is a hemisphere H plus circular base B—the latter a physical boundary that is perfectly reflective. The mesh covers H but not B: it appears rectangular in cylindrical projection, with longitudes equally spaced. Strategic positioning is therefore a matter of latitude selection. Several schemes are discussed based on different notions of optimality, the means of calculating weights for each scheme are shown, and numerical evidence is compiled to indicate that levels of accuracy attainable, by applying the quadrature formulas to various test functions (chiefly monopoles). The rapid fluctuations that can occur in the sound intensity function and the reasons for this condition are also discussed.