Conditions for the inference of upper-bound estimates of sound power from close-in measurements of sound pressure

Current measurement standards do not provide adequate guidance for the evaluation of the uncertainty involved in using measured sound pressures, rather than sound intensities, to estimate the sound power radiated by a source. In this presentation, conditions are derived which are sufficient to ensure that an estimate of sound power based on close-in sound-pressure measurements over a surface enveloping the source (in a free field or free field over a reflecting plane) is, in fact, for perfect sampling, an upper bound to the true sound power. Conditions for this upper bound to be the least upper bound are also derived for the case of the absence of a priori information regarding the directivity of the source. Experimental data are presented which support the analytical findings. Some implications of sampling error in the measurement process are also discussed.