An angle-error model for enveloping surface sound power measurements

Free-field sound power measurement methods based on enveloping surfaces, namely ISO 3744 and ISO 3745, contain an inherent source of measurement inaccuracy associated with the angle between the vector normal to the measurement surface and the intensity vector of the incident sound wave. Instead of using the normal component of the intensity vector in the sound power computation, only the magnitude is considered. The standards broadly acknowledge the uncertainty, but they do not offer an implementable solution to correct for the bias of this angle error. The multivariate nature of the angle error as a function of one or more sources, receivers, and methods, each of which with their own unique definitions, complicates the ability to calculate and correct the error for any sound power measurement. This paper applies a computational approach based on a ray-tracing model of a point source and its image source to calculate the angle error associated with standardized free-field sound power measurement methods for various enveloping surfaces. Simplifying assumptions are leveraged to generate a model of the angle error over a range of enveloping surface measurement scenarios.