Evaluation of the Accuracy of the Sound Field Separation Method under Variations in the Location of the Sampling Points

Context:  Measuring the directivity characteristics and the frequency response of acoustic sources is a difficult process, as the dimensions and boundary conditions of the testing rooms used could constrain the measurement procedure. The testing room should guarantee a free-field condition, which is usually satisfied by using big acoustic absorbers with fibrous materials with high absorption coefficients. However, standing wave patterns can be easily developed due to the frequency range exciting the testing room. Method: The sound field separation method can isolate the radiated field of an acoustic source by sampling the sound field around it over two holographic spheres. The coordinates of the sampling points are used in a set of equations, whose solution can estimate the radiated field. In this paper, the effect of the variability on the actual positions of these sampling points is investigated. Results: Two numerical simulations with and without external sources outside the holographic spheres were performed. In all simulations, variations in the radial position of the sampling points were induced, and the relative reconstruction error, the directivity index, and the frequency response were studied. The results indicate that, for the estimation of the directivity of low-frequency acoustic sources, regardless of the presence of external sources, radial positioning of the sensors does not have to be exact to obtain an accurate reconstruction. Conclusions: This study suggests that, in the experimental characterization in conventional testing rooms of the radiated field from acoustic sources whose main frequency region corresponds to low frequencies, e.g. subwoofers, the SFS method could be used, thus obtaining high accuracy in the estimation of the directivity of the source.