Uncertainties of Room Acoustics Simulation Due to Directivity Data of Musical Instruments

Simulationsand auralization methods in the field of room acoustics require the directivity of sound sources in third-octave frequency bands, which simplifies the calculation algorithms but introduces uncertainty. However, this uncertainty is not well known. A better understanding of the uncertainty is relevant because it can lead to improved accuracy of simulations, or at least allow users to quantify the uncertainty. In this article, a dataset of measurements of musical instruments is analyzed to study the uncertainty of the directional factor in bands. First, the directional factors of each partial is estimated as a reference. Then, different methods for estimating the directional factor in third-octave bands are analyzed, and the method of averaging directional indices is selected due to its lower uncertainty and error. Finally, the uncertainty propagation due to the selected method compared to the reference is studied based on predictions of sound level and loudness temporal profiles of about 50000 played notes of 41 musical instruments in a concert hall. The effects of source-receiver positions and instruments are shown through probability density function estimations of the sound level differences and excess loudness ratios. About 50% of the studied data shows sound level differences close to
$\pm 5\ \text{dB}$
and loudness excess ratio close to about
$\pm 35{\%}$
. This work provides a method for building future datasets of directivity in bands and a better understanding of the uncertainty of room acoustics simulations.