Measurements in room acoustics

Abstract

Regardless of the field, measurements are essential for validating theories and making well-founded decisions. A criterion for the validity and comparability of measured values is their uncertainty. The "Guide to the Expression of Uncertainty in Measurement" (GUM) provides a standardized framework for determining and interpreting measurement uncertainty. Still, in room acoustical measurements, the application of these rules is not yet widespread. Firstly, this is due to the fact that well established 2-CH-FFT correlation techniques rely on a complex principle, which is not covered by the classical guide. In addition, the effect of input variables on an individual measurement can only be determined after considerable effort. An example are fluctuations of room acoustical quantities over small distances between measurement locations in concert halls. This variation of the sound field by position is sometimes considerable and can only be predicted in relatively simple boundary value problems. This raises the question of the validity and interpretability of room acoustical measurements.The goal of this thesis is to provide a GUM-compliant discussion of uncertainties in measuring room acoustical single-number quantities. This starts with a structured search of variables that potentially influence the measurement of room impulse responses. In a second step, this uncertainty is propagated through the algorithm that determines room acoustical single-number quantities.Further emphasis is placed on the investigation of spatial fluctuations of the sound field in auditoria. The influence of an uncertain measurement position on the overall measurement uncertainty is discussed. To reach general conclusions, the relation between changes in the measurement location and the corresponding changes in measured room acoustical quantities is investigated empirically in extensive measurement series. To this end, a measurement apparatus was designed that allows automatic, high-resolution sampling of sound fields over large areas. The collected data creates the foundation to apply the principle of uncertainty propagation using a Monte Carlo method. IIThis study shows how precisely a measurement position must be defined to ensure a given uncertainty of room acoustical single-number quantities. The presented methods form a foundation that can be flexibly extended in future investigations to include additional influences on the measurement uncertainty. IVDie Ergebnisse dieser Untersuchung zeigen, wie genau ein Messort bei raumakustischen Messungen definiert werden muss, um eine zuvor festgelegte Unsicherheit raumakustischer Einzahlkennwerte zu gewährleisten. Die vorgestellten Methoden bilden eine Grundlage, die flexibel erweitert werden kann, um weitere Einflüsse auf die Messunsicherheit in zukünftigen Untersuchungen zu berücksichtigen.

Measurements in Room Acoustics How Good Are We at It

“…Even though a clear focus is placed on the equipment used in this study, the presented method may serve as a blueprint for other studies to evaluate the capabilities of their own measurement chains. For reasons of brevity, the reader is referred to Witew (2022) for the detailed discussion leading to the combined uncertainty in room acoustical measurements. The influences given in Table 2 are considered.…”

“…To apply the principle of uncertainty propagation the partial derivatives of the measurement function in respect to all uncertain input variables has to be determined. For the sake of brevity the reader is once again referred to Witew (2022) for the mathematical calculation of the uncertainty. Although the uncertainty of room acoustic quantities depends on the individual underlying RIR, an upper bound on the uncertainty can be estimated based on the large number of measurements made in this study.…”

“…Depending on the individual setup and equipment used, adjustments to respective entries may be necessary. The procedure pursued in Witew (2022) to compile this table can serve as a practical example to quantify one's own measurement capabilities. Finally, the shown data provides clear evidence for which influence quantities to target in order to have the greatest impact in affecting the combined measurement uncertainty.…”