Measurements in Room Acoustics : : Uncertainties and Influence of the Measurement Position / / Ingo B. Witew.

• Superior document: Aachener Beiträge zur Akustik
• VerfasserIn: Witew, Ingo B.,
• Place / Publishing House: Berlin, Germany : : Logos Verlag Berlin GmbH,, 2022.
• Year of Publication: 2022
• Language: English
• Series: Aachener Beiträge zur Akustik.
• Physical Description: 1 online resource (292 pages)

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. Still, in room acoustical measurements, the application of established rules to interpret uncertainties in measurement is not yet widespread. This raises the question of the validity and interpretability of room acoustical measurements. This work discusses the uncertainties in measuring room acoustical single-number quantities that complies with the framework of the "Guide to the Expression of Uncertainty in Measurement"(GUM). Starting point is 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 single-number quantities. A second emphasis is placed on the investigation of spatial fluctuations of the sound field in auditoria. The spatial variance of the sound field in combination with an uncertain measurement position marks a major contribution to the overall measurement uncertainty. 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. This 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 exibly extended in future investigations to include additional influences on the measurement uncertainty.

Table of Contents

1 Introduction 1 -- 1.1 Defining the scope of this work . 4 -- 2 Fundamentals and previous work 5 -- 2.1 Theoretical principles behind spatial fluctuations . 5 -- 2.1.1 Amplitude distribution due to changes in position 5 -- 2.1.2 The impulse response and other room acoustical quantities 10 -- 2.1.3 Variance of the reverberation time over space . 13 -- 2.1.4 Reference to the research question . 14 -- 2.2 Acoustical measurements in auditoria . 15 -- 2.2.1 Principles and established practice . 15 -- 2.2.2 Measurement uncertainty in architectural acoustics 18 -- 2.2.3 Observations in other fields of acoustics 21 -- 2.3 Uncertainties in measurements . 23 -- 2.3.1 General metrological terms . 23 -- 2.3.2 The guide to the expression of uncertainty -- in measurement 24 -- 2.4 The perception of sound in auditoria 33 -- 3 General Methodology 37 -- 4 Uncertainty of room impulse response measurements 41 -- 4.1 Introduction 41 -- 4.2 Uncertainty budget for room impulse response measurements 42 -- 4.3 Discussion . 45 -- 4.4 Conclusions 45 -- 5 Design of a measurement array 47 -- 5.1 Introduction 47 -- 5.2 Methodology . 48 -- 5.2.1 Requirements for the measurement setup . 48 -- 5.2.2 Design of a measurement device 52 -- 5.2.3 Acoustical measurements 53 -- 5.2.4 Data analysis . 56 -- 5.3 Results . 57 -- 5.3.1 Visualization of sound fields . 57 -- 5.3.2 Data for the uncertainty discussions 60 -- 5.4 Discussion . 60 -- 5.5 Conclusions 62 -- 6 Uncertain input quantities of the measurement function 65 -- 6.1 Introduction 65 -- 6.2 Uncertainty of room acoustical quantities . 66 -- 6.2.1 Methodology . 66 -- 6.2.2 Results 74 -- 6.3 Uncertainty of the sampling location 82 -- 6.3.1 Introduction . 82 -- 6.3.2 Initial methodology . 84 -- 6.3.3 Results 87 -- 6.3.4 Revised methodology . 88 -- 6.3.5 Results 88 -- 6.4 Discussion . 90 -- 6.5 Conclusions 91 -- 7 Measurement function 93 -- 7.1 Introduction 93 -- 7.2 Establishing the measurement function . 94 -- 7.2.1 Methodology . 94 -- 7.2.2 Results and discussion 99 -- 7.3 Compensating the effect of a finite sampling area . 103 -- 7.3.1 Methodology . 103 -- 7.3.2 Results and discussion 104 -- 7.4 Reducing the complexity . 106 -- 7.4.1 Methodology . 106 -- 7.4.2 Results 107 -- 7.5 Discussion . 108 -- 7.6 Conclusions 110 -- 8 Validity of the measurement function 111 -- 8.1 Introduction 111 -- 8.2 Methodology . 111 -- 8.2.1 Repeatability . 112 -- 8.2.2 Reproducibility 112 -- 8.3 Results . 117 -- 8.3.1 Repeatability . 119 -- 8.3.2 Reproducibility 121 -- 8.4 Discussion . 139 -- 8.5 Conclusions 141 -- 9 How accurately must a measurement position be defined? 143 -- 9.1 Introduction 143 -- 9.2 Methodology . 144 -- 9.2.1 Establishing the input quantity distribution 145 -- 9.2.2 Implementing the measurement function 147 -- 9.2.3 Determining the measurement uncertainty using Monte -- Carlo simulations . 148 -- 9.3 Results . 150 -- 9.3.1 Uncertainty of room acoustical quantities . 151 -- 9.3.2 Effect of the auditorium's reverberation 156 -- 9.3.3 Effect of the evaluation interval (time) . 159 -- 9.3.4 Effect of the center frequency 162 -- 9.3.5 Effect of the bandwidth . 164 -- 9.4 Discussion . 166 -- 9.4.1 Uncertainty of broadband measurements 166 -- 9.4.2 Reference to theory . 168 -- 9.4.3 Appropriateness of regression models 173 -- 9.4.4 Influence of early reflections . 174 -- 9.4.5 Necessity for measurements . 175 -- 9.5 Conclusions 175 -- 10 General results 179 -- 10.1 Uncertainty of measured impulse responses 179 -- 10.2 Uncertainty of room acoustical quantities . 180 -- 10.3 Uncertainty due to spatial fluctuations . 181 -- 11 General Discussion 187 -- 11.1 Uncertainty of measured impulse responses 188 -- 11.2 Uncertainty of room acoustical quantities . 189 -- 11.3 Uncertainty due to spatial fluctuations . 190 -- 11.4 Critical aspects 191 -- 11.5 Implications 192 -- 12 General conclusions and outlook 195 -- 12.1 General conclusions 195 -- 12.2 Outlook 196 -- 13 Acknowledgements 199 -- Bibliography 201 -- A Detailed discussion of uncertainties in -- room impulse response measurements 215 -- A.1 Introduction 215 -- A.2 Formulation stage 215 -- A.2.1 The output quantity . 215 -- A.2.2 The input quantities . 216 -- A.2.3 The measurement model . 219 -- A.3 Results - Calculation stage 260 -- A.4 Discussion . 263 -- A.5 Conclusions 265 -- B Influence of the measurement apparatus on the sound field 267 -- B.1 Introduction 267 -- B.2 Analytical approach . 268 -- B.2.1 Methodology . 268 -- B.2.2 Results 270 -- B.3 Empirical approaches . 275 -- B.3.1 Methodology . 275 -- B.3.2 Results 277 -- B.4 Discussion . 279 -- B.5 Conclusions 281 -- C Uncertainty propagation for room acoustical quantities 283 -- C.1 Energy decay curve 283 -- C.2 Reverberation times . 285 -- C.3 Clarity.