A discussion on the uncertainty of absorption characteristics measured by ensemble averaging technique for room acoustics simulations

Transcription

1 Challenges and Solutions in Acoustical Measurements and Design: Paper ICA A discussion on the uncertainty of absorption characteristics measured by ensemble averaging technique for room acoustics simulations Toru Otsuru (a), Reiji Tomiku (a), Noriko Okamoto (b), Emi Ueda (c), Asami Nakamura (c) (a) Faculty of Engineering, Oita University, Japan, otsuru@oita-u.ac.jp (b) Faculty of Environmental Engineering, The University of Kitakyushu, Japan (c) Graduate School of Engineering, Oita University, Japan Abstract The authors proposed an in-situ sound absorption measurement method using an ensemble averaging technique, EA metod, for short. Herein, EA method measurements are conducted nine times repeatedly with three pressure-velocity sensors (Microflow; pu-sensor) to prove the effect of sensor difference on resulting sound absorption coefficients and to examine if the uncertainty stays within such a small range as is suitable for room acoustics simulations. EA method conducted here follows the configuration given in our earlier papers and sound absorption coefficients of a glass-wool board, a needle felt sheet and a slice form sheet were measured. To prove the effect of pusensor difference on the resulting sound absorption coefficient three pu-sensors were employed. The sensors were calibrated using an acoustic tube with a diameter of 10 cm just before or after a series of measurement. The results of nine times measurement of the glasswool board showed slight differences only at 100 Hz, 500 Hz and 1250 Hz and uncertainties (standard deviation) of sound absorption coefficient stay less than The results of the other two materials are rather in better agreements with less uncertainty. The measurement results of sound absorption coefficient obtained using the three pu-sensors showed good agreements each other for the three materials. The maximum difference 0.04 is observed for the glass-wool board at 1250 Hz. Such larger differences are observed at both limits of the frequency range of the acoustic tube used for pu-sensor calibration. Except the frequencies, uncertainties of sound absorption coefficients measured by EA method with different three pu-sensors stayed the values within suitable range for room acoustics simulations. Keywords: Sound absorption measurement, Measurement uncertainty, Room acoustics simulation, Ensemble averaging technique

2 A discussion on the uncertainty of absorption characteristics measured by ensemble averaging technique for room acoustics simulations 1 Introduction For conducting room acoustics simulations of significance scientifically, M. Vorländer [1] raised an important issue on the uncertainty included in sound absorption coefficient measurements. Based on several example calculations of a music hall with volume of 11,000 m 3, he pointed out that the uncertainty of the absorption coefficient supplied into the calculation must remain less than 0.04 to keep the uncertainty of calculated reverberation time below its just noticeable difference (JND). Though the required uncertainty depends on the room s volume and absorption, such a small uncertainty is practically hard to be achieved by standard measurement methods. While, aiming mainly for the construction of boundary conditions of wavebased room acoustics simulations, the authors proposed a method for measuring sound absorption of materials using ensemble averaging technique (EA method, hereafter). Practically, there are two types of EA method: one which utilizes two-microphone [2]; and another with pressure-velocity sensor [3] (Microflown PU-sensor [4]). We published comparisons with other methods and geometrical configuration of the method [5], and we confirmed the reproducibility of EA method with pu-sensor both in various reverberation rooms and in-situ conditions as well [6]. Then, the mathematical-physical model of ensemble averaging was presented to clarify the measuring mechanism and trial applications on sound absorption measurements of outside road surfaces were successfully conducted and reported [7, 8]. Herein, uncertainty of EA method are discussed from the view points of repeatability and of sensor difference to clarify whether EA method can achieve the M. Vorländer s requirement. A series of EA method measurement with the same configuration is repeated nine times on different three days. Sound absorption coefficients of three materials are measured and compared. In the measurements, three pu-sensors are employed to confirm the effectiveness of calibration conducted using an acoustic tube on site. The results given below are of significance not only for the room acoustics simulations but for various fields of room acoustics and noise control engineering where more reliable as well as practical sound absorption measurement technique is in need. 2 Method outline Figure 1 illustrates the measurement setup of EA method: one with a two-microphone and another with a pu-sensor. In this manuscript, the latter is focused on for simplicity. If particle velocity and sound pressure are measured at a point on a material s surface, ensemble averaged surface normal impedance Z n and corresponding absorption coefficient α can 2

3 Figure 1: Schematic diagram of the measurement setup with (a) a pu-sensor, and (b) two microphones. be calculated by the following equations: Z n = P surf U n,surf, (1) α = 1 Z n 1 2 Z n + 1, (2) here, U n,surf and P surf respectively denote particle velocity normal to the material surface and sound pressure at the material surface in frequency domain. The symbol x expresses ensemble average of a valuable x. In a practical measurement, ensemble averaged values in the right side of eq. (1) are obtainable from standard outputs of a fast-fourier-transform (FFT) instrument connected to a pu-sensor, if the sensor is small enough to be placed at the material surface. In reality, however, an acoustical sensor has a certain size; and all the pu-sensors (Microflown, PU Regular) employed in the following investigations have the diameter of half inch. Our former studies revealed, however, both experimentally and computationally that the distance d between pu-sensor and material surface brings not significant difference in measured sound absorption coefficients in case d is less than 13 mm [5]. In this article, the distance is fixed to 10 mm as is used in our previous studies. 3 Uncertainty of sound absorption coefficient measured by EA method 3.1 Measurement configuration Sound absorption measurements by EA method conducted here follow the configuration given in our earlier papers [3, 5, 6]. To prove the effect of pu-sensor difference onto the resulting sound absorption coefficients α, three pu-sensors (Microflown; PU Regular) were employed: namely, pu-22, pu-45 and pu-82. One of the pu-sensors was placed in turn at the position of d =10 mm above the material surface and was plugged into a 2ch-FFT instrument (B&K; Type 3160-A-042). All the measurements were conducted in the reverberation room having volume of 168 m 3 at Oita University. Incoherent filtered pink noise of Hz was emitted from six full range 3

4 loudspeakers (Fostex; FE-103) mounted in wooden boxes. A sub-woofer (JVC; SX-DW77) was added to supply low frequency noise roughly below 250 Hz. With the same measurement configuration, sound absorption coefficient α of the material was measured three times on a single day with each pu-sensor (pu-82, pu-45 and pu-22); and the measurements were repeated on different three days for each pu-sensor. That is, the repeating number equals nine for the measurement with each pu-sensor. Each sensor was calibrated using an acoustic tube with the diameter of 10 cm (Micloflown; acoustic tube) on site, i.e. calibration values for each pu-sensor were measured once on a day just before or after a series of EA method measurement in the acoustic tube which was placed in the reverberation room where the EA method measurement have been undertaken. All the measured impedance values with a pu-sensor can be calibrated by multiplying the calibration values and measured Z n together, first. Then, calibrated sound absorption coefficients are calculated using eq. (2). The diameter of the square tube restricts measurable frequency range to below 1700 Hz and the geometrical distance between a pu-sensor and the tube s hard end, 5 cm ± 6.3 mm, causes an antinode for sound pressure (node for particle velocity) at the pu-sensor s position around 1700 Hz ± 200 Hz. Then, the measurable octave band center frequencies are considered to be from 100 Hz to 1250 Hz. In every measurements, three materials were measured: glass-wool board (32 kg/m 3, mm 3 ), needle felt sheet ( mm 3 ) and slice form sheet (Urethan form with no membrane, mm 3 ). The materials are selected so as to represent both absorptive and less absorptive building materials and measurement points are set at the center points of the materials surafaces. 3.2 Comparison of sound absorption coefficients measured in nine-times measurement In this subsection, dispersions found in measured sound absorption coefficients obtained by repeated measurements with the same configuration are examined. Results of the nine-times EA method measurement with pu-82 are compared in Figure 2. Though, due to limitations of space, only the results of pu-82 are plotted first, quantitative discussions including those of the others will be given afterward. In Figure 2, one third octave band average values of sound absorption coefficients are depicted and compared. There is no significant difference between the values measured by each single measurement and several slight differences could be observed at 100 Hz, 500 Hz and 1250 Hz. The differences at 100 Hz and 1250 Hz are attributable to the fact that the frequencies are both ends of the measurement frequency range. Though the upper cutoff frequency of the one third octave band centered at 1250 Hz is around 1431 Hz, above mentioned tube s antinode around 1500 Hz might disturb the result. The dispersions observed at 500 Hz might be attributable to what so called edge diffraction effect [10, 11], and the authors previous papers exhibited both computationally and experimentally that ensemble averaging eliminate it effectively [3]. Then, plate vibration of the glass-wool 4

5 Figure 2: Comparison of sound absorption coefficient α of glass-wool board measured by EA method using pu-sensor pu-82. Measurement with the same configuration was repeated three times (#1, #2 and #3) on three days (day1, day2 and day3). Figure 3: Uncertainties (Standard deviations) of nine-times measurement of sound absorption coefficients by three pu-sensors (pu-22, pu-45 and pu-82). board could be considered to cause the dispersion. The problem is, however, to be investigated in another studies in detail and, in the following discussion, all the measured sound absorptions are included on the safe side. To deepen the discussion more quantitatively, uncertainties (standard deviation, σ) of the sound absorption coefficients measured by pu-82 are plotted in Figure 3 together with those by the other two pu-sensors. The uncertainties of pu-82 are plotted in solid-black line and all the values except for 1250 Hz stay less than 0.02; and the uncertainty at 1250 Hz is equal to For pu-22 (broken-red line), greater uncertainty values of are observed at the frequencies 100 Hz and 500 Hz. For pu-45 (dash-dot-blue line), almost similar or less values are observed at all the frequencies from 100 Hz to 1250 Hz comparing to those of the other two pu-sensors. Thus, with the same measurement configuration, nine-times repeated measurements of sound absorption of glass-wool board revealed that all the uncertainties of the three pu-sensors stay less than Almost similar results, or with less uncertainty values, are confirmed for the other materials, needle felt sheet and slice form sheet. 5

6 Figure 4: Comparison of average sound absorption coefficients of glass-wool board between three pu-sensors (pu-22, pu-45 and pu-82) used in EA method. Figure 5: Comparison of average sound absorption coefficients of needle felt sheet between three pu-sensors (pu-22, pu-45 and pu-82) used in EA method. Figure 6: Comparison of average sound absorption coefficients of slice form sheet between three pu-sensors (pu-22, pu-45 and pu-82) used in EA method. 3.3 Effect of pu-sensor difference on sound absorption coefficient measured by EA method Based on the discussion on the uncertainty in the previous subsection, mean average of the sound absorption coeffients obtained in the nine-times measurements are compared to investi- 6

7 gate the effect of pu-sensor difference used in the measurement. Average sound absorption coefficients over nine repetitions of the three materials are respectively plotted in Figures 4, 5 and 6 to compare the effect of pu-sensor difference. On the whole, the agreements of the results of the three pu-sensors are good regardless of materials. For glass-wool board, the maximum difference 0.04 is observed at 1250 Hz. Such considerably greater differences are observed at both 100 Hz and 1250 Hz, which are both ends of the measurement frequency range. Similar dispersion can be confirmed for needle felt sheet at 1250 Hz. However, excellent agreements with smaller dispersions are observable for slice form sheet throughout the frequency range. Thus, at 1250 Hz, the results of glass-wool board and needle felt sheet showed rather greater dispersions. It might be attributable to above mentioned antinode in the calibration tube. However, if we employ another acoustic tube with different geometry, such dispersions could simply be eliminated. Therefore, within the scope of this study, the effect of pu-sensor difference on measured absorption coefficient is regarded as not significant. It is notable that all calibration values were measured in acoustic tube on site. 4 Conclusions To examine resulting uncertainty included in EA method measurement from the view point of room acoustics simulations, measurement repeatability and pu-sensor difference effect are discussed. Nine-times repeated sound absorption measurements by EA method using three pusensors in turn with the same configuration conducted in three days revealed that EA method uncertainty stays within the acceptable range for room acoustics simulations. The average values over the repetitions showed that the effect of employed pu-sensor difference in EA method is not very significant within the scope of this study. All the measurements were conducted in a reverberation room and each pu-sensor was calibrated on site just before or after a series of sound absorption measurement. Further studies are undergoing on EA method including effective calibration techniques as well as in-situ measurements to establish it as more reliable measurement technique not only for room acoustics simulations but for various fields of acoustics for the 21 st century. Acknowledgements The authors would like to thank to Ms. S. Yamauchi for her contribution as an undergraduate student. This work was partly supported by JSPS, a Grant-in Aid for Scientific Research (B) 16H044565, References [1] M. Vorländer, Computer simulations in room acoustics: Concepts and uncertainties, J. Acoust. Soc. Am., 133, (2013). 7

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