ISSUES ON THE REVERBERATION ROOM METHOD FOR MEASURING THE SCATTERING COEFFICIENTS -BORTHER SETTING AND REVOLUTION OF TEST SAMPLE-

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1 ISSUES ON THE REVERBERATION ROOM METHOD FOR MEASURING THE SCATTERING COEFFICIENTS -BORTHER SETTING AND REVOLUTION OF TEST SAMPLE- Hyojin LEE 1 ; Yuzo TSUCHIYA 2 ; Tetsuya SAKUMA 3 1,2,3 Graduate School of Frontier Sciences, University of Tokyo Kashiwanoha, Kashiwa-shi, Chiba , Japan a@sbk.k.u-tokyo.ac.jp; a@sbk.k.u-tokyo.ac.jp; 3 sakuma@k.u-tokyo.ac.jp Abstract The reverberation room method for measuring the random-incidence scattering coefficients has been already developed in ISO , however there exists some points to be better investigated. One point is that the scattering coefficient could be overestimated by the destructive diffraction from the uneven perimeter of a test sample. Another point is on the limitation of sample rotation, which is employed with a turntable in the continuous measurement of room impulse responses. At this moment, the limitation of the revolution speed is unclear, thus it is not yet specified in the ISO. This paper discusses the effect of border setting and revolution limitation of test samples through 1:4 scale model measurements. The results demonstrated that: 1) edge scattering can be suppressed by border setting around the circular base plate, 2) the revolution speed is limited by the angular step (the ratio of signal period to revolution period) and the frequency. Keywords: Diffuser,, Reverberation room method, Edge diffraction, Time invariance 1 Introduction Nowadays scattering coefficient [1] is widely utilized to improve the accuracy of geometric room acoustic simulation [2]. A measurement method of the random-incidence scattering coefficient in a reverberation room is standardized by ISO [3] as part 1, however there exist some points to be better investigated. One point is that the scattering coefficient could be overestimated by the destructive diffraction from the uneven perimeter of a test sample. The ISO method refers to that of absorption coefficient by ISO 354 [4], which edge absorption is excluded by using a mounting with border, however, recommends not to cover the perimeter with a rigid border of fixed height. Another point is on the limitation of sample 1

2 INTERNOISE 21 JUNE LISBON PORTUGAL incident 1 scattered (1-α)s (1-α)(1-s) specularly reflected reflected rough surface Figure 1 Scattering from rough surface (α : absorption coefficient, s : scattering coefficient). rotation, which is employed with a turntable in the continuous measurement of room impulse responses. There are two ways of impulse response measurement, step-by-step and continuous measurement. In case of step-by-step measurement, the ISO specifies its limitation, which the number of coherent averages n is in the interval 6 n 12. On the other hand, regarding the continuous measurement, there is no description on the limitation of the revolution speed in the ISO. There is a report [5] that the scattering coefficients would be apparently underestimated at high frequencies using 16 MLS signals with a period of 5.1 s during one revolution of 81.6 s. It is expected that the underestimation is caused by time variance in one signal period of MLS. In this paper, 1:4 scale model measurements are performed to investigate the effect of border setting of test samples and revolution limitation for impulse response measurement. Rigid borders with different heights and thicknesses are attached to reduce the overestimation by edge diffraction. Furthermore, impulse response measurements on the conditions of various signal lengths, revolution speeds and angular steps are performed to examine the revolution limitation. Finally, the results could suggest guidelines for application of the measurement technique. 2 Measurement principle The scattering coefficient is defined as the ratio of the non-specularly reflected acoustic energy to the totally reflected energy (see Figure 1) [3], which is simply represented by α spec α Espec sθ = = 1 (1) 1 α E where E total and E spec are the total and the specularly reflected energy, respectively. The two absorption coefficients, α is the absorption coefficient and α spec is the apparent specular absorption coefficient, are measured in accordance with ISO 354 [4] total V 1 1 4V α = 55.3 ( m2 m1 S c2t2 c1t ) (2) 1 S V 1 1 4V α spec = 55.3 ( m4 m3 S c4t4 c3t ) (3) 3 S where V is the volume of the reverberation room, S is the area of the test sample, T is the reverberation time, c is the speed of sound and m is the energy attenuation coefficient of air. The reverberation times are obtained on the conditions of Table 1. 2

3 INTERNOISE 21 JUNE LISBON PORTUGAL Table 1 Measurement conditions for the four different reverberation times. Reverberation time Test sample Turntable T 1 not present not rotating T 2 present not rotating T 3 not present rotating T 4 present rotating The ISO method for measuring the random-incidence scattering coefficient is based on the work by Vorländer and Mommertz [1]. The principle of the method is to extract the specular reflection components by coherent averaging of the impulse responses while rotating a circular sample on a turntable. In the reverberation room measurement, the process is very powerful for the direct determination of the random-incidence scattering coefficient. 3 Measurement with border setting around the base plate 3.1 Scale model set-up The measurements were performed in a 1:4 scale reverberation room, as shown in Figure 2. The room has a volume of 1.62 m 3, made of acrylic, and 1 plastic panels are fixed inside to improve sound diffusion. A MLS signal is used for the impulse response measurement and two source and three microphone positions (total six measurements) are located in the reverberation room. The reverberation time T 2 is obtained by the Schroeder backward integration method in the range from -5 db to -25 db. The signal length 1.37 s and the coherent averaging number 117 are given with the turntable of 8 seconds per revolution [6], thus during 2 revolutions. Figure 3 illustrates the test sample of circular shape with 1D periodic surface with 15 rectangular ribs. The wooden sample has a diameter of 75 mm and a structural wavelength of 5 mm. Table 2 presents the measurement conditions to investigate the effect of border height. The measurements are performed with/without border covering the perimeter of the test sample. The heights of borders are considered under, equal and above compared with the heights of test sample. Also, the thicknesses of borders are set to 1 and 25 mm for investigating the effect of border thickness, as shown in Table 3. 1,5 1,5 SpeakerA Mic.2 h=5mm 1,2 SpeakerB Mic.1 h=6mm Base plate Mic.3 h=4mm 9 SpeakerA,B Mic.1 h=6mm Base plate Mic.3 Mic.2 h=5mm h=4mm Turntable <Plan> < Vertical section > < Plan > < Vertical section > Figure 2 Specifications of the reverberation room (unit: mm). 3

4 INTERNOISE 21 JUNE LISBON PORTUGAL t hs hb 25 5 Border (a) t = 1 mm, plastic (b) t = 25 mm, wood Figure 3 Test sample with border, 15 periods (unit: mm). Table 2 Measurement conditions for different height of border (unit: mm). Structural depth of test sample, h s Height of border, h b Table 3 Measurement conditions for different thickness of border (unit: mm). Height of border, h b Thickness of border, t Material 1 plastic 5 25 wood 3.2 Results and discussion Height of border Figure 4 illustrates the random-incidence scattering coefficients of the sample with 1 mm thick border, where border heights are varied with its structural depths (Table 2). In the case of h s = 1 mm, the values are almost identical over the entire frequencies regardless of border. It is seen that the effect of diffraction from the uneven perimeter is negligible. In the other cases of h s = 25, 35, 45 mm, the differences of about.1 ~.2 occur due to the edge scattering at middle and high frequencies. It is seen that the values with border are generally lower than those without border, but those with 5 mm high border almost equal to those when the border height is equal to the structural depth. 4

5 INTERNOISE 21 JUNE LISBON PORTUGAL hb = mm hb = 5 mm hb = mm hb = 35 mm hb = 5 mm (a) h s = 1 mm (c) h s = 35 mm hb h = mm hb h = 5 25 mm hb = 5 mm hb = mm hb = 35 mm hb = 5 mm (b) h s = 25 mm (d) h s = 45 mm Figure 4 s measured for different border height: structural depths of test sample (a) 1 mm, (b) 25 mm, (c) 35 mm and (d) 45 mm. The ISO recommends the structural depth of test sample should be less than d/16, where d is the diameter of the turntable. In this scale model, the height of 5 mm almost corresponds to the limitation of structural depth. Thus, it is recommended that the height of rigid border is more than the structural depth h s and less than d/ Thickness of border Figure 5 illustrates the random-incidence scattering coefficients of the sample with 5 mm high border, where borders are made of 1 mm thick plastic and 25 mm thick wood (Figure 3, Table 3). It is seen that the values are nearly equal in despite of using the different border thickness. The results indicate that the differences of thickness and material of border hardly affect the random-incidence scattering coefficients Comparison with the numerical results Figure 6 shows the random-incidence scattering coefficients measured with the ISO method [3] and calculated with the directivity correlation method [7] for the test sample with/without border. For the calculation, the test sample without border is only modeled. The measured values of test sample with structural depth of 1 mm correspond well to the calculated ones, regardless of border (Figure 6a). On the other hand, the measured values without border is higher at mid and high frequencies compared to the calculated ones, however, the measured values with border become fairly close to the calculated ones (Figure 6b). One possible reason is that edge diffraction hardly affect the directional scattering coefficient by the 5

6 INTERNOISE 21 JUNE LISBON PORTUGAL t = 1 mm, plastic t = 25 mm, wood (a) h s = 1 mm t = 1 mm, plastic t = 25 mm, wood (b) h s = 25 mm Figure 5 s measured for different border thickness meas. (w/o border) meas. (w/ border) calc. (a) h s = 1 mm meas. (w/o border) meas. (w/ border) calc. (b) h s = 25 mm Figure 6 Comparison of the measured and calculated results with/without border. directivity correlation method. From the above results, it is verified that edge scattering can be suppressed by border setting around the circular base plate. 4 Impulse responses measurement during continuous rotation 4.1 Scale model set-up The measurement set-ups are identical with those in the previous section, except the reverberation time and the revolution of turntable. Reverberation time T 15 (-5 ~ -2 db) was used and revolution speed of turntable is changeable [8]. As shown in Figure 7, the test sample is made with 32 wooden hemispheres placed in equal rectangular grids on the base plate. Table 4 presents the measurement conditions of impulse responses during continuous rotation. MLS signal lengths are set on the three conditions and revolution speeds varies depending on the number of coherent averages while one revolution. 6

7 INTERNOISE 21 JUNE LISBON PORTUGAL radius = 375 Figure 7 Test sample (unit: mm). < Plan > > < Vertical < section > > Table 4 Measurement conditions of impulse responses (revolution 1). Signal length [s] Revolution speed [s/rev] Angular step [deg] Averaging number Results and discussion Study A: Fixed signal length Figure 8 shows the random-incidence scattering coefficients on the conditions that signal lengths are fixed at.68, 1.37 and 2.73 s. In general, the values tend to decrease from high frequencies as the revolution speed becomes faster. In case of the signal length.68 s, the values of revolution speed 41 s/rev very slightly decrease. The values with the signal lengths of 1.37 and 2.73 s, begin to decrease at the revolution speed of 82 and, respectively. Figure 11 illustrates the energy decay curves of reverberation time T 4 (test sample: present, turntable: rotating) on the condition of the signal length 1.37 s. It is found that the reverberation times are overestimated as the revolution speed becomes faster. The above results indicate that a too fast revolution leads to underestimation at higher frequencies. Therefore, when the signal length is long, the revolution speed is needed to be slow Study B: Fixed revolution speed Figure 9 shows the random-incidence scattering coefficients on the conditions of fixed revolution speeds. In the cases of the revolution speed 41, 82 and, the values begin to decrease at the signal length of.68, 1.37 and 2.73 s, respectively. The energy decay curves of T 4 at the fixed revolution speed of, as illustrated in Figure 12, the reverberation times are overestimated as the signal length is longer. It indicates that a too long signal period leads to underestimation at higher frequencies. The revolution speed setting for the practical application should be slower as signal length gets longer. 7

8 INTERNOISE 21 JUNE LISBON PORTUGAL s/rev 328 s/rev 2.5 s/rev 41 s/rev 328 s/rev 328 s/rev -.2 (a).68 s (b) 1.37 s (c) 2.73 s Figure 8 s measured with fixed signal lengths s 1.37 s.68 s 1.37 s 2.73 s.68 s 1.37 s 2.73 s -.2 (a) 41 s/rev (b) (c) Figure 9 Scattering measured with fixed revolution speeds s/rev 41 s/rev 328 s/rev -.2 (a) 12 deg (b) 6 deg (c) 3 deg Figure 1 Scattering measured with fixed angular steps Study C: Fixed angular step Figure 1 shows the random-incidence scattering coefficients on the conditions that angular steps are 12, 6 and 3 deg by changing the signal length and the revolution speed. Except the case of 12 deg, the measured values only depend on the angular step, whereas the value of the angular step 6 deg slightly decreases at 4k Hz. It can be concluded that an angular step of more than 6 deg leads to underestimation at higher frequencies. For the measurement up to 4 khz, 6 deg may be the maximum limitation. Here, a value of 6 deg is consistent with the minimum required number of coherent averages for step-by-step measurement (6 n 12). 8

9 INTERNOISE 21 JUNE LISBON PORTUGAL s/rev 41 s/rev 328 s/rev 125 Hz 25 Hz 5 Hz 1k Hz s 1.37 s 2.73 s 125 Hz 25 Hz 5 Hz 1k Hz k Hz 4k Hz k Hz 4k Hz Time [s] Time [s] Time [s] Time [s] Figure 11 Energy decay curves of signal length 1.37 s. Figure 12 Energy decay curves of revolution speed. 5 Conclusions To investigate the effect of border setting and revolution limitation of test samples on the reverberation room method for measuring the random-incidence scattering coefficients, 1:4 scale model measurements were performed. From the measurement with border setting around the circular base plate, we can identify the followings: Edge scattering can be suppressed by border setting around the circular base plate. The surface of the perimeter of the test sample should be covered with a rigid border of which height is more than the structural depth h s and less than d/16, where d is the diameter of the turntable. Through the impulse response measurement using a MLS signal during continuous rotation, the followings are demonstrated: Continuous measurement should be performed on condition that time invariance is considered to be satisfied in one signal period of MLS. The revolution speed is limited by the angular step (the ratio of signal period to revolution period) and the frequency. We recommend that the number of periods of a periodic pseudo-random signal should be in the interval of 6 n 12. In practice, in order to shorten the total measurement duration (suppress the time variance of temperature), a shorter signal period is preferred as far as the measurement of impulse responses is guaranteed. And the revolution period is fixed by multiplying the signal period by n = 6. The results could suggest guidelines for application of the measurement technique. 9

10 INTERNOISE 21 JUNE LISBON PORTUGAL Acknowledgments This project was supported by the Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science (No ). References [1] M. Vorländer; E. Mommertz. Definition and measurement of random-incidence scattering coefficients. Applied Acoustics, Vol 6, 2, pp [2] B.-I. Dalenbäck. CATT-acoustic ver. 8.. User s manual. CATT, Gothenburg, 22. [3] ISO : Acoustics-sound-scattering properties of surfaces - Part 1: Measurements of the random-incidence scattering coefficient in a reverberation room, 24. [4] ISO 354: Acoustics - Measurement of sound absorption in a reverberation room, 23. [5] Fang-Ming Lin; Pei-Yu Hong; Chia-Yen Lee. An experimental investigation into the sound-scattering performance of wooden diffusers with different structures. Applied Acoustics, Vol 71, 21, pp [6] Turntable. Type 3922, Brüel & Kjær, Denmark. [7] T Sakuma; Y Kosaka. Relationship between the scattering coefficients determined with coherent averaging and with directivity correlation. Acta Acustica united with Acustica, Vol 95, 29, pp [8] Turntable. TT-1, Nittobo Acoustic Engineering Co., LTD, Japan. 1