INTER-NOISE DECEMBER 2006 HONOLULU, HAWAII, USA

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1 INTER-NOISE DECEMBER 2006 HONOLULU, HAWAII, USA Numerical analysis of sound propagation between open-type classrooms Akihiro Nakajima a Graduate School, University of Tokyo, Komaba, Meguro-ku, Tokyo, Japan Kanako Ueno b Institute of Industrial Science, University of Tokyo, Komaba, Meguroku, Tokyo, Japan Shinichi Sakamoto Institute of Industrial Science, University of Tokyo, Komaba, Meguroku, Tokyo, Japan Hideki Tachibana Chiba Institute of Technology, Tsudanuma, Narashino, Japan ABSTRACT In Japan, open-plan type classroom is becoming popular in elementary schools. Although this planning has various merits for educational activity, sound propagation between adjacent classrooms tends to be a serious acoustical problem. In this study, therefore, the sound propagation between closely located two classrooms connected by an open-space is investigated by numerical simulation using FDTD method. In the simulation, two classrooms and the open-space connecting them were modeled by combining rectangular parallelepiped spaces and the configuration of the rooms and sound absorption treatment on the room boundaries were examined. As a result, it has been found that sound absorption treatment on the ceiling and architectural/acoustic treatment for the wall of the open-space which makes mirror-reflection are effective to mitigate the sound propagation between the classrooms. 1 INTRODUCTION As school buildings in Japan, the traditional side-corridor type has been adopted all over the country for a long time. In the 19s, the educational paradigm for elementary schools has been shifted from teaching to learning and classes in which children s initiatives and personalities can be esteemed have become much more respected. As an architectural idea to realize these policies, so-called open-plan schoolroom system with spatial continuity and flexibility has become popular [1]. Figure 1 shows two examples of typical open-plan type classrooms in Japan. In these cases, the classrooms with a floor area of about 8 m square are connected by so-called open-space. In this type of classroom arrangement, the sound propagation between the adjacent rooms tends to cause an acoustical interference [2, 3]. In spite of such acoustical problem, the number of opentype classroom system is increasing in Japan. In this background, it is needed to develop a method to improve the acoustical environment in elementary school buildings by mitigating the sound propagation between closely connected classrooms. In this study, therefore, the sound propagation in open-type classroom arrangement was investigated by numerical analysis method and its validity was checked by comparing with the results of field measurements. In addition, various architectural treatments to mitigate the sound propagation between rooms were examined by the numerical analysis. a nakajima@iis.u-tokyo.ac.jp b ueno@ iis.u-tokyo.ac.jp

2 Fig. 1 Examples of open-plan type classroom in elementary schools in Japan. 2 NUMERICAL ANALYSIS 2.1 Outline of FDTD method The numerical analysis using the finite difference time domain (FDTD) method was applied [4]. Here, the spatial grid size was set at 0.05 m in a 3-dimentional sound field and the discrete time step was set at 0.08 ms. As the initial condition assuming an impulse source, a smoothly continuous distribution of sound pressure with a half-sine-wave shape was set. Under the assumption of locally reactive boundary, the normal component of the particle velocity on the boundary is expressed as follows. p u n = (1) boundary Z n Where u n boundary is the normal component of the particle velocity on the boundary, p is the sound pressure and Z n is the normal acoustic impedance on the boundary. To simplify the problem, it was assumed that the normal acoustic impedance on the boundary had only the real part in this study. In this case, the relationship between Z n and the normal sound absorption coefficient α n can be express as follows α n Z n = ρc (2) 1 1 α n By changing the arrangement and boundary condition of the two adjacent classrooms and the open-space connecting them in various configurations, the sound propagation properties between the rooms were examined as mentioned later. 2.2 Results of the FDTD calculation 1) Visualization of sound propagation In the FDTD calculation, the sound pressure at each grid-point at each time-step was obtained. From these results, the sequence of instantaneous sound pressure distribution on the horizontal plane of 1.2 m above the floor was visualized as a movie picture. This presentation makes it easy to have intuitive understanding of the effect of architectural and acoustic treatments of respective building elements. As an example, Fig. 2 shows snap shots of the results of the calculations which was performed to examine the effectiveness of absorption treatment on the ceiling for the basic configuration of the classrooms (see Fig. 6(A)).

3 20ms 40ms 60ms ms 100ms Reflective (α = 0.1) Absorptive (α = 0.8) Acoustical condition of the ceiling Fig. 2 Snap-shots of sound propagation between two rooms through the open-space.

4 2) Contour map of sound pressure distribution By time-integrating the square of the sound pressure at each grid point, the sound exposure level (L pe ) was obtained. This calculation was performed for respective points on the 50-cm grid plane at a height of 1.2 m above the floor. The results of L pe obtained for the same condition as the case shown in Fig. 2 for 500 Hz in octave band are shown in Fig. 3. In this presentation, the sound energy of the impulsive sound source (L J ) was assumed to be 100 db in the frequency band. (L J and L pe can be read as sound power level, L W, and the sound pressure level, L p, respectively, in steady state.) 3) Average sound pressure level in the receiving room For the comparison between the conditions under examination, spatial average of L pe on the 1-m grid more than 50 cm apart from the walls in the receiving room at a height of 1.2 m above the floor was calculated (see Fig. 6). As shown in Fig. 3, this averaged L pe is 79.3 db for the condition without absorption treatment on the ceiling and 72.2 db for the one with absorption treatment. Avg. L pe = 79.3 [db] Avg. L pe = 72.2 [db] Reflective ceiling (α = 0.1) Absorptive ceiling (α = 0.8) Fig. 3 Contour maps of the sound exposure level. (Comparison between with and without sound absorption treatment on the ceiling) 3 VALIDITY OF THE NUMERICAL ANALYSES To examine the validity of the numerical analyses mentioned above, a field measurement and a calculation were performed for the open-plan type classrooms with the same geometry (see Fig. 4). In the measurement, a dodecahedral omni-directional loudspeaker system was located in one of the classrooms at a height of 1.5 m above the floor and a broadband noise was radiated. At each receiving point, omni-directional microphone was set at a height of 1.2 m above the floor. The finishing materials used for respective room surfaces in the classrooms and their sound absorption coefficients assumed in the calculation are shown in Table 1. Figure 5 shows the comparison between L pe obtained by the calculation and L p obtained by the measurement under the assumption that both L J for the calculation and L W for the measurement were 100 db for 500 Hz in octave band. As shown in the figure, it can be seen that the result of the numerical analysis is in fairly good agreement with the measured result. It suggests that the numerical analysis method using the FDTD method is applicable to this kind of study.

5 A A M1 Sound source Open space M3 M Thickness: Classroom 00 M2 M5 : Receiving points PLAN AA -SECTION Fig. 4 Open-plan type classrooms under investigation. Fig.5 Results of the measurement and numerical analysis. 4 NUMERICAL STUDY ON SOUND PROPAGATION BETWEEN ROOMS Based on the results obtained in the previous study mentioned above, the sound propagation between open-plan type classrooms was investigated using the FDTD numerical analysis by changing the classroom arrangement and room boundary conditions. As shown in Fig. 2 and 3, absorption treatment on the ceiling is considerably effective to mitigate the sound propagation. Therefore, in the following investigation, condition of sound absorption coefficient on the ceiling was set at 0.8. Figure 6 shows the condition of the classroom arrangement and the parameters examined in this study. The results are shown in Figs. 7 and 8. In this paper, the results for 500 Hz in octave band are presented. 4.1 Effect of Classroom Arrangement and Acoustical Treatments 00 Sound 音圧レベル pressure level [db] Sound 音圧暴露レベル exposure level [db] Table 1 Interior finishing of classrooms used in field measurement and α assumed in numerical analysis. Part ceiling wall floor Interior finishing material rock-wool board plaster board wooden flooring Sound absorption coefficient (α) 測定結果 Calculations 計算結果 Measurements 0 M M1 1 M M2 2 M M3 3 M M4 4 M M5 5 6 Receiving 受音点 points Distance between adjacent classrooms Since separating the adjacent classrooms was expected to lessen the sound transmission between them, FDTD calculation was performed by changing the distance between the rooms in four steps of 0 m (basic model), 4 m, 6 m and 8 m. Figures 7(A) and 7(B) show the comparison of the L pe contour between the results for the cases of 0 m and 8 m. In fig. 8, the plots for (A) for the condition of 0 m and (B) for the conditions of 4 m, 6 m and 8 m are almost the same level. As a result, it has been found that only a slight effect can be obtained by such separation Width of the open-space The effect of the open-space connecting the two classrooms was investigated by changing its width in steps of 4 m and 8 m. The results are shown in Figs. 7(C-1) and 7(C-2) and Fig. 8(C), in which it is seen that the sound propagating into the receiving room can be lessened by making the open-space wider

6 (A) Basic Model 6000 Conditions of classroom arrangement (B) Distance between classrooms: 0m(= (A)), 4m, 6m, 8m Sound source Receiving room Thickness Calculating area of average sound pressure level All conditions: Ceiling height: 3000 Ceiling α: 0.8 Wall, Floor α: 0.1 α: sound absorption coefficient 00 Open-space width: 4m, 8m Conditions of wall in the open-space (D) α: 0.8 α: 0.1 Outward inclining (5 and 10 deg. inclination) Fig. 6 Basic model and its variations examined by the calculation. 4.2 Effect of Architectural/Acoustic Treatment for the Wall in the Open-space From the results of the numerical study mentioned above, it has been clarified that the wall in the open-space causes mirror reflection and it can be expected that the sound propagation could be mitigated by dealing with the wall properly. To investigate this point, the following studies were performed Absorption treatment The simplest idea for mitigating the reflection on the wall is to make it sound absorptive. Thus, the reduction of the sound propagation by making a half of the area of the wall absorptive (sound absorption coefficient: 0.8). The calculation result is shown in Fig. 7(D) and Fig. 8(D). By comparing the result with that for the basic model shown in Fig. 8(A), it is seen that a reduction of 3.4 db can be obtained by the sound absorption treatment on the wall Den at the wall To give spatial variety to the wall, den, small space made by partly dented wall, can be designed. Such architectural means can be effective to change the reflection property of the wall and a numerical study was performed. The calculation condition is shown in Fig. 6(E) and the result is shown in Fig. 7(E) and Fig. 8(E). By comparing the result with that for the basic model, it is seen that a reduction of 5.5 db can be obtained by setting the den at the wall Outward inclining the wall As another architectural means to mitigate the reflection on the wall of the open-space, the effect of inclining the wall outward was investigated by changing the inclination angle in two steps of 5-degree and 10-degree. The results are shown in Fig. 7(F) and Fig. 8(F). By comparing these results with that for the basic model, it is seen that a reduction of 4.4 db can be obtained when the wall is inclined outward by 10-degree. This effect is caused by changing the direction of the reflected sound upward so as to increase the effect of sound absorption by the ceiling. (C) (E) (F) 6000 Den 3000

7 (A): basic model. (B): The two rooms are separated by 8m. (C-1): The width of the open-space is 4m. 2m 4m 2m (D): α of the wall in the open-space is 0.8 (half part) (C-2): The width of the open-space is 8m. (F): The wall in the open-space is inclined outward by 10 degrees. Fig. 7 Contour maps of sound exposure level (L pe ) indicating the effect of architectural/acoustical treatments. 65 (E): Den is designed at the wall. 65 Avg. LpE [db] 4 m 6 m 8 m 4 m 8 m 5-degree 10-degree (A) Basic model (B) Distance between classrooms (C) Width of open space (D) Absorption treatment on the wall (E) Den at the wall (F) Outward inclining the wall Fig. 8 Comparison of average sound exposure level (L pe ) for respective conditions.

8 5 CONCLUSIONS For the purpose of dealing with acoustic problems in open-plan type elementary school buildings, the applicability of the FDTD numerical analysis to the calculation of sound propagation between classrooms was examined first. By applying this method, the ways to mitigate the sound transmission between adjacent classrooms was investigated. As a result, it has been indicated that sound absorption treatment on the ceiling is essentially required. It has also been found that sound absorption treatment on the wall of the open-space which makes mirrorreflection are effective to mitigate the sound propagation between the classrooms. Besides, such architectural design as setting a den at the wall of the open-space and inclining the wall outward are effective to weaken the sound reflection. It is said that the open-plan type classroom will be mostly adopted in the elementary schools in Japan in the foreseeable future. This type of classroom arrangement has various merits in educational activities, but such demerits as acoustical problems should be recognized and sufficient measures should be taken in the process of architectural design. For this purpose, the numerical analysis investigated in this study is useful as an acoustical design tool. [1] Hideki Tachibana, Kanako Ueno and Ami Aoki, Study on acoustical conditions in elementary schools of open-plan type in Japan Part1: Plan features and acoustic properties of schoolrooms, Proceedings of Inter-Noise 2002, N323 (2002). [2] Kanako Ueno, Hideki Tachibana and Ami Aoki, Study on acoustical conditions in elementary schools of open-plan type in Japan Part2: Observation of classworks and inquiring survey Proceedings of Inter-Noise 2002, N324 (2002). [3] Yuzo Tsuchiya, Tadao Fukuyama, Katsuo Inoue and Yoshio Yamasaki, Actual condition survey and evaluation on acoustic environment of open type classroom, Proceedings of ICA 2004, II (2004). [4] Takatoshi Yokota, Shinichi Sakamoto and Hideki Tachibana, Visualization of sound propagation and scattering in rooms, Acoustical Science and Technology, Vol. 23, No. 1, pp (2002).