- Email: [email protected]
An experimental investigation into the sound-scattering performance of wooden diffusers with different structures
Applied Acoustics 71 (2010) 68–78
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Technical Note
An experimental investigation into the sound-scattering performance of wooden diffusers with different structures Fang-Ming Lin a, Pei-Yu Hong a, Chia-Yen Lee b,* a b
Department of Wood Science and Design, National Pingtung University of Science and Technology, Pingtung, Taiwan Department of Materials Engineering, National Pingtung University of Science and Technology, Pingtung 912, Taiwan
a r t i c l e
i n f o
Article history: Received 8 January 2009 Received in revised form 25 May 2009 Accepted 2 June 2009 Available online 22 August 2009 Keywords: Absorption coefficient Diffuser Edge effect Flutter Scattering coefficient
a b s t r a c t An experimental investigation is performed to determine the random-incident scattering coefficients of wooden diffuser structures characterized by different materials, geometrical designs, groove depths and baffle features. In general, it is found that the reliability of the measurement results obtained using the ISO 17497-1 standard can be improved by inserting the test sample into the rotating turntable in order to reduce the edge effect. The experimental results show that a higher scattering coefficient is obtained when the diffuser is fitted with flutters, has a double-triangular upper-surface profile, and has a greater groove depth. The results and discussions presented in this study provide architectural acousticians with a useful framework for evaluating the sound-scattering performance of various wooden diffuser structures in indoor environments. Ó 2009 Published by Elsevier Ltd.
1. Introduction One of the most challenging problems facing architectural acousticians when designing indoor environments intended for public gatherings or musical performances is that of predicting the overall sound quality before the design is committed to construction. Accordingly, the problem of acoustic design for such venues as town halls and concert halls has long attracted significant interest in the literature [1,2]. Hargreaves et al. [3,4] proposed an approach for quantifying the angular distribution of the acoustic energy reflected from baffled and unbaffled surfaces utilizing a surface diffusion coefficient. Haan and Kwon [5] proposed a method for measuring the diffusivity of various types of surface in a hall through computer modeling and field measurements. In the proposed approach, a new criterion (Dx) was introduced to quantify the phase difference of the room’s acoustical parameters based upon the signals received at two microphones positioned in front of and behind the rear wall of the hall, respectively. It was found that in halls with a high diffusivity, the sound pressure level (SPL), early decay time (EDT) and clarity index (C80) all decreased for sound with a high frequency (>500 Hz), but increased for sound in the low-frequency range (<250 Hz). Thus, it was inferred that in halls of surfaces with a high diffusivity reflect or diffuse high frequency sound, but diffract low-frequency sound. Vorländer and Mommertz [6] presented a method for measuring the scattering coefficients of rough surfaces in order to support the * Corresponding author. E-mail address: [email protected] (C.-Y. Lee). 0003-682X/$ - see front matter Ó 2009 Published by Elsevier Ltd. doi:10.1016/j.apacoust.2009.06.005
acoustic modeling of interior environments. Samples with various surface characteristics were placed in a reverberation chamber and exposed to sound with frequencies ranging from 1 Hz to 30 kHz. Following the phase-locked superpositioning of a sufficient number of impulse responses, the coherent reflected sound energy was found to be identical to the zero-order lobe of the reflection pattern, i.e. the specularly reflected part of the incident energy. For each sample, the scattering coefficient d was obtained from the reflected sound energy by
d¼1
Espec Etotal
ð1Þ
where Espec is the specularly reflected energy and Etotal is the total incident energy. The literature contains many studies investigating the determinants of the scattering coefficient in indoor and outdoor environments [7–10]. In general, the results show that the soundscattering performance of any environment is fundamentally dependent upon the surface characteristics of the walls (or facades) which form its boundaries. Many methods have been proposed for designing effective sound diffusing surfaces and for predicting and measuring their acoustic properties [11,12]. For example, ISO 354 [13] prescribes a method for measuring the sound absorption coefficients of acoustical materials in a reverberation room or for determining the equivalent sound absorption area of objects such as furniture or people [13]. The acoustic performance of internal environments is commonly enhanced by attaching some form of diffuser structure to the ceiling and/or walls. Broadly speaking, diffusers can
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
be categorized as either one-dimensional (1-D) or two-dimensional (2-D). Diffusers of the former type have a depth variation in one direction only and scatter the incident sound uniformly over a hemi-disc. By contrast, the sound energy scattered from a 2-D diffuser is uniformly distributed over the surface of a hemisphere. 2-D diffusers are therefore applied when the scattered energy is to be in music production rooms or when it is necessary to prevent a strong specular reflection [14]. Fujiwara et al. [15] presented a method for visualizing the sound fields within the wells of a Schroeder diffuser (a quadratic-residue type diffuser, QRD). The distribution of the sound field was analyzed numerically and compared with the experimentally measured distribution. The results showed that different sound fields were developed for different QRD well arrangements in different frequency ranges. In 2004, Vorländer et al. [16] compared random-incidence scattering coeffi-
cients of different shapes of samples and found lower scattering coefficients could be obtained than those in squared samples on a turntable as squared samples were mounted in a square recess with its top plane placed flush with a circular base plate. Therefore, the ‘‘edge effect” was reduced because difference of additional scattering contributed from the sides of the squared samples was decreased as they were mounted in a circular base plate and the diffraction in the resulting averaged impulse response caused by the edges was independently equal from the orientation of the circular plate.
Fig. 1. Scattering from rough surfaces [6].
Fig. 2. Reflected pulses obtained for three different sample orientations [18].
69
Fig. 4. Photograph of reverberation room.
Fig. 3. Structures of sample diffusers with and without flutters.
70
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
This study conducts a systematic experimental investigation into the sound-scattering and absorption properties of wooden diffusers characterized by different materials (e.g. Japanese cedar, plywood and medium density fiberboard (MDF)), different upperplate profiles (e.g. flat or angled), and different baffling characteristics (e.g. with or without flutters). The experiments are conducted in a standard reverberation room in accordance with a modified version of the test procedure prescribed in the ISO 17497-1 standard. It is shown that the reliability of the measurement results can be improved by embedding the diffuser samples within the turntable rather than positioning them on the turntable surface. Overall, the experimental results presented in this study provide a useful insight into the diffusion properties of a wide range of common 2-D diffuser structures.
2. Measurement method
ð1 sÞð1 aÞ þ Specular
a
Absorbed
þ sð1 aÞ ¼ 1;
ð2Þ
Scattered
where a is the absorption coefficient of the incident surface. The scattering coefficient generally depends on both the frequency and the angle of incidence of the sound energy. However, as with the random-incidence absorption coefficient obtained in reverberation rooms, an angular average of the scattering coefficient, i.e. the random-incidence scattering coefficient, can also be derived from the measured directivity pattern [18]. 2.2. Measurement method The measurement experiments performed in this study are based upon the ISO 17497-1 standard (‘‘Measurement of the random-incidence scattering coefficient in a reverberation room”) [19], in which in addition to conventional measurements of the absorption coefficient, the sample is placed on a turntable and impulse responses are obtained for different sample orientations [20].
2.1. Scattering Traditionally, the scattering properties of a diffusive surface are expressed in terms of the directivity pattern; measured or calculated for sound with a particular frequency and angle of incidence [6]. However, the detailed directivity pattern of the scattered sound is of interest in only a minority of cases. Of far more practical interest is the scattering coefficient, s, defined as the ratio of the non-specularly reflected sound energy to the totally reflected energy (see Fig. 1). In general, the relationship between the specularly reflected energy and the scattered energy is given by [17]
2.2.1. Theory Fig. 2 illustrates the impulse responses (i.e. the reflected sound) measured at three different microphone positions relative to the diffuser sample. (Note that the results are reproduced directly from [19].) It is observed that the three signals are virtually superimposed in the initial response period, but become increasingly affected by their respective orientation relative to the sample in the latter part of the impulse response. Consequently, the latter parts of the reflected pulses contain the energy in the ‘‘tail”. Accordingly, after a synchronized averaging of the impulse re-
Fig. 5. Schematic illustration of (a) experimental arrangement and (b) positions of sound sources A and B.
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78 9.00 8.00 7.00
RT (sec)
6.00 5.00 4.00 3.00 2.00 1.00 0.00 100 125 160 200 250 315 400 500 630 800
1k 1.25k 1.6k
2k
2.5k 3.15k 4k
5k
frequency (Hz)
71
in which V is the volume of the reverberation chamber, c1–c4 are the speeds of sound in air during the measurement of T1–T4, S is the surface area of the test sample, T1 is the reverberation time when the test sample is not present and the turntable is not rotating, and T2 is the reverberation time when the test sample is present and the turntable is not rotating. Similarly T3 is the reverberation time when the test sample is not present and the turntable is rotating, and T4 is the reverberation time when the test sample is present and the turntable is rotating. Finally, m1 m4 are the energy attenuation coefficients of air calculated in accordance with ISO 9613-1 using the prevailing temperature and relative humidity values when measuring T1–T4, respectively. Note that in theory, the scattering coefficient obtained from Eq. (1) varies in the range 0–1. However, in practice, the edge effect may result in a scattering coefficient greater than 1.
Fig. 6. Reverberation time distribution of test arrangement at different frequencies.
sponses, the scattering coefficient can be obtained by extracting the specular energy from the reflected pulses. 2.2.2. Calculation The scattering coefficient is given by
s¼
aspec as ; 1 as
ð3Þ
where aspec is the specular absorption coefficient and as is the random-incidence absorption coefficient, defined, respectively, as [19]:
V 1 1 4V ðm4 m3 Þ; S c4 T 4 c3 T 3 S V 1 1 4V ðm2 m1 Þ; as ¼ 55:3 S c2 T 2 c1 T 1 S
aspec ¼ 55:3
ð4Þ ð5Þ
2.2.3. Test arrangement In the present experiments, the reverberation room (volume = 171.6 m3) had a scale factor of N = 2. Thus, in accordance with the guidelines laid down in ISO 17497-1, the diameter (d) of the turntable was specified as 2.0 m (i.e. greater than 3.0 m/N). Furthermore, the specimen was positioned at a distance of 2.5 m (at least 1.0 m/N) from the boundary of the reverberation room. In the experiments, the impulse responses were obtained for periodic deterministic signals. For each diffuser sample, six impulse response signals were recorded (corresponding to two sources and three microphone positions). For each combination of source and receiver positions, a multiple of a periodic pseudo-random signal was continuously radiated and received while the turntable was rotating. The total measurement duration was equal to the time of one revolution of the turntable (81.6 s). Using a pseudo-random periodic signal with a period of 5.1 s, 16 signal periods were continuously radiated [19]. The revolution speed of the turntable was 0.735 rpm.
Fig. 7. (a) Photograph of experimental setup and (b) section view of turntable and alternative sample positions.
72
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
Fig. 8. Comparison of scattering coefficients of various plywood diffusers positioned on top of turntable and within turntable, respectively: (a) flat diffusers with flutters, (b) flat diffusers without flutters and (c) double-triangular-profile diffusers without flutters.
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
73
Fig. 9. Comparison of random-incidence absorption coefficients of flat diffusers with and without flutters, respectively: (a) plywood diffusers, (b) MDF diffusers and (c) Japanese cedar diffusers.
74
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
Fig. 10. Comparison of scattering coefficients of flat diffusers with and without flutters, respectively: (a) plywood diffusers, (b) MDF diffusers and (c) Japanese cedar diffusers.
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
3. Test specimens and measurement procedure The objective of the current experiments was to identify a diffuser design which resulted in a high value of the scattering coefficient for sound frequencies in the range 100 Hz–5 kHz. Accordingly, the experiments were performed using sample wooden diffusers (L W: 1340 mm 1340 mm) characterized by different materials (i.e. lauan plywood, medium density fiberboard (MDF), and Japanese cedar), different geometrical designs (i.e. flat or angled top plates), different baffle features (i.e. with or without flutters), and different groove depths (i.e. 4 cm, 6 cm or 8 cm). The various samples are illustrated schematically in Fig. 3. As shown in Fig. 4, the diffusers were located on a turntable in a reverberation room. During the experiments, the MLS signals were produced by two sound sources
75
(OS002, 01 dB-METRAVIB: 200 Hz–10 kHz), respectively, located toward the two upper corner of the reverberation room (Fig. 5). The resulting impulse signals were detected in three different positions within the reverberation room by microphones (MCE 212, 01 dBMETRAVIB: 1/2 in.). For the test arrangement, the measurement results of the reverberation time are shown in Fig. 6, which were obtained after 7 min in an empty room with closed doors. 4. Results and discussion 4.1. Edge effect Edge effects prompted by variations of the sample height along its edge can result in scattering coefficients greater than those
Fig. 11. Comparison of scattering coefficients of: (a) Japanese cedar diffusers with flutters and different inclination angles, and (b) Japanese cedar and plywood diffusers with flutters and inclination angle of 45°.
76
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
which would otherwise be obtained if the sample were of an infinite surface area. On occasion, edge effects may even cause the scattering coefficient to exceed a value of s > 1 [19]. In an attempt to resolve this problem, this study commenced by performing a series of experiments in which the sample diffusers were inserted into the turntable in order to minimize the difference in height between the sample and the turntable surface (see Fig. 7). Fig. 8 presents the measured values of the scattering coefficients obtained for flat diffusers with flutters (Fig. 8a), flat diffusers without flutters (Fig. 8b) and double-triangular diffusers without flutters (Fig. 8c) for the case where the samples were positioned firstly on top of the turntable and then inserted within it. (Please note that the frequency was given as the equivalent full-scale frequency (f/2) with the scale factor of N = 2 in the study.) In every case, it is
observed that the measured scattering coefficients exceed a value of 1.0 (s > 1) for medium-frequency sound when the diffusers are placed on the upper surface of the turntable. However, the scattering coefficients have a value of less than 1.0 for all values of the sound frequency when the samples are inserted into the turntable. In other words, the reliability of the measurement results is significantly enhanced as a result of the reduced edge effect [16]. As a consequence, the sample diffusers were inserted into the turntable in all the remaining experiments performed in this study. 4.2. Calculation of random-incidence absorption coefficient The random-incidence absorption coefficients were first measured and calculated [19]. Fig. 9a–c compare the absorption coeffi-
Fig. 12. Comparison of scattering coefficients of: (a) Japanese cedar diffusers with triangular and double-triangular profiles and flutters and (b) plywood diffusers with triangular and double-triangular profiles and without flutters.
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
cients obtained at frequencies of 100 Hz–5 kHz for flat diffusers with and without flutters fabricated from lauan plywood, MDF and Japanese cedar, respectively. It can be found the absorption coefficients are 0.2 for lauan plywood and 0 for MDF and Japanese cedar as the frequency is 5 kHz. The results show that the sound absorption effect of the plywood sample is high as the frequency is high (5 kHz), but there is no absorption effect for the MDF and Japanese cedar diffusers at the same frequency. 4.3. Effects of diffuser flutter Fig. 10a–c compare the scattering coefficients obtained at frequencies of 100 Hz–5 kHz for flat diffusers with and without flutters fabricated from lauan plywood, MDF and Japanese cedar, respectively. Note that the groove depth is 8 cm in every case. Fig. 10a shows that the scattering coefficient of the plywood diffusers with flutters is slightly higher than that of the diffusers without flutters over the frequency range 160 Hz–2.5 kHz. However, the scattering coefficients of both types of plywood diffuser are greater than 0.6 for frequencies in the range 500 Hz–2.5 kHz. The results presented in Fig. 10b show that the addition of flutters to the MDF diffuser has no apparent effect on the scattering coefficient at frequencies lower than 800 Hz. However, at frequencies in the range 800 Hz–4 kHz, the addition of flutters yields a notable improvement in the scattering coefficient. Finally, Fig. 10c shows that the addition of flutters to the Japanese cedar wood diffusers has little effect on the scattering coefficient over the entire frequency range. However, a reasonable scattering performance (i.e. s > 0.6) is obtained from both diffusers at all frequencies in the range 500 Hz–2.5 kHz. It can also be found that the scattering coefficients of the different diffusers with flutters are averagely higher than those without flutters due to their higher surface roughness. Please note that when the surface is rough in comparison to the wavelength of the applied sound waves, diffuse reflection appears and helps enhance the scattering coefficients of the diffusers. For plywood diffusers, the scattering coefficient decreases to 0 as the applied sound frequency is 5 kHz due to their high absorption coefficients at the high frequency (Fig. 9a). Over the low-frequency
77
range, the enhancement of the scattering coefficients of the diffusers with flutters is not apparent because the wavelength is high enough not to be influenced by the roughness of the diffuser surface.
4.4. Effect of installation angle of diffuser top plate To clarify the effect on the scattering coefficient of the angle of the diffuser top plate, a series of experiments was performed using Japanese cedar diffusers with inclination angles of 30° and 45°, respectively. The corresponding results are presented in Fig. 11a and show that the inclination angle of the top plate has only a marginal effect on the scattering performance of the diffuser due to the small roughness difference of the diffuser surface. Fig. 11b illustrates the variation of the scattering coefficient with the sound frequency for Japanese cedar and plywood diffusers fitted with flutters and having an upper plate inclination angle of 45°. A good agreement is observed between the two sets of results over the full frequency range, and thus it is inferred that the diffuser material has only a slight effect on the scattering coefficient when the upper plate is inclined at an angle to the horizontal.
4.5. Effect of diffuser shape Fig. 12a presents the scattering coefficients of Japanese cedar diffusers (with flutters) and triangular or double-triangular top plate profiles over the frequency range 100 Hz–5 kHz. The results show that the double-triangular top plate profile yields an improvement in the scattering performance; particularly at medium and higher values of the sound frequency (i.e. >800 Hz.). Meanwhile, Fig. 12b shows the scattering coefficients of plywood diffusers (without flutters) with triangular or double-triangular top plate profiles. In general, it is observed that for each type of diffuser, the double-triangle profile of the upper plates influences on the value of the scattering coefficient over the frequency range 100 Hz–5 kHz due to the higher roughness caused by double-triangle shapes.
Fig. 13. Comparison of scattering coefficients of Japanese cedar diffusers with flutters and different groove depths.
78
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
4.6. Effect of diffuser groove depth
References
The effect of the diffuser groove depth on the scattering coefficient was evaluated using flat Japanese cedar wood diffusers with flutters. Fig. 13 shows that for a given value of the noise frequency, the scattering coefficient increases with an increasing groove depth due to the higher roughness of the diffuser surface.
[1] Harold Marshall A. Acoustical design and evaluation of Christchurch Town hall. New Zealand. J Acoust Soc Am 1979;65:751–7. [2] Beranek LL. Concert hall acoustics–1992. J Acoust Soc Am 1992;92:1–39. [3] Hargreaves TJ, Cox TJ, Lam YW, D’Antonio P. Diffusion coefficients (A). J Acoust Soc Am 1998;104:1858. [4] Hargreaves TJ, Cox TJ, Lam YW, D’Antonio P. Surface diffusion coefficients for room acoustics: free-field measures. J Acoust Soc Am 2000;108:1710–20. [5] Haan CH, Kwon KW. A method of evaluating surface diffusivity of rooms – I: computer modeling and field measurement. Appl Acoust 2001;62:1313–27. [6] Vorländer M, Mommertz E. Definition and measurement of random-incidence scattering coefficients. Appl Acoust 2000;60:187–99. [7] Quis D. Scattering by a barrier in a room. Appl Acoust 1999;56:1–24. [8] Godinho L, António J, Tadeu A. 3D sound scattering by rigid barriers in the vicinity of tall buildings. Appl Acoust 2001;62:1229–48. [9] Onaga H, Rindel JH. Acoustic characteristics of urban streets in relation to scattering caused by building facades. Appl Acoust 2007;68:310–25. [10] Wang LM, Rathsam J. The influence of absorption factors on the sensitivity of a virtual room’s sound field to scattering coefficients. Appl Acoust 2008;69:1249–57. [11] D’Antonio P, Cox TJ. Two decades of sound diffuser design and development. Part 1: applications and design. J Audio Eng Soc 1998;46:955–76. [12] D’Antonio P, Cox TJ. Two decades of sound diffuser design and development. Part 2: prediction, measurement and characterization. J Audio Eng Soc 1998;46:1075–91. [13] ISO 354. Acoustics – Measurement of sound absorption in a reverberation room; 2003. [14] D’Antonio P, Cox TJ. Diffusor application in rooms. Appl Acoust 2000;60:113–42. [15] Fujiwara K, Nakai K, Torihara H. Visualization of the sound field around a Schroeder diffuser. Appl Acoust 2000;60:225–35. [16] Vorländer M, Embrechts J, Geetere LD, Vermeir G, Gomes MHA. Case studies in measurement of random incidence scattering coefficients. Acta Acust United Acust 2004;90:858–67. [17] Zeng X, Chrestensen CL, Rindel JH. Practical methods to define scattering coefficients in a room acoustics computer model. Appl Acoust 2006;67:771–86. [18] Mommertz E. Determination of scattering coefficients from the reflection directivity of architectural surfaces. Appl Acoust 2000;60:201–3. [19] ISO 17497–1. Acoustics – sound-scattering properties of surfaces – Part 1: measurement of the random-incidence scattering coefficient in a reverberation room; 2004. [20] Jeon JY, Lee SC, Vorländer M. Development of scattering surfaces for concert halls. Appl Acoust 2004;65:341–55.
5. Conclusions This study has conducted an experimental investigation into the scattering performance of wooden diffusers fabricated from various materials (i.e. Japanese cedar, MDF or plywood), and having various upper plate profiles (i.e. flat, single-triangular or doubletriangular), baffle features (i.e. with or without flutters) and groove depths (i.e. 4 cm, 6 cm or 8 cm). The results have shown that the reliability of the measurement results obtained using the ISO 17497-1 standard can be improved by placing the sample within the turntable rather than on its upper surface such that the edge effect is reduced. In addition, the experimental results have shown that the sound-scattering coefficient can be improved by fitting the diffuser structure with flutters, designing the top plate with a double-triangular profile, and increasing the groove depth. Overall, the experimental results presented in this study provide designers with a useful source of reference for predicting the sound-scattering performance of wooden diffusers with various geometrical structures in indoor environments. Acknowledgements The authors gratefully acknowledge the financial support provided to this study by the National Science Council of Taiwan under Grant numbers NSC 97-2221-E-020-028, NSC 97-2218-E-006-012 and NSC 96-2218-E-006-004. The contributions of Prof. Che-Ming Chiang and Prof. Rong-Ping Lai are also acknowledged.
Contents lists available at ScienceDirect
Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Technical Note
An experimental investigation into the sound-scattering performance of wooden diffusers with different structures Fang-Ming Lin a, Pei-Yu Hong a, Chia-Yen Lee b,* a b
Department of Wood Science and Design, National Pingtung University of Science and Technology, Pingtung, Taiwan Department of Materials Engineering, National Pingtung University of Science and Technology, Pingtung 912, Taiwan
a r t i c l e
i n f o
Article history: Received 8 January 2009 Received in revised form 25 May 2009 Accepted 2 June 2009 Available online 22 August 2009 Keywords: Absorption coefficient Diffuser Edge effect Flutter Scattering coefficient
a b s t r a c t An experimental investigation is performed to determine the random-incident scattering coefficients of wooden diffuser structures characterized by different materials, geometrical designs, groove depths and baffle features. In general, it is found that the reliability of the measurement results obtained using the ISO 17497-1 standard can be improved by inserting the test sample into the rotating turntable in order to reduce the edge effect. The experimental results show that a higher scattering coefficient is obtained when the diffuser is fitted with flutters, has a double-triangular upper-surface profile, and has a greater groove depth. The results and discussions presented in this study provide architectural acousticians with a useful framework for evaluating the sound-scattering performance of various wooden diffuser structures in indoor environments. Ó 2009 Published by Elsevier Ltd.
1. Introduction One of the most challenging problems facing architectural acousticians when designing indoor environments intended for public gatherings or musical performances is that of predicting the overall sound quality before the design is committed to construction. Accordingly, the problem of acoustic design for such venues as town halls and concert halls has long attracted significant interest in the literature [1,2]. Hargreaves et al. [3,4] proposed an approach for quantifying the angular distribution of the acoustic energy reflected from baffled and unbaffled surfaces utilizing a surface diffusion coefficient. Haan and Kwon [5] proposed a method for measuring the diffusivity of various types of surface in a hall through computer modeling and field measurements. In the proposed approach, a new criterion (Dx) was introduced to quantify the phase difference of the room’s acoustical parameters based upon the signals received at two microphones positioned in front of and behind the rear wall of the hall, respectively. It was found that in halls with a high diffusivity, the sound pressure level (SPL), early decay time (EDT) and clarity index (C80) all decreased for sound with a high frequency (>500 Hz), but increased for sound in the low-frequency range (<250 Hz). Thus, it was inferred that in halls of surfaces with a high diffusivity reflect or diffuse high frequency sound, but diffract low-frequency sound. Vorländer and Mommertz [6] presented a method for measuring the scattering coefficients of rough surfaces in order to support the * Corresponding author. E-mail address: [email protected] (C.-Y. Lee). 0003-682X/$ - see front matter Ó 2009 Published by Elsevier Ltd. doi:10.1016/j.apacoust.2009.06.005
acoustic modeling of interior environments. Samples with various surface characteristics were placed in a reverberation chamber and exposed to sound with frequencies ranging from 1 Hz to 30 kHz. Following the phase-locked superpositioning of a sufficient number of impulse responses, the coherent reflected sound energy was found to be identical to the zero-order lobe of the reflection pattern, i.e. the specularly reflected part of the incident energy. For each sample, the scattering coefficient d was obtained from the reflected sound energy by
d¼1
Espec Etotal
ð1Þ
where Espec is the specularly reflected energy and Etotal is the total incident energy. The literature contains many studies investigating the determinants of the scattering coefficient in indoor and outdoor environments [7–10]. In general, the results show that the soundscattering performance of any environment is fundamentally dependent upon the surface characteristics of the walls (or facades) which form its boundaries. Many methods have been proposed for designing effective sound diffusing surfaces and for predicting and measuring their acoustic properties [11,12]. For example, ISO 354 [13] prescribes a method for measuring the sound absorption coefficients of acoustical materials in a reverberation room or for determining the equivalent sound absorption area of objects such as furniture or people [13]. The acoustic performance of internal environments is commonly enhanced by attaching some form of diffuser structure to the ceiling and/or walls. Broadly speaking, diffusers can
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
be categorized as either one-dimensional (1-D) or two-dimensional (2-D). Diffusers of the former type have a depth variation in one direction only and scatter the incident sound uniformly over a hemi-disc. By contrast, the sound energy scattered from a 2-D diffuser is uniformly distributed over the surface of a hemisphere. 2-D diffusers are therefore applied when the scattered energy is to be in music production rooms or when it is necessary to prevent a strong specular reflection [14]. Fujiwara et al. [15] presented a method for visualizing the sound fields within the wells of a Schroeder diffuser (a quadratic-residue type diffuser, QRD). The distribution of the sound field was analyzed numerically and compared with the experimentally measured distribution. The results showed that different sound fields were developed for different QRD well arrangements in different frequency ranges. In 2004, Vorländer et al. [16] compared random-incidence scattering coeffi-
cients of different shapes of samples and found lower scattering coefficients could be obtained than those in squared samples on a turntable as squared samples were mounted in a square recess with its top plane placed flush with a circular base plate. Therefore, the ‘‘edge effect” was reduced because difference of additional scattering contributed from the sides of the squared samples was decreased as they were mounted in a circular base plate and the diffraction in the resulting averaged impulse response caused by the edges was independently equal from the orientation of the circular plate.
Fig. 1. Scattering from rough surfaces [6].
Fig. 2. Reflected pulses obtained for three different sample orientations [18].
69
Fig. 4. Photograph of reverberation room.
Fig. 3. Structures of sample diffusers with and without flutters.
70
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
This study conducts a systematic experimental investigation into the sound-scattering and absorption properties of wooden diffusers characterized by different materials (e.g. Japanese cedar, plywood and medium density fiberboard (MDF)), different upperplate profiles (e.g. flat or angled), and different baffling characteristics (e.g. with or without flutters). The experiments are conducted in a standard reverberation room in accordance with a modified version of the test procedure prescribed in the ISO 17497-1 standard. It is shown that the reliability of the measurement results can be improved by embedding the diffuser samples within the turntable rather than positioning them on the turntable surface. Overall, the experimental results presented in this study provide a useful insight into the diffusion properties of a wide range of common 2-D diffuser structures.
2. Measurement method
ð1 sÞð1 aÞ þ Specular
a
Absorbed
þ sð1 aÞ ¼ 1;
ð2Þ
Scattered
where a is the absorption coefficient of the incident surface. The scattering coefficient generally depends on both the frequency and the angle of incidence of the sound energy. However, as with the random-incidence absorption coefficient obtained in reverberation rooms, an angular average of the scattering coefficient, i.e. the random-incidence scattering coefficient, can also be derived from the measured directivity pattern [18]. 2.2. Measurement method The measurement experiments performed in this study are based upon the ISO 17497-1 standard (‘‘Measurement of the random-incidence scattering coefficient in a reverberation room”) [19], in which in addition to conventional measurements of the absorption coefficient, the sample is placed on a turntable and impulse responses are obtained for different sample orientations [20].
2.1. Scattering Traditionally, the scattering properties of a diffusive surface are expressed in terms of the directivity pattern; measured or calculated for sound with a particular frequency and angle of incidence [6]. However, the detailed directivity pattern of the scattered sound is of interest in only a minority of cases. Of far more practical interest is the scattering coefficient, s, defined as the ratio of the non-specularly reflected sound energy to the totally reflected energy (see Fig. 1). In general, the relationship between the specularly reflected energy and the scattered energy is given by [17]
2.2.1. Theory Fig. 2 illustrates the impulse responses (i.e. the reflected sound) measured at three different microphone positions relative to the diffuser sample. (Note that the results are reproduced directly from [19].) It is observed that the three signals are virtually superimposed in the initial response period, but become increasingly affected by their respective orientation relative to the sample in the latter part of the impulse response. Consequently, the latter parts of the reflected pulses contain the energy in the ‘‘tail”. Accordingly, after a synchronized averaging of the impulse re-
Fig. 5. Schematic illustration of (a) experimental arrangement and (b) positions of sound sources A and B.
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78 9.00 8.00 7.00
RT (sec)
6.00 5.00 4.00 3.00 2.00 1.00 0.00 100 125 160 200 250 315 400 500 630 800
1k 1.25k 1.6k
2k
2.5k 3.15k 4k
5k
frequency (Hz)
71
in which V is the volume of the reverberation chamber, c1–c4 are the speeds of sound in air during the measurement of T1–T4, S is the surface area of the test sample, T1 is the reverberation time when the test sample is not present and the turntable is not rotating, and T2 is the reverberation time when the test sample is present and the turntable is not rotating. Similarly T3 is the reverberation time when the test sample is not present and the turntable is rotating, and T4 is the reverberation time when the test sample is present and the turntable is rotating. Finally, m1 m4 are the energy attenuation coefficients of air calculated in accordance with ISO 9613-1 using the prevailing temperature and relative humidity values when measuring T1–T4, respectively. Note that in theory, the scattering coefficient obtained from Eq. (1) varies in the range 0–1. However, in practice, the edge effect may result in a scattering coefficient greater than 1.
Fig. 6. Reverberation time distribution of test arrangement at different frequencies.
sponses, the scattering coefficient can be obtained by extracting the specular energy from the reflected pulses. 2.2.2. Calculation The scattering coefficient is given by
s¼
aspec as ; 1 as
ð3Þ
where aspec is the specular absorption coefficient and as is the random-incidence absorption coefficient, defined, respectively, as [19]:
V 1 1 4V ðm4 m3 Þ; S c4 T 4 c3 T 3 S V 1 1 4V ðm2 m1 Þ; as ¼ 55:3 S c2 T 2 c1 T 1 S
aspec ¼ 55:3
ð4Þ ð5Þ
2.2.3. Test arrangement In the present experiments, the reverberation room (volume = 171.6 m3) had a scale factor of N = 2. Thus, in accordance with the guidelines laid down in ISO 17497-1, the diameter (d) of the turntable was specified as 2.0 m (i.e. greater than 3.0 m/N). Furthermore, the specimen was positioned at a distance of 2.5 m (at least 1.0 m/N) from the boundary of the reverberation room. In the experiments, the impulse responses were obtained for periodic deterministic signals. For each diffuser sample, six impulse response signals were recorded (corresponding to two sources and three microphone positions). For each combination of source and receiver positions, a multiple of a periodic pseudo-random signal was continuously radiated and received while the turntable was rotating. The total measurement duration was equal to the time of one revolution of the turntable (81.6 s). Using a pseudo-random periodic signal with a period of 5.1 s, 16 signal periods were continuously radiated [19]. The revolution speed of the turntable was 0.735 rpm.
Fig. 7. (a) Photograph of experimental setup and (b) section view of turntable and alternative sample positions.
72
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
Fig. 8. Comparison of scattering coefficients of various plywood diffusers positioned on top of turntable and within turntable, respectively: (a) flat diffusers with flutters, (b) flat diffusers without flutters and (c) double-triangular-profile diffusers without flutters.
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
73
Fig. 9. Comparison of random-incidence absorption coefficients of flat diffusers with and without flutters, respectively: (a) plywood diffusers, (b) MDF diffusers and (c) Japanese cedar diffusers.
74
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
Fig. 10. Comparison of scattering coefficients of flat diffusers with and without flutters, respectively: (a) plywood diffusers, (b) MDF diffusers and (c) Japanese cedar diffusers.
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
3. Test specimens and measurement procedure The objective of the current experiments was to identify a diffuser design which resulted in a high value of the scattering coefficient for sound frequencies in the range 100 Hz–5 kHz. Accordingly, the experiments were performed using sample wooden diffusers (L W: 1340 mm 1340 mm) characterized by different materials (i.e. lauan plywood, medium density fiberboard (MDF), and Japanese cedar), different geometrical designs (i.e. flat or angled top plates), different baffle features (i.e. with or without flutters), and different groove depths (i.e. 4 cm, 6 cm or 8 cm). The various samples are illustrated schematically in Fig. 3. As shown in Fig. 4, the diffusers were located on a turntable in a reverberation room. During the experiments, the MLS signals were produced by two sound sources
75
(OS002, 01 dB-METRAVIB: 200 Hz–10 kHz), respectively, located toward the two upper corner of the reverberation room (Fig. 5). The resulting impulse signals were detected in three different positions within the reverberation room by microphones (MCE 212, 01 dBMETRAVIB: 1/2 in.). For the test arrangement, the measurement results of the reverberation time are shown in Fig. 6, which were obtained after 7 min in an empty room with closed doors. 4. Results and discussion 4.1. Edge effect Edge effects prompted by variations of the sample height along its edge can result in scattering coefficients greater than those
Fig. 11. Comparison of scattering coefficients of: (a) Japanese cedar diffusers with flutters and different inclination angles, and (b) Japanese cedar and plywood diffusers with flutters and inclination angle of 45°.
76
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
which would otherwise be obtained if the sample were of an infinite surface area. On occasion, edge effects may even cause the scattering coefficient to exceed a value of s > 1 [19]. In an attempt to resolve this problem, this study commenced by performing a series of experiments in which the sample diffusers were inserted into the turntable in order to minimize the difference in height between the sample and the turntable surface (see Fig. 7). Fig. 8 presents the measured values of the scattering coefficients obtained for flat diffusers with flutters (Fig. 8a), flat diffusers without flutters (Fig. 8b) and double-triangular diffusers without flutters (Fig. 8c) for the case where the samples were positioned firstly on top of the turntable and then inserted within it. (Please note that the frequency was given as the equivalent full-scale frequency (f/2) with the scale factor of N = 2 in the study.) In every case, it is
observed that the measured scattering coefficients exceed a value of 1.0 (s > 1) for medium-frequency sound when the diffusers are placed on the upper surface of the turntable. However, the scattering coefficients have a value of less than 1.0 for all values of the sound frequency when the samples are inserted into the turntable. In other words, the reliability of the measurement results is significantly enhanced as a result of the reduced edge effect [16]. As a consequence, the sample diffusers were inserted into the turntable in all the remaining experiments performed in this study. 4.2. Calculation of random-incidence absorption coefficient The random-incidence absorption coefficients were first measured and calculated [19]. Fig. 9a–c compare the absorption coeffi-
Fig. 12. Comparison of scattering coefficients of: (a) Japanese cedar diffusers with triangular and double-triangular profiles and flutters and (b) plywood diffusers with triangular and double-triangular profiles and without flutters.
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
cients obtained at frequencies of 100 Hz–5 kHz for flat diffusers with and without flutters fabricated from lauan plywood, MDF and Japanese cedar, respectively. It can be found the absorption coefficients are 0.2 for lauan plywood and 0 for MDF and Japanese cedar as the frequency is 5 kHz. The results show that the sound absorption effect of the plywood sample is high as the frequency is high (5 kHz), but there is no absorption effect for the MDF and Japanese cedar diffusers at the same frequency. 4.3. Effects of diffuser flutter Fig. 10a–c compare the scattering coefficients obtained at frequencies of 100 Hz–5 kHz for flat diffusers with and without flutters fabricated from lauan plywood, MDF and Japanese cedar, respectively. Note that the groove depth is 8 cm in every case. Fig. 10a shows that the scattering coefficient of the plywood diffusers with flutters is slightly higher than that of the diffusers without flutters over the frequency range 160 Hz–2.5 kHz. However, the scattering coefficients of both types of plywood diffuser are greater than 0.6 for frequencies in the range 500 Hz–2.5 kHz. The results presented in Fig. 10b show that the addition of flutters to the MDF diffuser has no apparent effect on the scattering coefficient at frequencies lower than 800 Hz. However, at frequencies in the range 800 Hz–4 kHz, the addition of flutters yields a notable improvement in the scattering coefficient. Finally, Fig. 10c shows that the addition of flutters to the Japanese cedar wood diffusers has little effect on the scattering coefficient over the entire frequency range. However, a reasonable scattering performance (i.e. s > 0.6) is obtained from both diffusers at all frequencies in the range 500 Hz–2.5 kHz. It can also be found that the scattering coefficients of the different diffusers with flutters are averagely higher than those without flutters due to their higher surface roughness. Please note that when the surface is rough in comparison to the wavelength of the applied sound waves, diffuse reflection appears and helps enhance the scattering coefficients of the diffusers. For plywood diffusers, the scattering coefficient decreases to 0 as the applied sound frequency is 5 kHz due to their high absorption coefficients at the high frequency (Fig. 9a). Over the low-frequency
77
range, the enhancement of the scattering coefficients of the diffusers with flutters is not apparent because the wavelength is high enough not to be influenced by the roughness of the diffuser surface.
4.4. Effect of installation angle of diffuser top plate To clarify the effect on the scattering coefficient of the angle of the diffuser top plate, a series of experiments was performed using Japanese cedar diffusers with inclination angles of 30° and 45°, respectively. The corresponding results are presented in Fig. 11a and show that the inclination angle of the top plate has only a marginal effect on the scattering performance of the diffuser due to the small roughness difference of the diffuser surface. Fig. 11b illustrates the variation of the scattering coefficient with the sound frequency for Japanese cedar and plywood diffusers fitted with flutters and having an upper plate inclination angle of 45°. A good agreement is observed between the two sets of results over the full frequency range, and thus it is inferred that the diffuser material has only a slight effect on the scattering coefficient when the upper plate is inclined at an angle to the horizontal.
4.5. Effect of diffuser shape Fig. 12a presents the scattering coefficients of Japanese cedar diffusers (with flutters) and triangular or double-triangular top plate profiles over the frequency range 100 Hz–5 kHz. The results show that the double-triangular top plate profile yields an improvement in the scattering performance; particularly at medium and higher values of the sound frequency (i.e. >800 Hz.). Meanwhile, Fig. 12b shows the scattering coefficients of plywood diffusers (without flutters) with triangular or double-triangular top plate profiles. In general, it is observed that for each type of diffuser, the double-triangle profile of the upper plates influences on the value of the scattering coefficient over the frequency range 100 Hz–5 kHz due to the higher roughness caused by double-triangle shapes.
Fig. 13. Comparison of scattering coefficients of Japanese cedar diffusers with flutters and different groove depths.
78
F.-M. Lin et al. / Applied Acoustics 71 (2010) 68–78
4.6. Effect of diffuser groove depth
References
The effect of the diffuser groove depth on the scattering coefficient was evaluated using flat Japanese cedar wood diffusers with flutters. Fig. 13 shows that for a given value of the noise frequency, the scattering coefficient increases with an increasing groove depth due to the higher roughness of the diffuser surface.
[1] Harold Marshall A. Acoustical design and evaluation of Christchurch Town hall. New Zealand. J Acoust Soc Am 1979;65:751–7. [2] Beranek LL. Concert hall acoustics–1992. J Acoust Soc Am 1992;92:1–39. [3] Hargreaves TJ, Cox TJ, Lam YW, D’Antonio P. Diffusion coefficients (A). J Acoust Soc Am 1998;104:1858. [4] Hargreaves TJ, Cox TJ, Lam YW, D’Antonio P. Surface diffusion coefficients for room acoustics: free-field measures. J Acoust Soc Am 2000;108:1710–20. [5] Haan CH, Kwon KW. A method of evaluating surface diffusivity of rooms – I: computer modeling and field measurement. Appl Acoust 2001;62:1313–27. [6] Vorländer M, Mommertz E. Definition and measurement of random-incidence scattering coefficients. Appl Acoust 2000;60:187–99. [7] Quis D. Scattering by a barrier in a room. Appl Acoust 1999;56:1–24. [8] Godinho L, António J, Tadeu A. 3D sound scattering by rigid barriers in the vicinity of tall buildings. Appl Acoust 2001;62:1229–48. [9] Onaga H, Rindel JH. Acoustic characteristics of urban streets in relation to scattering caused by building facades. Appl Acoust 2007;68:310–25. [10] Wang LM, Rathsam J. The influence of absorption factors on the sensitivity of a virtual room’s sound field to scattering coefficients. Appl Acoust 2008;69:1249–57. [11] D’Antonio P, Cox TJ. Two decades of sound diffuser design and development. Part 1: applications and design. J Audio Eng Soc 1998;46:955–76. [12] D’Antonio P, Cox TJ. Two decades of sound diffuser design and development. Part 2: prediction, measurement and characterization. J Audio Eng Soc 1998;46:1075–91. [13] ISO 354. Acoustics – Measurement of sound absorption in a reverberation room; 2003. [14] D’Antonio P, Cox TJ. Diffusor application in rooms. Appl Acoust 2000;60:113–42. [15] Fujiwara K, Nakai K, Torihara H. Visualization of the sound field around a Schroeder diffuser. Appl Acoust 2000;60:225–35. [16] Vorländer M, Embrechts J, Geetere LD, Vermeir G, Gomes MHA. Case studies in measurement of random incidence scattering coefficients. Acta Acust United Acust 2004;90:858–67. [17] Zeng X, Chrestensen CL, Rindel JH. Practical methods to define scattering coefficients in a room acoustics computer model. Appl Acoust 2006;67:771–86. [18] Mommertz E. Determination of scattering coefficients from the reflection directivity of architectural surfaces. Appl Acoust 2000;60:201–3. [19] ISO 17497–1. Acoustics – sound-scattering properties of surfaces – Part 1: measurement of the random-incidence scattering coefficient in a reverberation room; 2004. [20] Jeon JY, Lee SC, Vorländer M. Development of scattering surfaces for concert halls. Appl Acoust 2004;65:341–55.
5. Conclusions This study has conducted an experimental investigation into the scattering performance of wooden diffusers fabricated from various materials (i.e. Japanese cedar, MDF or plywood), and having various upper plate profiles (i.e. flat, single-triangular or doubletriangular), baffle features (i.e. with or without flutters) and groove depths (i.e. 4 cm, 6 cm or 8 cm). The results have shown that the reliability of the measurement results obtained using the ISO 17497-1 standard can be improved by placing the sample within the turntable rather than on its upper surface such that the edge effect is reduced. In addition, the experimental results have shown that the sound-scattering coefficient can be improved by fitting the diffuser structure with flutters, designing the top plate with a double-triangular profile, and increasing the groove depth. Overall, the experimental results presented in this study provide designers with a useful source of reference for predicting the sound-scattering performance of wooden diffusers with various geometrical structures in indoor environments. Acknowledgements The authors gratefully acknowledge the financial support provided to this study by the National Science Council of Taiwan under Grant numbers NSC 97-2221-E-020-028, NSC 97-2218-E-006-012 and NSC 96-2218-E-006-004. The contributions of Prof. Che-Ming Chiang and Prof. Rong-Ping Lai are also acknowledged.