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Comments on “Reverberation time in an almost-two-dimensional diffuse field” [J. Sound Vib., 111, 391–398, 1986]
Journal of Sound and Vibration 333 (2014) 2995–2998
Contents lists available at ScienceDirect
Journal of Sound and Vibration journal homepage: www.elsevier.com/locate/jsvi
Discussion
Comments on “Reverberation time in an almost-two-dimensional diffuse field” [J. Sound Vib., 111, 391–398, 1986] P. Jafari Shalkouhi n Department of Environmental Engineering, Graduate School of the Environment and Energy, Science and Research Branch, Islamic Azad University, Tehran, Iran
a r t i c l e i n f o Article history: Received 29 November 2013 Received in revised form 12 January 2014 Accepted 10 February 2014 Handling Editor: M.P. Cartmell Available online 12 March 2014
1. Introduction As Tohyama and Suzuki [1] have correctly noted, it is difficult to propose a three-dimensional equation in order to predict accurately the reverberation time of a room in which the floor and ceiling are covered by absorbant materials, while the walls are acoustically hard. This condition is known as a non-diffuse sound field among acousticians. Hence, for this situation, Tohyama and Suzuki [1] proposed a two-dimensional diffuse field formula for calculation of reverberation time as follows: T 60 ¼
0:128S L lnð1 αxy Þ
(1)
where T60 is the reverberation time (s), L is the total length of the two-dimensional space (m), αxy is the average absorption coefficient in the xy-two-dimensional field and S is the surface area of the room (m2).
2. Discussion The height dimension is not included in Eq. (1) proposed by Tohyama and Suzuki. Fig. 1 shows two rooms with the same width, length and average absorption coefficient of the surfaces but with different ceiling heights. In practice the room with the pyramid ceiling (the left hand side room) has a greater reverberation time than the room with the flat ceiling (the right hand side room). While according to the Tohyama and Suzuki equation the reverberation time of the two rooms is equal. In addition, Fig. 2 shows two rooms with the same width, length and height but with different average absorption coefficients of the surfaces. In practice the typical room (the left hand side room) has a greater reverberation time than the n
Tel.: þ 98 9354296468. E-mail address: [email protected]
http://dx.doi.org/10.1016/j.jsv.2014.02.015 0022-460X & 2014 Elsevier Ltd. All rights reserved.
2996
P.J. Shalkouhi / Journal of Sound and Vibration 333 (2014) 2995–2998
Fig. 1. The Tohyama and Suzuki reverberation time in rooms of different ceiling geometries.
Fig. 2. The Tohyama and Suzuki reverberation time in rooms of different average absorption coefficients of surfaces.
roofless room (the right hand side room). While according to the Tohyama and Suzuki equation the reverberation time of the two rooms is equal. In contrast, Coley [2] used the Sabine equation [3] to indicate that increasing the height of a space will not increase the reverberation time provided that the average absorption coefficient of the additional walls is greater than twice the average absorption coefficient of the former room. In addition Coley concluded that in practice the height of the original wall is likely to be greater than 3 m, the average absorption coefficient of the original space of less than 0.3 and the space is not square. The reverberation time equation proposed by Sabine is RT ¼ 0:16
V αA
(2)
where V is the room volume (m3), A is the total surface area of the room (m2), α is the average absorption coefficient of the surfaces and RT is the reverberation time (s) [3].
P.J. Shalkouhi / Journal of Sound and Vibration 333 (2014) 2995–2998
2997
If V1, A1 and α1 are the volume, total surface area and average absorption coefficient of the original space, respectively, then increasing the ceiling height gives the additional V2, A2 and α2. Therefore, the reverberation time of the new space will be [2] RTnew ¼
0:16ðV 1 þ V 2 Þ α1 A1 þ α2 A2
(3)
Moreover, in order to achieve the necessary guideline the reverberation time of the new space must not be greater than the reverberation time of the original space [2]: RT Z RTnew
(4)
0:16V 1 0:16ðV 1 þV 2 Þ Z α1 A1 þ α2 A2 α1 A1
(5)
0:16h1 lw 0:16ðh1 lw þ h2 lwÞ Z α1 ð2ðl þ wÞh1 þ 2lwÞ α1 ð2ðl þ wÞh1 þ2lwÞ þ 2h2 α2 ðl þ wÞ
(6)
α2 4 2α1
(7)
Therefore we will have
Expanding the equation as follows:
Finally, Coley [2] found that if
Then the reverberation time of the new space will not increase. Therefore, according to Coley's finding it can be stated that when the ceiling geometry of a typical space is changed to any type of geometry, provided that the volume of the new space is not equal to the volume of the old room then the reverberation time of the new space based on the Tohyama and Suzuki equation is reliable if the average absorption coefficient of the additional walls is greater than twice the average absorption coefficient of the original room [2]. Furthermore, Hodgson [4] proposed a two-dimensional formula for calculation of room reverberation time, as EDTu ¼ 1:4395 þ 0:0024LW 5:0589α1 kHz þ 0:1632refl 0:1973absdist þ0:2981basic
(8)
where EDT is the room early decay time (s), the subscript “u” represents the unoccupied room, L and W are the average length and width of the room in m, respectively, LW is the floor area (m2), α1 kHz is the average 1 kHz absorption coefficient, ‘refl’ and ‘absdist’ represent the eventual benefit from reflecting surfaces and from absorption distributions, respectively (1 if present, 0 if absent), and “basic” represents the absence of sound absorbing features (1 if absent, 0 if present). Shalkouhi [5] reported that when a room ceiling height is decreased or increased, the Hodgson equation is not a reliable method for prediction of the reverberation time of the new space if the average absorption coefficient of the additional walls is equal to the average absorption coefficient of the previous room. The Hodgson equation considers the average absorption coefficient of the whole space while the Tohyama and Suzuki formula considers the average absorption coefficient in the xy-two-dimensional field. Hence, it can be stated that the major difference between the Hodgson formula and the Tohyama and Suzuki equation is that unlike the Tohyama and Suzuki formula, the Hodgson equation can predict the reverberation time of a room when it is changed to a roofless room, and vice versa. Moreover, the ceiling of a space can play an important role in the reverberation time. For example Knecht et al. [6] reported that reducing the ceiling height of a classroom to the level of 10 ft or less will be useful in achieving acceptable reverberation time. Also, Zannin and Marcon [7] results revealed that the application of perforated plywood for the classroom ceiling can considerably reduce the reverberation time. 3. Conclusions Therefore, when the ceiling geometry of a typical room is changed to any type of geometry, the reverberation time of the new space cannot be computed based on the Tohyama and Suzuki equation provided that the volume of the new space is not equal to the volume of the old room. Moreover, if a typical room is changed to a roofless room, and vice versa, the reverberation time of the new space cannot be predicted by the Tohyama and Suzuki equation. Hence, to cover all possible practical cases of interest with regard to prediction of reverberation time the two following variables must be added to the Tohyama and Suzuki equation:
The dimension “height” as a predictor variable must be included in the Tohyama and Suzuki equation. The average absorption coefficient of the whole space must be embodied in the Tohyama and Suzuki equation. Nevertheless, by considering the above variables one will achieve the Eyring reverberation time formula [8] which is based on the assumption of a diffuse sound field. Therefore, when the ceiling geometry of a typical room with a non-homogeneous distribution of absorbant materials is changed to any type of geometry, it is recommended to measure the reverberation time of the new space instead of using
2998
P.J. Shalkouhi / Journal of Sound and Vibration 333 (2014) 2995–2998
the Tohyama and Suzuki equation provided that the volume of the new space is not equal to the volume of the former room. Moreover, if a typical room with a non-homogeneous distribution of absorbant materials is changed to a roofless room, and vice versa, it is recommended to measure the reverberation time of the new space instead of using the Tohyama and Suzuki equation. References [1] [2] [3] [4] [5] [6]
M. Tohyama, A. Suzuki, Reverberation time in an almost-two-dimensional diffuse field, Journal of Sound and Vibration 111 (1986) 391–398. D.A. Coley, The reverberation time of tall spaces, Journal of Sound and Vibration 254 (2002) 595–598. W.C. Sabine, Collected Papers on Acoustics, Harvard University Press, 1922 (Reprinted by Dover Publications, New York, 1964). M. Hodgson, Empirical prediction of speech levels and reverberation in classrooms, Building Acoustics 8 (2001) 1–14. P.J. Shalkouhi, Comments on “Empirical prediction of speech levels and reverberation in classrooms”, Building Acoustics 19 (2012) 139–144. H.A. Knecht, P.B. Nelson, G.M. Whitelaw, L.L. Feth, Background noise levels and reverberation times in unoccupied classrooms: predictions and measurements, American Journal of Audiology 11 (2002) 65–71. [7] P.H.T. Zannin, C.R. Marcon, Objective and subjective evaluation of the acoustic comfort in classrooms, Applied Ergonomics 38 (2007) 675–680. [8] C.F. Eyring, Reverberation time in “dead” rooms, Journal of the Acoustical Society of America 1 (1930) 217–241.
Contents lists available at ScienceDirect
Journal of Sound and Vibration journal homepage: www.elsevier.com/locate/jsvi
Discussion
Comments on “Reverberation time in an almost-two-dimensional diffuse field” [J. Sound Vib., 111, 391–398, 1986] P. Jafari Shalkouhi n Department of Environmental Engineering, Graduate School of the Environment and Energy, Science and Research Branch, Islamic Azad University, Tehran, Iran
a r t i c l e i n f o Article history: Received 29 November 2013 Received in revised form 12 January 2014 Accepted 10 February 2014 Handling Editor: M.P. Cartmell Available online 12 March 2014
1. Introduction As Tohyama and Suzuki [1] have correctly noted, it is difficult to propose a three-dimensional equation in order to predict accurately the reverberation time of a room in which the floor and ceiling are covered by absorbant materials, while the walls are acoustically hard. This condition is known as a non-diffuse sound field among acousticians. Hence, for this situation, Tohyama and Suzuki [1] proposed a two-dimensional diffuse field formula for calculation of reverberation time as follows: T 60 ¼
0:128S L lnð1 αxy Þ
(1)
where T60 is the reverberation time (s), L is the total length of the two-dimensional space (m), αxy is the average absorption coefficient in the xy-two-dimensional field and S is the surface area of the room (m2).
2. Discussion The height dimension is not included in Eq. (1) proposed by Tohyama and Suzuki. Fig. 1 shows two rooms with the same width, length and average absorption coefficient of the surfaces but with different ceiling heights. In practice the room with the pyramid ceiling (the left hand side room) has a greater reverberation time than the room with the flat ceiling (the right hand side room). While according to the Tohyama and Suzuki equation the reverberation time of the two rooms is equal. In addition, Fig. 2 shows two rooms with the same width, length and height but with different average absorption coefficients of the surfaces. In practice the typical room (the left hand side room) has a greater reverberation time than the n
Tel.: þ 98 9354296468. E-mail address: [email protected]
http://dx.doi.org/10.1016/j.jsv.2014.02.015 0022-460X & 2014 Elsevier Ltd. All rights reserved.
2996
P.J. Shalkouhi / Journal of Sound and Vibration 333 (2014) 2995–2998
Fig. 1. The Tohyama and Suzuki reverberation time in rooms of different ceiling geometries.
Fig. 2. The Tohyama and Suzuki reverberation time in rooms of different average absorption coefficients of surfaces.
roofless room (the right hand side room). While according to the Tohyama and Suzuki equation the reverberation time of the two rooms is equal. In contrast, Coley [2] used the Sabine equation [3] to indicate that increasing the height of a space will not increase the reverberation time provided that the average absorption coefficient of the additional walls is greater than twice the average absorption coefficient of the former room. In addition Coley concluded that in practice the height of the original wall is likely to be greater than 3 m, the average absorption coefficient of the original space of less than 0.3 and the space is not square. The reverberation time equation proposed by Sabine is RT ¼ 0:16
V αA
(2)
where V is the room volume (m3), A is the total surface area of the room (m2), α is the average absorption coefficient of the surfaces and RT is the reverberation time (s) [3].
P.J. Shalkouhi / Journal of Sound and Vibration 333 (2014) 2995–2998
2997
If V1, A1 and α1 are the volume, total surface area and average absorption coefficient of the original space, respectively, then increasing the ceiling height gives the additional V2, A2 and α2. Therefore, the reverberation time of the new space will be [2] RTnew ¼
0:16ðV 1 þ V 2 Þ α1 A1 þ α2 A2
(3)
Moreover, in order to achieve the necessary guideline the reverberation time of the new space must not be greater than the reverberation time of the original space [2]: RT Z RTnew
(4)
0:16V 1 0:16ðV 1 þV 2 Þ Z α1 A1 þ α2 A2 α1 A1
(5)
0:16h1 lw 0:16ðh1 lw þ h2 lwÞ Z α1 ð2ðl þ wÞh1 þ 2lwÞ α1 ð2ðl þ wÞh1 þ2lwÞ þ 2h2 α2 ðl þ wÞ
(6)
α2 4 2α1
(7)
Therefore we will have
Expanding the equation as follows:
Finally, Coley [2] found that if
Then the reverberation time of the new space will not increase. Therefore, according to Coley's finding it can be stated that when the ceiling geometry of a typical space is changed to any type of geometry, provided that the volume of the new space is not equal to the volume of the old room then the reverberation time of the new space based on the Tohyama and Suzuki equation is reliable if the average absorption coefficient of the additional walls is greater than twice the average absorption coefficient of the original room [2]. Furthermore, Hodgson [4] proposed a two-dimensional formula for calculation of room reverberation time, as EDTu ¼ 1:4395 þ 0:0024LW 5:0589α1 kHz þ 0:1632refl 0:1973absdist þ0:2981basic
(8)
where EDT is the room early decay time (s), the subscript “u” represents the unoccupied room, L and W are the average length and width of the room in m, respectively, LW is the floor area (m2), α1 kHz is the average 1 kHz absorption coefficient, ‘refl’ and ‘absdist’ represent the eventual benefit from reflecting surfaces and from absorption distributions, respectively (1 if present, 0 if absent), and “basic” represents the absence of sound absorbing features (1 if absent, 0 if present). Shalkouhi [5] reported that when a room ceiling height is decreased or increased, the Hodgson equation is not a reliable method for prediction of the reverberation time of the new space if the average absorption coefficient of the additional walls is equal to the average absorption coefficient of the previous room. The Hodgson equation considers the average absorption coefficient of the whole space while the Tohyama and Suzuki formula considers the average absorption coefficient in the xy-two-dimensional field. Hence, it can be stated that the major difference between the Hodgson formula and the Tohyama and Suzuki equation is that unlike the Tohyama and Suzuki formula, the Hodgson equation can predict the reverberation time of a room when it is changed to a roofless room, and vice versa. Moreover, the ceiling of a space can play an important role in the reverberation time. For example Knecht et al. [6] reported that reducing the ceiling height of a classroom to the level of 10 ft or less will be useful in achieving acceptable reverberation time. Also, Zannin and Marcon [7] results revealed that the application of perforated plywood for the classroom ceiling can considerably reduce the reverberation time. 3. Conclusions Therefore, when the ceiling geometry of a typical room is changed to any type of geometry, the reverberation time of the new space cannot be computed based on the Tohyama and Suzuki equation provided that the volume of the new space is not equal to the volume of the old room. Moreover, if a typical room is changed to a roofless room, and vice versa, the reverberation time of the new space cannot be predicted by the Tohyama and Suzuki equation. Hence, to cover all possible practical cases of interest with regard to prediction of reverberation time the two following variables must be added to the Tohyama and Suzuki equation:
The dimension “height” as a predictor variable must be included in the Tohyama and Suzuki equation. The average absorption coefficient of the whole space must be embodied in the Tohyama and Suzuki equation. Nevertheless, by considering the above variables one will achieve the Eyring reverberation time formula [8] which is based on the assumption of a diffuse sound field. Therefore, when the ceiling geometry of a typical room with a non-homogeneous distribution of absorbant materials is changed to any type of geometry, it is recommended to measure the reverberation time of the new space instead of using
2998
P.J. Shalkouhi / Journal of Sound and Vibration 333 (2014) 2995–2998
the Tohyama and Suzuki equation provided that the volume of the new space is not equal to the volume of the former room. Moreover, if a typical room with a non-homogeneous distribution of absorbant materials is changed to a roofless room, and vice versa, it is recommended to measure the reverberation time of the new space instead of using the Tohyama and Suzuki equation. References [1] [2] [3] [4] [5] [6]
M. Tohyama, A. Suzuki, Reverberation time in an almost-two-dimensional diffuse field, Journal of Sound and Vibration 111 (1986) 391–398. D.A. Coley, The reverberation time of tall spaces, Journal of Sound and Vibration 254 (2002) 595–598. W.C. Sabine, Collected Papers on Acoustics, Harvard University Press, 1922 (Reprinted by Dover Publications, New York, 1964). M. Hodgson, Empirical prediction of speech levels and reverberation in classrooms, Building Acoustics 8 (2001) 1–14. P.J. Shalkouhi, Comments on “Empirical prediction of speech levels and reverberation in classrooms”, Building Acoustics 19 (2012) 139–144. H.A. Knecht, P.B. Nelson, G.M. Whitelaw, L.L. Feth, Background noise levels and reverberation times in unoccupied classrooms: predictions and measurements, American Journal of Audiology 11 (2002) 65–71. [7] P.H.T. Zannin, C.R. Marcon, Objective and subjective evaluation of the acoustic comfort in classrooms, Applied Ergonomics 38 (2007) 675–680. [8] C.F. Eyring, Reverberation time in “dead” rooms, Journal of the Acoustical Society of America 1 (1930) 217–241.