0
Research Papers

Theoretical and Numerical Determination of Low-Frequency Reverberant Characteristics of Coupled Rooms

[+] Author and Article Information
Mirosław Meissner

Institute of Fundamental Technological Research,
Polish Academy of Sciences,
Pawińskiego 5B,
Warsaw 02-106, Poland
e-mail: mmeissn@ippt.pan.pl

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 6, 2014; final manuscript received February 18, 2015; published online April 15, 2015. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 137(4), 041013 (Aug 01, 2015) (9 pages) Paper No: VIB-14-1289; doi: 10.1115/1.4029991 History: Received August 06, 2014; Revised February 18, 2015; Online April 15, 2015

The main aim of room acoustics is to predict reverberant properties of enclosures from measured or numerically simulated room responses. In this paper, this issue was examined in low-frequency range where acoustic characteristics of rooms are strongly frequency dependent due to differences in a modal damping. A theoretical description of a decaying sound field was based on a modal expansion of the sound pressure, and a reverberant response of the room was initiated by emission of Dirac delta time impulse or by switching off a time-harmonic source. Theoretical findings were employed to determine reverberant characteristics of a coupled-room system containing two connected rectangular subrooms. Simulation results have shown that a sound decay after steady-state harmonic excitation is strongly influenced by the sound frequency and due to large fluctuations in a decaying pressure; numerical techniques for smoothing decay curves are needed. Calculations also revealed that in some one-third octave bands, the decay function found via backward integration of squared room impulse response (RIR) changes very irregularly impeding a proper qualifying of nature of sound decay.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bradley, J., 2005, “Using ISO 3382 Measures, and Their Extensions, to Evaluate Acoustical Conditions in Concert Halls,” Acoust. Sci. Technol., 26(2), pp. 170–178. [CrossRef]
Cerdá, S., Giménez, A., Montell, R., Barba, A., Lacatis, R., Segura, J., and Cibrián, R., 2013, “On the Relations Between Audio Features and Room Acoustic Parameters of Auralizations,” ASME J. Vib. Acoust., 135(6), p. 064501. [CrossRef]
Magrini, A., and Ricciardi, P., 2003, “Churches as Auditoria: Analysis of Acoustical Parameters for a Better Understanding of Sound Quality,” Build. Acoust., 10(2), pp. 135–157. [CrossRef]
Martellotta, F., 2009, “Identifying Acoustical Coupling by Measurements and Prediction-Models for St. Peter's Basilica in Rome,” J. Acoust. Soc. Am., 126(3), pp. 1175–1185. [CrossRef] [PubMed]
Anderson, J., Bratos-Anderson, M., and Doany, P., 1997, “The Acoustics of a Large Space With a Repetitive Pattern of Coupled Rooms,” J. Sound Vib., 208(2), pp. 313–329. [CrossRef]
Jasa, T., and Xiang, N., 2009, “Efficient Estimation of Decay Parameters in Acoustically Coupled-Spaces Using Slice Sampling,” J. Acoust. Soc. Am., 126(3), pp. 1269–1279. [CrossRef] [PubMed]
Summers, J., Torres, R., and Shimizu, Y., 2004, “Statistical-Acoustics Models of Energy Decay in Systems of Coupled Rooms and Their Relation to Geometrical Acoustics,” J. Acoust. Soc. Am., 116(2), pp. 958–969. [CrossRef] [PubMed]
Summers, J., 2012, “Accounting for Delay of Energy Transfer Between Coupled Rooms in Statistical-Acoustics Models of Reverberant-Energy Decay,” J. Acoust. Soc. Am., 132(2), pp. EL129–EL134. [CrossRef] [PubMed]
Schroeder, M., 1996, “The ‘Schroeder Frequency’ Revisited,” J. Acoust. Soc. Am., 99(5), pp. 3240–3241. [CrossRef]
Xiang, N., Yun Jing, Y., and Bockman, A., 2009, “Investigation of Acoustically Coupled Enclosures Using a Diffusion-Equation Model,” J. Acoust. Soc. Am., 126(3), pp. 1187–1198. [CrossRef] [PubMed]
Luizard, P., Polack, J.-P., and Katz, B., 2014, “Sound Energy Decay in Coupled Spaces Using a Parametric Analytical Solution of a Diffusion Equation,” J. Acoust. Soc. Am., 135(5), pp. 2765–2776. [CrossRef] [PubMed]
Summers, J., Torres, R., Shimizu, Y., and Dalenbäk, B., 2005, “Adapting a Randomized Beam-Axis-Tracing Algorithm to Modeling of Coupled Rooms Via Late-Part Ray Tracing,” J. Acoust. Soc. Am., 118(3), pp. 1491–1502. [CrossRef]
Lehmann, E., and Johansson, A., 2008, “Prediction of Energy Decay in Room Impulse Responses Simulated With an Image-Source Model,” J. Acoust. Soc. Am., 124(1), pp. 269–277. [CrossRef] [PubMed]
Sum, K., and Pan, J., 2006, “Geometrical Perturbation of an Inclined Wall on Decay Times of Acoustic Modes in a Trapezoidal Cavity With an Impedance Surface,” J. Acoust. Soc. Am., 120(6), pp. 3730–3743. [CrossRef] [PubMed]
Meissner, M., 2010, “Simulation of Acoustical Properties of Coupled Rooms Using Numerical Technique Based on Modal Expansion,” Acta Phys. Pol., A, 118(1), pp. 123–127.
Fazenda, B., Wankling, M., Hargreaves, J., Elmer, L., and Hirst, J., 2012, “Subjective Preference of Modal Control Methods in Listening Rooms,” J. Audio Eng. Soc., 60(5), pp. 338–349.
Welti, T., and Devantier, A., 2006, “Low-Frequency Optimization Using Multiple Subwoofers,” J. Audio Eng. Soc., 54(5), pp. 347–364.
Bradley, D., and Wang, L., 2009, “Quantifying the Double Slope Effect in Coupled Volume Room Systems,” Build. Acoust., 16(1), pp. 105–123. [CrossRef]
Xiang, N., Goggans, P., Jasa, T., and Robinson, P., 2011, “Bayesian Characterization of Multiple-Slope Sound Energy Decays in Coupled-Volume Systems,” J. Acoust. Soc. Am., 129(2), pp. 741–752. [CrossRef] [PubMed]
Bradley, D., and Wang, L., 2010, “Optimum Absorption and Aperture Parameters for Realistic Coupled Volume Spaces Determined From Computational Analysis and Subjective Testing Results,” J. Acoust. Soc. Am., 127(1), pp. 223–232. [CrossRef] [PubMed]
Meissner, M., 2009, “Computer Modelling of Coupled Spaces: Variations of Eigenmodes Frequency Due to a Change in Coupling Area,” Arch. Acoust., 34(2), pp. 157–168.
Meissner, M., 2009, “Spectral Characteristics and Localization of Modes in Acoustically Coupled Enclosures,” Acta Acust. Acust., 95(2), pp. 300–305. [CrossRef]
Meissner, M., 2007, “Computational Studies of Steady-State Sound Field and Reverberant Sound Decay in a System of Two Coupled Rooms,” Cent. Eur. J. Phys., 5(3), pp. 293–312. [CrossRef]
Kuttruff, H., 2009, Room Acoustics, 5th ed., Spon Press, Abingdon, UK, pp. 94–96.
Meissner, M., 2008, “Influence of Wall Absorption on Low-Frequency Dependence of Reverberation Time in Room of Irregular Shape,” Appl. Acoust., 69(7), pp. 583–590. [CrossRef]
Meissner, M., 2013, “Acoustic Behaviour of Lightly Damped Rooms,” Acta Acust. Acust., 99(5), pp. 845–847. [CrossRef]
Hahn, S., 1996, The Hilbert Transforms in Signal Processing, Artech House, Boston, MA, pp. 3–54.
Meissner, M., 2009, “Application of Hilbert Transform-Based Methodology to Computer Modelling of Reverberant Sound Decay in Irregularly Shaped Rooms,” Arch. Acoust., 34(4), pp. 491–505.
Draper, N., and Smith, H., 1998, Applied Regression Analysis, 3rd ed., Wiley, New York, pp. 461–472.
Schroeder, M., 1965, “New Method of Measuring Reverberation Time,” J. Acoust. Soc. Am., 37(3), pp. 409–412. [CrossRef]
Nakayama, T., and Yakubo, K., 2001, “The Forced Oscillator Method: Eigenvalue Analysis and Computing Linear Response Functions,” Phys. Rep., 349(3), pp. 239–299. [CrossRef]
Botteldooren, D., 1995, “Finite-Difference Time-Domain Simulation of Low-Frequency Room Acoustic Problems,” J. Acoust. Soc. Am., 98(6), pp. 3302–3308. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Analyzed coupled-room system consisting of two connected rectangular subrooms denoted by A and B. Points indicate positions of the source and the receiver.

Grahic Jump Location
Fig. 2

Sound pressure decay simulated in the observation point for absorbing material distributions: (a)–(c) α1 = α2 = 0.15 and (d)–(f) α1 = 0.05, α2 = 0.3, and source frequencies: (a) and (d) 55 Hz, (b) and (e) 75 Hz, and (c) and (f) 100 Hz

Grahic Jump Location
Fig. 3

Decay functions L(t) and Lav(t) determined on the basis of simulation data in Fig. 2. Absorbing material distributions: (a)–(c) α1 = α2 = 0.15 and (d)–(f) α1 = 0.05, α2 = 0.3. Source frequencies: (a) and (d) 55 Hz, (b) and (e) 75 Hz, and (c) and (f) 100 Hz.

Grahic Jump Location
Fig. 4

Decay times EDT, T10, T15, T20, T30, and LDT determined from a decrease in the decay function Lav(t) and the ratio LDT/T10. Absorbing material distributions: (a)–(c) α1 = α2 = 0.15 and (d)–(f) α1 = 0.05, α2 = 0.3. Source frequencies: (a) and (d) 55 Hz, (b) and (e) 75 Hz, and (c) and (f) 100 Hz.

Grahic Jump Location
Fig. 5

Decay times EDT, T10, T15, T20, T30, and LDT determined from a decrease in the energy level L¯ and the ratio LDT/T10. Absorbing material distributions: (a)–(c) α1 = α2 = 0.15 and (d)–(f) α1 = 0.05, α2 = 0.3. Source frequencies: (a) and (d) 55 Hz, (b) and (e) 75 Hz, and (c) and (f) 100 Hz.

Grahic Jump Location
Fig. 6

Decay times T10 (solid lines) and LDT (dashed lines) determined from a decrease in the energy level L¯ versus the source frequency f for absorbing material distributions: (a) α1 = α2 = 0.15 and (b) α1 = 0.05, α2 = 0.3

Grahic Jump Location
Fig. 7

Decay function Ls(t) and corresponding decay times EDT, T10, T15, T20, T30, LDT and the ratio LDT/T10 for absorbing material distributions: (a) and (b) α1 = α2 = 0.15; (c) and (d) α1 = 0.05, α2 = 0.3

Grahic Jump Location
Fig. 8

Decay function Ls(t) for one-third octave bands with the center frequency from 31.5 Hz to 160 Hz. Uniform distribution of absorbing material: α1 = α2 = 0.15.

Grahic Jump Location
Fig. 9

Decay times EDT, T10, T15, T20, T30, LDT and the ratio LDT/T10 for one-third octave bands with the center frequency: (a) 31.5 Hz, (b) 40 Hz, (c) 50 Hz, (d) 63 Hz, (e) 80 Hz, (f) 100 Hz, (g) 125 Hz, and (h) 160 Hz. Uniform distribution of absorbing material: α1 = α2 = 0.15.

Grahic Jump Location
Fig. 10

Decay function Ls(t) for one-third octave bands with the center frequency from 31.5 Hz to 160 Hz. Nonuniform distribution of absorbing material: α1 = 0.05, α2 = 0.3.

Grahic Jump Location
Fig. 11

Decay times EDT, T10, T15, T20, T30, LDT and the ratio LDT/T10 for one-third octave bands with the center frequency: (a) 31.5 Hz, (b) 40 Hz, (c) 50 Hz, (d) 63 Hz, (e) 80 Hz, (f) 100 Hz, (g) 125 Hz, and (h) 160 Hz. Nonuniform distribution of absorbing material: α1 = 0.05, α2 = 0.3.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In