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.
Issue Section:
Research Papers
Keywords:
Modal analysis
Topics:
Absorption,
Acoustics,
Computer simulation,
Damping,
Excitation,
Fluctuations (Physics),
Impulse (Physics),
Modal analysis,
Modeling,
Numerical analysis,
Potential energy,
Pressure,
Signals,
Sound pressure,
Sound absorption,
Steady state,
Architectural acoustics,
Density,
Eigenfunctions,
Shapes,
Sound reverberation,
Simulation,
Simulation results
References
1.
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
.10.1250/ast.26.1702.
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
.10.1115/1.40238353.
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
.10.1260/1351010037689659884.
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
.10.1121/1.31923465.
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
.10.1006/jsvi.1997.12196.
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
.10.1121/1.31589347.
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
.10.1121/1.17639748.
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
.10.1121/1.47345919.
Schroeder
, M.
, 1996
, “The ‘Schroeder Frequency’ Revisited
,” J. Acoust. Soc. Am.
, 99
(5
), pp. 3240
–3241
.10.1121/1.41486810.
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
.10.1121/1.316850711.
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
.10.1121/1.487070612.
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
.10.1121/1.200077213.
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
.10.1121/1.293636714.
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
.10.1121/1.235771815.
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
.16.
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
.17.
Welti
, T.
, and Devantier
, A.
, 2006
, “Low-Frequency Optimization Using Multiple Subwoofers
,” J. Audio Eng. Soc.
, 54
(5
), pp. 347
–364
.18.
Bradley
, D.
, and Wang
, L.
, 2009
, “Quantifying the Double Slope Effect in Coupled Volume Room Systems
,” Build. Acoust.
, 16
(1
), pp. 105
–123
.10.1260/13510100978891327519.
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
.10.1121/1.351877320.
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
.10.1121/1.326860421.
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
.22.
Meissner
, M.
, 2009
, “Spectral Characteristics and Localization of Modes in Acoustically Coupled Enclosures
,” Acta Acust. Acust.
, 95
(2
), pp. 300
–305
.10.3813/AAA.91815223.
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
.10.2478/s11534-007-0016-724.
Kuttruff
, H.
, 2009
, Room Acoustics
, 5th ed., Spon Press
, Abingdon, UK
, pp. 94
–96
.25.
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
.10.1016/j.apacoust.2007.02.00426.
Meissner
, M.
, 2013
, “Acoustic Behaviour of Lightly Damped Rooms
,” Acta Acust. Acust.
, 99
(5
), pp. 845
–847
.10.3813/AAA.91866327.
Hahn
, S.
, 1996
, The Hilbert Transforms in Signal Processing
, Artech House
, Boston, MA
, pp. 3
–54
.28.
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
.29.
Draper
, N.
, and Smith
, H.
, 1998
, Applied Regression Analysis
, 3rd ed., Wiley
, New York
, pp. 461
–472
.30.
Schroeder
, M.
, 1965
, “New Method of Measuring Reverberation Time
,” J. Acoust. Soc. Am.
, 37
(3
), pp. 409
–412
.10.1121/1.190934331.
Nakayama
, T.
, and Yakubo
, K.
, 2001
, “The Forced Oscillator Method: Eigenvalue Analysis and Computing Linear Response Functions
,” Phys. Rep.
, 349
(3
), pp. 239
–299
.10.1016/S0370-1573(00)00115-032.
Botteldooren
, D.
, 1995
, “Finite-Difference Time-Domain Simulation of Low-Frequency Room Acoustic Problems
,” J. Acoust. Soc. Am.
, 98
(6
), pp. 3302
–3308
.10.1121/1.413817Copyright © 2015 by ASME
You do not currently have access to this content.
