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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.

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Figures

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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.

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