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Nov 1988

Volume 84, Issue S1, pp. S2-S224

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back to top Session V. Architectural Acoustics IV: Reverberant Sound Fields in Rooms
Contributed Papers
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Sound power determination in reverberation chambers (A)

Dah‐You Maa

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S64-S64 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The determination of sound power in reverberation chambers is discussed in the light of normal mode theory. It is known that the sound power emission of a source depends on its position in the reverberation chamber and on interference pattern results in the sound field excited. As a consequence, the measured sound pressure varies widely from point to point. It is shown that the sound pressure is proportional to the average contribution of the product of the normal functions at the source and at the receiver. Based on this relation, the determination of sound power emitted by the source at a particular point in the room is devised through the measurements of average sound field as well as by a corner microphone. It is also shown that sound power determined in reverberation chambers by the standard method is always less than the free‐field power, and the difference increases as the frequency decreases. This is just what happens in practice, and good agreement with the theory is obtained with earlier experiments. A statistical formula of the sound pressure in a reverberation chamber developed from the exact theory is used to this end.
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Steady‐state acoustic energy distribution in a reverberation chamber at low frequencies (A)

Daniel R. Flynn, Thomas W. Bartel, and Simone L. Yaniv

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S64-S64 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The spatial variation of the mean‐square sound pressure in a hard‐walled rectilinear reverberation chamber is analyzed by extending the “Waterhouse theory” (based on a free‐wave model for an omnidirectional sound field impinging on the corner formed by three orthogonal planes) to apply to a closed chamber at low frequencies. This is done by expressing the mean‐square sound pressure in terms of the contributions from the actual pressure microphone and from an infinite array of image microphones due to multiple reflections in the chamber walls, and then transforming this expression into a weighted sum of the normal eigenfunctions for the chamber. Experimental sound‐pressure levels, measured along different linear paths in the 425‐m3 NBS reverberation chamber, are compared with the predictions of this analysis. It is found that the spatial dependence of sound‐pressure level is accurately predictable, at least in the NBS chamber, to significantly lower frequencies than has usually been thought possible. Expressions are given for relating the spatial average (over the volume of the chamber) mean‐square sound pressure to that which is measured at a given position in the room. The implications of these findings to sound power determinations are discussed.
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Kinetic and potential energies of a stationary sound field (A)

Richard K. Cook

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S64-S64 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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There is a continuing need for accurate measurement of radiated sound power by compact noisy sources. Examples are the noises of fans, motors, machinery, etc. One of the standard methods of measurement makes use of a reverberation chamber. The potential energy of the sound radiated into the chamber is measured by sampling the sound pressure at various points, from which the time‐space‐averaged potential energy is calculated. The kinetic energy is assumed to equal the potential energy; then in the standard method, the sum of the two is used as the total energy for calculation of the radiated sound power. In experiments on a source having an accurately known radiated power, we found that the power determined in a standard‐method chamber was about 20% (0.9 dB) less than the true power. A likely source of the systematic difference is the possibly false assumption that the time‐space averaged kinetic energy is equal to the potential energy. It is shown that, in general, in a sound field stationary in an enclosure, the two energies are not equal. Several examples are presented. Included are fields in enclosures having sound absorbers. An accurate ratio of the energies requires detailed knowledge of the field.
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Impulse response and reverberation time measurements using a periodic pseudorandom sequence (A)

W. T. Chu

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S64-S64 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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The cross‐correlation method using a periodic pseudorandom sequence or M sequence for impulse response and reverberation time measurements proposed by Schroeder and his colleagues [H. Alrutz and M. R. Schroeder, Proc. 11th Congr. Acoust., Paris (1983)] represents a very significant contribution to the fields of Architectural Acoustics and Noise Control. With this technique, it is not only possible to make measurements in auditoria or offices without disturbing the audience or the occupants, but also in factories or construction sites without closing down their operations. Implementation of this method requires special signal processing techniques which will be reviewed in this presentation. Examples of measurements in simulated noisy environments will also be presented.
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Analysis of sound fields in rooms by Bergeron's method (A)

Hidemaro Shimoda, Norinobu Yoshida, and Ichiro Fukai

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S64-S65 (1988); (2 pages)

Online Publication Date: 13 Aug 2005

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The behavior of sound wave motion in rooms is so complicated that it is not easy to treat it theoretically unless simple geometrical shapes or simple boundary conditions are assumed. This study presents a formulation applying Bergeron's method, developed for an electromagnetic field simulation by computer [N. Yoshida et al., Trans. IECE Japan, J62‐B, 6, 511–518 (1979)], to room acoustics. In this formulation, the sound field is represented by an electrical equivalent circuit composed of distributed lines corresponding to the acoustic equation, and nodal equations for each connection of the lines are derived. As an example, consider a cube‐shaped room with uniform absorption by each wall. The transient responses to the sinusoidal waves and the 1/3‐octave‐band tone burst are calculated, and the stationary sound‐pressure distribution and the reverberation time are obtained from these responses. The results show the validity of the formulation and prove the effectiveness of the application of this method to room acoustics.
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Measurements of short reverberation times using a real time analyzer (A)

Klaus Højbjerg

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S65-S65 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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Classical measurements of reverberation time with use of the interrupted noise method is known to almost everybody working with acoustics. However, there seems to be less knowledge about the limitations of the method, i.e., the connection between measurement bandwidth and minimum averaging time and what that means for minimum reverberation time measured. Another method is impulse excitation followed by a backwards integration. Here, the analysis can be done in two ways, either direct frequency analysis of the response signal giving the same limitations as with the interrupted noise method or by recording the time signal and then feeding the signal reversed to the filter bank giving possibilities of measuring very short reverberation times. The methods of measuring reverberation time will be discussed and examples of measurements shown.
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Frequency distribution of normal modes of vibration in rectangular rooms; A new look (A)

Ludwig W. Sepmeyer

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S65-S65 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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In a previous study on the frequency and angular distribution of the normal modes of vibration in rectangular rooms, published in 1965, the criterion for judging the frequency distribution of the modes was called the mode spacing irregularity MSI. The MSI, based on the ratio of the actual mode spacing between two adjacent modes to the ideal spacing between two modes predicted by Maa's equation, is quite insensitive to changes in room dimension ratios. In this paper, a new criterion called the modal volume distribution index, MVDI, is proposed. The MVDI is based on the difference in spherical volume enclosed by two adjacent modal vectors in frequency space and the difference in volume between two similar ideal vectors. In this way, larger and smaller than ideal spacings are weighted equally. Results, quite different from those inferred from the MSI, are given for a few selected dimension ratios. Revisions to National and International Standards that require sound‐pressure level measurements in reverberation rooms are recommended.
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Calculation of sound radiation from an aperture of a building by means of Kirchhoff's diffraction formula (A)

Nobuo Hara and Yoshihiro Furue

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S65-S65 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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When a noise source is located in a very large room as compared to the wavelength concerned, the integral equation method to calculate the sound field is not applicable because of limitations in computer capacity. In this case, an approximate approach based on Kirchhoff's diffraction formula becomes more practical. This formula requires the velocity potential and its normal derivative at the aperture, which are unknown. These unknowns may be assumed to consist of the direct wave from the source and the diffused ones. The latter are assumed to be plane waves with the same amplitude but random phase. The relation between the amplitude of the direct wave and the reflected ones is determined by geometrical acoustics. Thus the radiated sound field can be readily evaluated from the aperture by Kirchhoff's formula. The numerical results for a scale model of a reverberation chamber with a rectangular aperture are shown with measurements. The agreement between the calculations and the measurements is satisfactory.
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Analysis of the sound field in a room with uneven surfaces by the hybrid method combining geometrical theory and wave theory (A)

Kyoji Fujiwara

J. Acoust. Soc. Am. Volume 84, Issue S1, pp. S65-S65 (1988); (1 page)

Online Publication Date: 13 Aug 2005

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This study presents a new way of estimating the sound field in a room with walls that do not reflect the incident sound specularly. So far the reflection characteristics of these walls have been considered to be perfectly diffuse or a mixture of partially diffuse and partially specular. The aim of this study is to introduce the real reflection characteristics of the walls into the simulation procedure for the sound field. The estimation procedure is essentially based on the Monte Carlo simulation method. For simplicity, the uneven walls are assumed to be periodically corrugated. Prior to the simulation, the reflection characteristics of the periodically corrugated wall are analyzed by wave theoretical methods, and the result, which contains the directions and magnitudes of the reflected waves, is used in the simulation procedure. The energy impulse responses estimated by the method presented are compared with those obtained by the ordinary method based only on geometrical theory.
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