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Mean Free Path Length for Radiating Point Sources in Specular Reflecting Enclosures

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This paper deals with the calculation of Mean Free Path Length (MFPL) especially for lower frequencies and non diffuse sound fields. Using the classical formula the MFPL is under-estimated. To show this the different spatial distributions and the methods of calculating the mean free path length are compared. Here the special case of non-diffuse sound fields is regarded.

There are several possible ways of calculating the ensemble mean. The harmonic ensemble mean is related to the mean of the impact rate. Both methods yields the MFPL for diffuse sound fields. In the case of a sphere however, and radiation from a surface point the harmonic mean leads to a physical inconsistency if a specular reflection law is assumed.

In general it can be shown for convex rooms that the arithmetic ensemble mean in case of specular reflection gives longer values than the harmonic ensemble mean. The "convexity" and thus the mean free path length of the enclosure can be regarded as dependent from the ratio of wavelength to structural dimensions of the room. For long wavelengths the room may look convex neglecting the small surfaces, even if the room is concave for small wavelengths. So, the longer reverberation times at low frequencies in many rooms can be explained even for frequency independent absorption. A formula is introduced for calculating the harmonic mean for general room shapes. Examples are derived for spherical and rectangular enclosures and compared with integral equation theory and measured results.
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Document Type: Research Article

Publication date: 1997-07-01

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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