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New Methodological Trials of Evaluating the Sound Intensity Fluctuations at Three Observation Points with Arbitrary Correlation in a Diffuse Sound Field

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This paper discusses several types of the mutual cor-relation of information among stochastic fluctuations of the sound intensity at three observation points on the basis of a tri-variate joint probability distribution. First of all, the statistical Laguerre series expansion expression, taking the product of three Gamma distri-butions as its first term, and reflecting the linear and nonlinear correlations of fluctuations in each expan-sion coefficient, is introduced as the general frame-work of the tri-variate joint probability distribution. Needless to say, the Gamma distribution corresponds to a well-known probability distribution at a single observation point. Next, each expansion coefficient is derived in relation to the geometrical positions of the observation points, the frequency characteristics of the input, the time constant of the sound level meter, and so on.

Finally, the validity of the proposed theory is ex-perimentally confirmed by applying it to data actually observed at three points in a reverberation room.


In dieser Arbeit werden verschiedene Typen der Korrela-tion zwischen stochastischen Fluktuationen der Schall-intensität an drei Beobachtungspunkten auf der Grund-lage einer trivariaten Verbundwahrscheinlichkeitsvertei-lung diskutiert. Zuerst wird die statistische Laguerrerei-henentwicklung mit dem Produkt von drei Gamma-verteilungen als erstem Term, welche die linearen und nichtlinearen Korrelationen der Schwankungen jedem Entwicklungskoeffizient wiederspiegelt, als allgemeiner Rahmen der trivariaten Verbundwahrscheinlichkeitsver-teilung eingefuhrt. Es erübrigt sieh zu sagen, daß die Gammaverteilung als Wahrscheinlichkeitsverteilung in einem einzelnen Beobachtungspunkt wohlbekannt ist. Als nächstes wird jeder Entwicklungskoeffizient aus der geometrischen Lage der Beobachtungspunkte, der Fre-quenzcharakteristik des Eingangssignals, der Zeitkon-stante des Schallpegelmessers usw. abgeleitet.

Schließlich wird die Gültigkeit der vorgeschlagenen Theorie durch ihre Anwendung auf in drei Punkten eines Hallraumes beobachtete Daten experimentell bestätigt.


On examine divers types de corrélation mutuelle concer-nant l'information sur des fluctuations statistiques de l'intensité du son en trois points d'observation sur la base d'une distribution associée de probabilité trivariée. Tout d'abord on introduit l'expression statistique par dévelop-pement en séries de Laguerre, dont le premier terme sera le produit de trois distributions Gamma et dont chaque coefficient du développement exprime les corrélations linéaires et non-linéaires. Ce sera le cadre général de la distribution associée de probabilité trivariée. La distribu-tion Gamma correspond évidemment à une distribution de probabilité bien connue relative à un seul point d'ob-servation. Ensuite chaque coefficient du développement s'etablit en tenant compte des situations géométriques des points d'observation, des caractéristiques fréquentiel-les de l'intrant, de la constante de temps du sonométre et ainsi de suite.

Enfin on a vérifié expérimentalement la validité de la théorie proposée en l'appliquant à des données effective-ment mesurées en trois points d'une salle réverbérante.
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Document Type: Research Article

Publication date: September 1, 1991

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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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