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The saddle point method applied to selected problems of acoustics

Snakowska A., Idczak H.

Archives of Acoustics

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2006

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Vol. 31, No. 1

57-76

EN

The paper is aimed at the presentation of examples of applying the saddle point approximation method to some fundamental problems of acoustics and the discussion of some interesting couplings between applied mathematical methods and the physical interpretation of the results. The saddle point method is shortly reminded in its basic form, from which more advanced versions, improving the results and widening the range of possible applications, are derived. Two problems, solved at first for electromagnetic waves and then applied to acoustics by means of "the analogous method'', have been chosen as examples. The first one is the phenomenon of the reflection of a spherical wave at a plane interface between two media, the lower of which is characterised by a higher velocity (water/sand, air/water). In this case there is a critical angle above which a total reflection and a lateral wave occur. The second example is the far field radiated from the outlet of a semi-infinite circular duct. The physical insight into the understanding of the physical phenomena provided by the saddle point method is stressed.

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Warunki równoważności układów dwóch koherentnych źródeł punktowych

Idczak H., Snakowska A.

Prace Naukowe Instytutu Telekomunikacji i Akustyki Politechniki Wrocławskiej. Konferencje

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2001

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Vol. 83, nr 27

51-56

EN

The aim of the paper is to derive general equivalency conditions for any set of two coherent point sound sources, i.e. conditions which have to be fulfilled by the substitute source to ensure invariable the acoustic power output and the directivity pattern. In order to solve the problem the position, the acoustic power and the directivity coefficient of each source of the set are assumed to be known. As a result the formulae for the position, power and directivity of the equivalent source are presented.

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The saddle point method applied to some problems in acoustics

Snakowska A., Witkowski P., Idczak H.

Hydroacoustics

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1997

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Vol. 1

321--326

EN

The paper presents examples of applying the saddle point method (called also the method of the steepest descent path) to some problem s of acoustics. The method is shortly reminded in its basic form and more complex options which, however, improve the results and widen the range of eventual applications. As examples the phenomena of reflection and transmission of the spherical wave at a fluid-fluid interface and the far field radiated from the circular duet are discussed.