Acoustical cavity excitation.
A tutorial exposition is given of cavity excitations and it is shown that relatively simple analytical solutions for the excitation of acoustic fields in cavities with lossy walls can be obtained for a broad class of such cavities. The standard analytic procedure whereby one expresses the acoustic field as a sum over the eigenmodes of the cavity is reviewed and its limitations are pointed out. An alternate procedure is to seek to make use of Green's functions depending on a single coordinate and to not express such Green's functions as sums over eigenfunctions. Instead, one expresses the Green's function as a closed form function that has a discontinuous slope at the value of the coordinate corresponding to the source location. Although the class of cavities for which this approach is possible is limited, it is sufficiently broad to be of intrinsic interest and the results may be helpful to those seeking benchmark solutions and analytic insight. Displayed examples are for cavities whose shapes are spheres and cylinders, with interior monopole, dipole, line, and distributed sources. The formulation yields simple expressions for the total power absorbed by the cavity walls.
Levine
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Mathematics Department, Stanford University, California 94305, USA.