Finite-sized sources in the presence of boundaries

Abstract

Many methods of auralization convolve a source signal (e.g., cello recorded in an anechoic room) with a room’s impulse response (which has been computed using method of images, ray tracing, etc.). Many instruments are finite-sized sources because they produce music having frequencies where the product of the wavenumber and the instrument’s characteristic length is not small. Sound produced by a finite-sized source in the presence of boundaries can include scattering and diffraction, resulting from the presence of the source in its own field. These effects are not accounted for by the auralization types mentioned above. A geometrically simple example of a finite-sized pulsating sphere in the presence of a rigid infinite boundary is solved using the translational addition theorem for spherical wave functions (TATSWF). Using TATSWF, the original problem is solved by replacing the rigid infinite wall with an image of the finite-sized sphere. This is a surprisingly complicated problem to solve, given the simple geometry, and serves to illustrate how a source can perturb its field when near a boundary. Examples are presented for which significant changes in the pressure magnitude occur. [Work supported by the Applied Research Laboratory, Penn State.]