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Ocean and Seabed Acoustics: A Theory of Wave Propagation by George V. Frisk - Woods Hole Oceanographic Institution

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Chapter 4. Acoustic Sources and Green’s Functions

Mathematics possesses not only truth, but supreme beauty – a beautycold and austere, like that of sculpture, without appeal to any partof our weaker nature, yet sublimely pure, and capable of astern perfection such as only the greatest art can show.Bertrand Russell, 1903

4.1 Introduction

We have, until this point, considered solutions to the wave equation in the absence of sources. For example, we implicitly considered spherical wave solutions, as in Eq. (2.16), only for r ≠ 0. However, we have now reached a stage in the theoretical development where it is crucial that we introduce acoustic sources and the mathematical formalism by which we can incorporate them into solutions of the wave equation, ...

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