Abstract
The formal solution of the scalar wave equation is presented for a point source in a medium which is inhomogeneous one dimension with a particular sound-velocity dependence. This solution is another of the class of integrable solutions, based upon Bessel's equation, which can be expressed in closed form, allowing the use of available tables for numerical work. The particular sound velocity chosen, c = c0z(z2 − a2)−12, is interesting in that it corresponds in part to actual underwater measurements and that it yields a shadow zone. In addition, an integral involving products of Bessel functions is reduced to a simple form, not found in the literature on Bessel functions.
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