Wood is a complicated material: we model it as an elastic solid with cylindrical orthotropy. We consider the propagation of waves in slender (wooden) solids of revolution, such as a baseball bat. To solve the governing equations, we first scale the radial coordinate so as to map the bat onto a circular cylinder, and then we use the method of Frobenius (power series in the new radial variable). Before describing these calculations, we consider the simpler acoustic problem: sound waves in an axisymmetric tube with a slowly-varying cross-section. For this problem, we obtain a hierarchy of approximations, consisting of ordinary differential equations for the variation of some quantity along the tube. The simplest of these is usually known as Webster's horn equation.