  Webster's horn equation (1919) offers a one-dimensional approximation for
low-frequency sound waves along a rigid tube with a variable cross-sectional
area. It can be thought as a wave equation with a source term that takes into
account the nonlinear geometry of the tube. In this document we derive this
equation using a simplified fluid model of an ideal gas. By a simple change of
variables, we convert it to a Schr\"odinger equation and use the well-known
variational and perturbative methods to seek perturbative solutions. As an
example, we apply these methods to the Gabriel's Horn geometry, deriving the
first order corrections to the linear frequency. An algorithm to the harmonic
modes in any order for a general horn geometry is derived.
