  In this work we show an error estimate for a first order Gaussian beam at a
fold caustic, approximating time-harmonic waves governed by the Helmholtz
equation. For the caustic that we study the exact solution can be constructed
using Airy functions and there are explicit formulae for the Gaussian beam
parameters. Via precise comparisons we show that the pointwise error on the
caustic is of the order $O(k^{-5/6})$ where $k$ is the wave number in
Helmholtz.
