This work presents a sensitivity analysis for topology optimization of thin structures inside an acoustic horn in order to improve its far-field directivity properties. The objective function gradient is computed using an adjoint-based method, a well-known approach in the design optimization community due to its ability to compute the design sensitivities when there is a large number of design variables. The accuracy of the computed gradient is verified numerically against a first order finite difference approximation. The report also covers the matrix representations of the far-field pattern evaluation and the variational problem with an interface condition to model the thin structures.