Characterizing the frequency spectrums of acoustic sources from measured accelerometer or microphone data is a common inverse problem in engineering acoustics. Applications include acoustic testing of aerospace structures, room acoustics, and underwater acoustics. Typically, accelerometer or microphone pressures are measured, and it is desired to characterize the acoustic sources that produced these measurements. Many of these applications of interest involve large acoustic domains and high frequency ranges, thus making a finite element solution an attractive option for the forward problem. In this talk we will present a partial differential equation (PDE) constrained optimization approach for solving the inverse problem that is based on a coupling between a finite element-based massively parallel structural dynamics code (Sierra-SD) and a massively parallel optimization code (Rapid Optimization Library (ROL)). Gradients and solution iterates are exchanged between the codes during the solution process. The gradients for the optimization solver are computed using the adjoint method, which translates to forward and adjoint Helmholtz solves in the frequency domain. We will present results on several problems of interest. Sandia is a multiprogram engineering and science laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the US Department of Energy's National Nuclear Security Administration. (DE-AC04-94AL85000)