Adjoint state method is a well-known method to efficiently compute the gradient of a cost or objective function for a simulation-driven optimization problem. Essentially, it computes the adjoint action of Born operator (the linearized forward map) on any given vector. This report presents a derivation of adjoint state algorithm for an acoustic system discretized by staggered grid finite difference schemes, and discusses its implementation based on the modeling package IWAVE. Our goal is to construct a C++ wrapper of IWAVE, which fits into a general framework for inversion. This report is the second of several describing an implementation of such a wrapper.