Equivalent staggered grid scheme (ESG) is a new family of schemes based on the finite-difference method (FDM). The method is applied to acoustic wave propagation in variable density media and the results are compared with those from some classic FDM approaches. The main feature of this new family is that it is designed to generate results numerically equivalent to those using the standard staggered grid formulations (SSG), but with the same memory requirements of simple grid schemes. Hence, it results in a reduction of memory usage by 33% in 2D and 50% in 3D problems, compared to the memory usage of SSG. The first-order system of equations in terms of pressure and velocity is not used here. Instead, the formulation is based on applying new central difference operators to the second-order acoustic wave equation in terms of pressure, obtaining the same level of accuracy and stability as the SSG schemes. The equivalence between the ESG and SSG is mathematically demonstrated and issues concerning the application of seismic sources and the boundary conditions are addressed.