Our previous work revealed that the energy spectrum of cosmic rays produced by the standard diffusive shock acceleration (DSA) can be modified by downstream sound waves originated from inhomogeneity of the shock upstream medium. However, the background plasma was described by linear analytical solutions and nonlinear evolution of sound waves was not included. In this work, we investigate how nonlinear effects such as steepening and dissipation of sound waves affect particle acceleration by using test-particle simulations. First, we imitate weak shock waves steepened from sound waves by analytical sawtooth waves and show that large-scale waves can efficiently accelerate particles earlier than they dissipate. Next, we numerically solve shock propagation into an inhomogeneous medium and discuss particle acceleration by downstream waves. Our results imply additional acceleration by downstream sound waves works even when they evolve nonlinearly.