The significance of entropy-like terms is examined within the context of the finite-difference modeling of acoustic wave propagation. The numerical implications of dissipative mechanisms are tested for performance within two very distinct differencing algorithms. The two schemes which are reviewed with and without dissipation are (1) the standard central-difference scheme, and (2) the Lax-Wendroff two-step scheme. Numerical results are presented comparing the short-wavelength response of these schemes. In order to achieve this response, the linearized version of an exploding one-dimensional source is used.