The adiabatic form of the Euler equations are cast in a form emphasizing its signal propagation properties and solved using an approximate eigenfunction analysis. Second-order rarefaction waves appear as direct eigenfunction solutions. The underlying scalar equation describing nonlinear shock wave evolution is rederived as a first-order Burgers equation. The characteristic sonic boom N waves are predicted using an implicit aeroacousticbased finite-difference algorithm with numerical damping designed to suppress spurious oscillations at shock-wave discontinuities. The evolution of these sonic-boom-type signals to the mid- and far field are computed directly with the numerical method.