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We study the nonlinear inhomogeneous wave equation in one space dimension:$v_{tt} - T(v,x)_{xx} = 0$. By constructing some "decoupled" Riccati typeequations for smooth solutions, we provide a singularity formation resultwithout restrictions on the total variation of unknown, which generalizeearlier singularity results of Lax and the first author. These results areapplied to several one-dimensional hyperbolic models, such as compressibleEuler flows with a general pressure law, elasticity in an inhomogeneous medium,transverse MHD flow, and compressible flow in a variable area duct.

Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation