A study of set-up, propagation, and interaction of non-linear and linear magnetohydrodynamic waves driven by magnetic reconnection is presented. The source term of the waves generated by magnetic reconnection is obtained explicitly in terms of the initial background conditions and the local reconnection electric field. The non-linear solution of the problem found earlier, serves as a basis for formulation and extensive investigation of the corresponding linear initial-boundary value problem of compressible magnetohydrodynamics. In plane geometry, the Green's function of the problem is obtained and its properties are discussed. For the numerical evaluation it turns out that a specific choice of the integration contour in the complex plane of phase velocities is much more effective than the convolution with the real Green's function. Many complex effects like intrinsic wave coupling, anisotropic propagation characteristics, generation of surface and side wave modes in a finite beta plasma are retained in this analysis.