Since Schumacher introduced a time-domain model of single-reed instruments and McIntyre et al. gave the general concept of time-domain models of wind instruments, the time-domain models, namely, delayed feedback models, have become an important numerical tool for study of wind instruments due to their simplicity, easiness to handle, and reliability. However, those models only reproduce wave oscillations observed in mouthpieces of wind instruments. In this talk, we will propose a numerical technique, which is able to reproduce time dependent motions of spatial waves in an air-column. It is composed of inversed wave propagator matrices combined with the forward and backward Fourier transformations. The resultant spatial waves in the air-column exhibit very similar time-dependent behavior to those observed by an experiment for the clarinet. Actually, backward and forward rounded-off step waves are observed. We will also discuss difference in wave shapes and their time-dependent behavior depending on the shapes of air-columns, cylindrical one like the clarinet, conical one like the saxophone and horn-shaped one like brass instruments. For the conical and horn-shaped air-columns, Helmholtz-like waves are observed rather than the step waves observed for the cylindrical air-column.