The aim of this paper is to show how the analytical modelling of a simplified acoustic device (herein a simplified wind musical instrument) may be a relevant educational way to study several aspects of the behavior of an idealized component [herein a one-dimensional (1-D) resonator], which is the core component of the device considered. A time-dependent source, whether sinusoidal, impulse, or representing approximate valve-effects of the reed, is coupled to the resonator in the analytical modelling. The unavoidable thermo-viscous parietal dissipation, as well as an approximate radiation effect, are accounted for. After a brief presentation of the problem, precisely posed and solved in detail analytically in an approximate manner, results in both the frequency domain and in the time domain are presented. These results include the properties of the transient behaviors (both the starting transient and the transient decay), illustrating the main features of the resonator.