Notes: a). For open end, the longitudinal pressure wave is reflected with a phase change of 180, because the pressure at the open end must at the value Po, same as the environment's In this case, it likes the string fixed at both ends b For the closed end, the pressure can vary freely c).The superposition of the original and reflected waves gives a pattern of standing waves d) Resonance can happen, when the driving frequency matches one of the natural frequency of the system, which are determined by the length of the tube L)a).For open end, the longitudinal pressure wave is reflected with a phase change of , because the pressure at the open end must at the value , same as the environment’s. In this case, it likes the string fixed at both ends. b).For the closed end, the pressure can vary freely. c).The superposition of the original and reflected waves gives a pattern of standing waves. d). Resonance can happen, when the driving frequency matches one of the natural frequency of the system, which are determined by the length of the tube (L).  180 P0 Notes: