It is known that when an arbitrary waveform propagates in a dispersive wave guide, it will develop gradually in time and space due to the dependence of the phase speed on the frequency. Since each progressive wave component propagates with a lightly different phase speed, the initial shape of the transient wave form is distorted in time. This is particularly true for an air-filled flexible tubing organized in a tree-like structure, such as the lung airway tree. The absorption of sound energy by the air increases rapidly with increasing frequency but the absorption by the flexible wall decreases. Thus, the sound propagation in the lung airways have both types of absorption. In addition to that, at each node the sound waves are partialy reflected and partialy transmited. In this present work we studied the propagation of a well defined waveform, called crackle sound, in a branching tree structure making a direct connection with the propagation of lung crackle sound.