The Purcell effect significantly improves the performance of various emission devices but is typically constrained by a narrow operational bandwidth due to inherent resonant mechanisms. This study achieves broadband acoustic Purcell effect, substantially boosting sound emission by exploring collective quasibound states in the continuum (QBICs). A six-cavity coupled system supporting five QBICs is introduced, wherein all of the QBICs interact strongly with an acoustic source. This system takes advantage of the high quality factors and the strong mode responses of the collective QBICs, leading to a substantial enhancement of the local density of states. Consequently, a considerable increase in sound emission is realized across the frequency range of 625-900 Hz. These findings provide insights into the physical mechanisms driving the broadband Purcell effect in resonant systems and open up promising avenues for the development of advanced acoustic emission devices.