We report a detailed observational study of two quasi-periodic fast-propagating (QFP) magnetosonic wave events occurred on 2011 March 09 and 10, respectively. Interestingly, both the two events have two wave trains (WTs): one main and strong (WT-1) whereas the second appears small and weak (WT-2). Peculiar and common characteristics of the two events are observed, namely: 1) the two QFP waves are accompanied with brightenings during the whole stage of the eruptions; 2) both the two main wave trains are nearly propagating along the same direction; 3) EUV waves are found to be associated with the two events. Investigating various aspects of the target events, we argue that: 1) the second event is accompanied with a flux rope eruption during the whole stage; 2) the second event eruption produces a new filament-like (FL) dark feature; 3) the ripples of the two WT-2 QFP waves seem to result from different triggering mechanisms. Based on the obtained observational results, we propose that the funnel-like coronal loop system is indeed playing an important role in the two WT-1 QFP waves. The development of the second WT-2 QFP wave can be explained as due to the dispersion of the main EUV front. The co-existence of the two events offer thereby a significant opportunity to reveal what driving mechanisms and structures are tightly related to the waves.
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