Large amplitude time-domain oscillations are detected in InxGa1-xN/GaN structures via femtosecond differential reflectivity spectroscopy. The oscillation amplitude increases with increasing indium fraction and abruptly disappears at a critical time that depends on GaN thickness. We show that spatially localized, coherent acoustic phonon wave packets are generated via the photoexcited carriers and propagate into the samples modulating the reflectivity. Our results show that a system with strong built-in strain can be a very effective source for ultrafast acoustic phonon wave packets which can be used as a powerful probe for nanoscale structures.