Smartphones and tablets are an integral part of our daily lives, and their capabilities extend well beyond communication and entertainment. With a broad choice of built-in sensors, using these mobile devices as experimental tools (MDETs) allows for a many different measurements, covering several fields of physics (mechanics, acoustics and waves, magnetism, optics, etc.). Building on this development, the present contribution is about exploring the potential of MDETs in physics undergraduate research. Two examples related to acoustics (bottle Helmholtz resonator, singing glasses) will be discussed in detail, and four further possibilities are referred to as perspectives. Results of these student research projects are encouraging throughout (accuracy, agreement with theory), in many cases providing a basis for further improvements and insight. Additionally, it is argued that these examples provide a "proof of concept" that the use of smartphones for experimental projects can mobilize and stimulate among students the educational potential of "higher order thinking skills" (HOTs) widely discussed in the literature on undergraduate research, such as autonomy, curiosity, creativity, and others.