Student understanding of wave behavior at a boundary: The limiting case of reflection at fixed and free ends

We investigated student understanding of wave behavior at a boundary in the context of pulses and periodic waves in water and in elastic media. The participants were science and engineering majors in introductory calculus-based physics. We document several conceptual and reasoning difficulties and describe the refinement and assessment of our instructional materials. The results show significant improvements in student learning of some aspects of superposition and reflection, but some reasoning patterns that yield incorrect predictions persist. Among these difficulties is the tendency to employ simple rule-based approaches in cases in which a systematic application of the superposition principle is necessary to predict the motion of points in the medium over an interval of time.