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We investigate the understanding of mechanical waves in a class of second-year physics majors at a Canadian university. We administered a previously-developed diagnostic test (Wittmann. Ph.D. thesis, University of Maryland. Unpublished. 1998.) pre- and post-instruction to second-year students, and pre-instruction to a group of first-year students. We find that common misconceptions identified in previous studies involving students in first-year physics courses persist among our second-year students, although the fraction of students holding these misconceptions decreases with instruction. We also find that application of wave concepts becomes more consistent, and that the correlation between the students’ own perception of their understanding and their diagnostic test scores increases significantly as their level of instruction advances. We describe two tutorial exercises developed to address areas in which conceptual understanding is weak.