This study reports on the development and application of a four-tier multiple-choice (4TMC) diagnostic instrument, which has not been reported in the literature. It is an enhanced version of the two-tier multiple-choice (2TMC) test. As in 2TMC tests, its answer and reason tiers measure students' content knowledge and explanatory knowledge, respectively. The two additional tiers measure the level of confidence of students in the correctness of their chosen options for the answer and reason tiers respectively. The 4TMC diagnostic test focused on the properties and propagation of mechanical waves. It was administered to 598 upper secondary students after they were formally instructed on the foregoing topics. The vast majority of the respondents were found to have an inadequate grasp of the topics tested. Mean scores and mean confidence associated with the answer tier was higher than those associated with the reason tier. The students tended to be poorly discriminating between what they know and what they do not know. Familiarity with the topic tested was associated with greater percentage of students giving correct answers, higher confidence, and better discrimination quotient. Nine genuine alternative conceptions (which were expressed with moderate levels of confidence by students) were identified.