We recently developed a multiple-choice conceptual survey in mechanical waves. The development, evaluation, and demonstration of the use of the survey were reported elsewhere [A. Tongchai et al. Int. J. Sci. Educ. 31 2437 (2009)]. We administered the survey to 902 students from seven different groups ranging from high school to second year university. As an outcome of that analysis we were able to identify several conceptual models which the students seemed to be using when answering the questions in the survey. In this paper we attempt to investigate the strength with which the students were committed to these conceptual models, as evidenced by the consistency with which they answered the questions. For this purpose we focus on the patterns of student responses to questions in one particular subtopic, wave propagation. This study has three main purposes: (1) to investigate the consistency of student conceptions, (2) to explore the relative usefulness of different analysis techniques, and (3) to determine what extra information a study of consistency can give about student understanding of basic concepts. We used two techniques: first, "categorizing and counting," which is widely used in the science education community, and second, "model analysis," recently introduced into physics education research. The manner in which categorizing and counting is used is very diverse while model analysis has been employed only in prescriptive ways. Research studies have reported that students often use their conceptual models inconsistently when solving a series of questions that test the same idea. Our results support their conclusions. Moreover, our findings suggest that students who have had more experiences in physics learning seem to use the scientifically accepted models more consistently. Further, the two analysis techniques have different advantages and disadvantages. Our findings show that model analysis can be used in more diverse ways, provides flexibility in analyzing multiple-choice questions, and provides more information about consistency and inconsistency of student conceptions. An unexpected finding is that studying waves in other contexts (for example, quantum mechanics or electromagnetism) leads to more consistent answers about mechanical waves. The suggestion is that studying more abstract topics may solidify students' understanding of more concrete waves. While this might be considered to be intuitive, we have not actually found direct empirical studies supporting this conjecture. (Contains 8 tables and 3 figures.)