We administered a multiple-choice conceptual survey in mechanical waves to 902 students ranging from high school to second year university. Analysis identified several conceptual models the students seemed to be using when answering survey questions. In this paper we investigate the strength with which 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 a 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: (1) categorizing and counting, and (2) model analysis, recently introduced into PER. Categorizing and counting is used in very diverse ways 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 with more experience in physics learning use the scientifically accepted models more consistently. Further, 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 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. This suggests studying more abstract topics may solidify students' understanding of more concrete waves. While perhaps intuitive, we have not actually found direct empirical studies supporting this conjecture.