Student difficulties measuring distances in terms of wavelength: Lack of basic skills or failure to transfer?

Abstract

In a previous paper that focused on the transmission of periodic waves at the boundary between two media, we documented difficulties with the basic concepts of wavelength, frequency, and propagation speed, and with the relationship v=fλ. In this paper, we report on student attempts to apply this relationship in problems involving two-source and thin-film interference. In both cases, interference arises from differences in the path lengths traveled by two waves. We found that some students (up to 40% on certain questions) had difficulty with a task that is fundamental to understanding these phenomena: expressing a physical distance, such as the separation between two sources, in terms of the wavelength of a periodic wave. We administered a series of questions to try to identify factors that influence student performance. We concluded that most incorrect responses stemmed from erroneous judgment about the type of reasoning required, not an inability to do said reasoning. A number of students do not seem to treat the spacing of moving wave fronts as analogous to immutable measurement tools (e.g., rulers).