Simulating waves and macroscopic phonons

Abstract

Wave phenomena are fundamental for many branches of physics, not only for mechanics. Thus, students at university level should become familiar with the underlying theory, and especially with solutions of the wave equation. This paper refers to a multimedia program for PCs, tablets or smartphones, and introduces and discusses several animated illustrations. The introduced program can illustrate the power of the wave equation. Basic wave phenomena can be computed with numerical methods. The finite difference method which is used can be lead back to fundamental assumptions of physics. Yet, this numerical method is capable of calculating a great variety of wave phenomena. Several examples can demonstrate the power of this numerical procedure. Phenomena like the propagation of circular waves diverging from a point source, Huygens's elementary waves, superposition of waves, reflexion, refraction and transmission at the interface between different media, scattering, interference phenomena, as well as dispersion and the Doppler effect can be studied in animated visualisations. This opens up a variety of teaching and learning strategies, e.g. the single concept principle and the inverted classroom concept, and the modelling of partial differential equations (the wave equation as well as the heat equation) can be supported. The conceptual approach is described here; an empirical study about learning will be a next step.