This is a series of 32 simulation-enhanced tutorials on the fundamentals of wave mechanics. The topics covered start with the simple properties of periodic motion and functions and extend to Fourier series, frequency dispersion, normal modes, and non-linear systems. Each tutorial includes introductory text, a simulation, and a set of questions and problems.
This material is designed to develop student understanding and reasoning skills regarding wave phenomena through interactive explorations. Students are lead through explorations with both specific and more open-ended questions.
Target Student Population:
The full set of tutorials is targeted at upper-division physics students. Some tutorials are suitable for an introductory course.
Prerequisite Knowledge or Skills:
Some of the tutorials require only basic algebra and trig. More advanced tutorials use calculus, differential equations, and partial differential equations to describe wave equations, dispersion relations, and oscillations.
Type of Material:
This is tutorial material that includes simulation-based illustrations and student explorations.
This is useful as supplemental tutorial material for a waves course. It might best be used in conjunction with a standard textbook or with other supplemental notes.
This material requires a java-enabled browser.
Evaluation and Observation
This set of tutorials provides a carefully crafted exploration of waves, a topic of importance to a great many fields of physics. The completeness of the topics covered is particularly noteworthy.
The java simulations are generally simple and do an excellent job of linking the mathematical description of waves with visual representations. The user can manipulate individual parameters in the models to explore the physical properties of the systems being studied. The tutorials cover topics which students often find difficult, such as phase and group velocity, longitudinal waves, interference, and dispersion. Connections are made between the physical motion of matter or fields in these waves and the graphical representations used to describe this motion.
The combination of visualization and mathematics, where students can explore the physics by manipulating both graphical and mathematical models of the waves, is important and noteworthy.
Some of the tutorials discuss the simplifications made in the models being used. This is important to help students understand the applicability of the models. More of these discussions would be useful.
The simulations are basic, consisting mostly of line graphs. Some students might need help understanding these graphical representations.
The examples given in the tutorials are quite standard to courses on waves. More applications to interesting or unqiue physical systems would be beneficial.
Potential Effectiveness as a Teaching Tool
The tutorials make very effective use of multimedia and computational tools and their interactive structure is excellent pedagogy. Each tutorial starts with a very short introduction and then provides a series of directed activities designed to encourage student exploration. The graphical illustrations provide immediate feedback for students.
There is a clear purpose and goal to each tutorial. The references included on the web site are a significant benefit.
One reviewer felt that the tutorial activities were overly scripted, providing exact parameters for students to enter and thus hindering exploration. Another reviewer felt that there was a good balance between prescribed and open-ended exercises. The author does include specific values for physical parameters in some tutorials to highlight important physics.
Instructors need to be careful when using the tutorials for introductory classes because of the variation in the level of mathematics used in different tutorials.
There are no specific recommendations on how these tutorials might best be used to improve student learning.
Ease of Use for Both Students and Faculty
These tutorials are easy to use. The navigation and structure of the material is immediately understandable. The navigation panel makes it easy to find content on particular topics.
The simulations are straightforward to run. There are appropriate instructions for using the simulations where needed. The tutorial pages are clearly divided into introductory text, simulation, and problems.
Some of the simulations take a while to load. Some simulations require the user to set parameters before pressing play, others don’t. Although this is explained in the text, it may be confusing in some cases.
The problem sets are sometimes very long, making it impossible to see problems and the simulation on a single screen.
Instructors wishing to collect student responses to the exercises will need to set up their own methods of doing this.
Other Issues and Comments:
This is an excellent example of the use of digital tools to help students learn concepts that are, by their very nature, not well represented using textbooks or other static media.