One of my responsibilities as a teaching assistant at BU Academy was to cover any classes the teacher (Mr. Gary Garber) could not make. This week he is traveling with the BU Academy FIRST Robotics team to the FIRST competitions and I'm covering some of his classes.
Right now, the class is just starting standing waves. It can be tricky to visualize how the waves actually reflect and interfere with each other. If you're using a spring or a rope to demonstrate this effect, damping is often an issue and other parameters can be difficult to control. If you're using a simulation, the waves usually travel too quickly and it can be difficult to see what's going on. I decided to write a quick MATLAB script to help my students visualize how standing waves form.
The script basically plots several cycles of a sine wave as it travels down a 'string'. Both the input and the string's response (what we actually see the string doing) are plotted on top of each other so that they can be compared. I took some screencasts and some screenshots to better illustrate the process. It's important to note that this simulation doesn't model resonance or harmonics; it simply reflects the incoming waveform off the wall and adds it to the rest of the wave form.
This video shows the typical standing wave we are used to seeing. The nodal points can clearly be seen. I took a few other videos showing different inputs, but they don't all fit here. Those videos have been left as an exercise for the reader.
Download the MATLAB file here.