Students were struggling with a homework question about waves that asked them to determine what the “snapshot” graph (displacement vs position along string at a given time) would look like based on the “history” graph (displacement vs. time for a given location on the string.
Here are two clicker questions I wrote to get us thinking and talking critically about it in class. This sequence of questions and discussion took 20-25 minutes, which was more than I was expecting, but there was a lot of productive struggle.
Among many rich points of conversation, three key points of confusion and insight were
Argument 1: Time on the history graph is always read from left to right, but events on a snapshot graph with a left traveling wave occur from right to left. So the shape should be opposite, since time is proceedings in different directions on the two graphs.
Argument 2: Whatever the source does first gets a head start on the wave, and so should be “out” in front, which way the wave is traveling.
Argument 3: We know each point on the graph goes up and then down. This means if you are at further down the string that the current snap shots shows (which hasn’t yet gone up or down yet), the closest part of the pulse needs to be an up part, because you are staring at what’s about to happen too you as it approaches you.