Wave Slicing and Remainders: a cool way to find the period of a periodic function

Last month, in Falmouth High School in Maine, some Honors Physics students were estimating the period of a mass hanging from a spring. They used InquirySpace/Data Games software and Vernier motion sensors, and got data that looks like this (Reading is in meters; Time in seconds):

oscillating data

To do their investigations, they needed the period of this wave.

  • Some students found the peak of one wave, and subtracted its time from the peak of the next wave. This is the most straightforward and obvious. But if you do that, your period will always be a multiple of the time between points, in this case, 0.05 seconds. (This is part of what must have happened in the previous post.)
  • Some students—sometimes with prodding—would take the time difference across several waves, and divide by the number of periods. It’s not obvious to students that this technique gives a more precise measurement for the period. It’s interesting to think about how we know that this is so; for example, if you use five periods, it’s now possible to get any multiple of 0.01 seconds; but does that mean it’s actually more precise? (Yes.) This technique also gives students a chance to be off by one: do you count the peaks? No. You have to count the spaces between the peaks. (Getting students to explain why is illuminating.)
  • We could imagine trying to fit a sinusoid (and some students would, but it’s hard) or using a Fourier Transform (which is a black box for most students).

But this post is about an alternative to all of these techniques—one that uses all the data and gives a much more precise result than the first two.

You can read about this is excruciating detail in a paper I wrote. And I made one particularly careful group of students this (awkward and quickly-made) video describing the technique. So I will be brief here. Continue reading Wave Slicing and Remainders: a cool way to find the period of a periodic function