# More than Mobile

Physics Toolbox apps were ultimately developed simply because they were extremely mobile and presented a nearly 1:1 ratio for my students, in contrast to most of the commercial science education probeware I had at my disposal.

However, I have recently realized as an educator that they have become something more. While most of the Lessons presented on our website are inquiry labs that are only slightly modified from what could be done anyone with any kind of probeware, there are a few that actually really couldn't have been easily done at all before using smartphones.

One of these is the *quantitative *experience of "beats." As an educator, I prided myself on having my students derive nearly every single equation from their own data and analysis. One of the few mathematical relationships that I let slip by, however, was the equation for calculating beats:

**Beat frequency = |tone 1 frequency - tone 2 frequency|**

This relationships seems extremely straight-forward, but the reality was that it was anything "but" for most of my students - easy to calculate, but not straight-forward in terms of its justification either thinking about the superposition of waves. Given the only the equation, students were left to rely only on authority.

Typically, my demonstration for beats would consist of two resonance boxes and the addition of a small metal weight or piece of clay to slightly decrease the frequency of one of the forks. The problem with this was that this did not lend itself to quantitative analysis in which students could derive the mathematical relationship for themselves. Using an FFT analyzer for each fork at its different frequency would resolve this issue, but wouldn't allow students to take control of the experiment in small groups or on their own. In the end, it was a fascinating interactive demonstration, but it would leave me wanting more for my students.

Using mobile devices as sound generators with known frequencies easily solved this problem. Not only can smartphones easily modify the tone they produce by a single Hertz, but the range of analysis is much wider than when working with a single resonance box and a mass to modify its frequency. Truly curious students will want to know if the relationships they observe hold for two interacting low frequencies as well as two interacting high frequencies. Now, with mobile devices, they can!

Check out a suggested Beats lesson template, and feel free to provide us feedback!