# Revisiting Wave Mathematics

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## Objective

Students will return to using the relationships between energy, frequency, and wavelength with regard to electromagnetic waves.

#### Big Idea

There are so many aspects to the study of electromagnetics - it is important to revisit and reinforce ideas on a regular basis.

## Warmup

25 minutes

As a followup to the previous lesson I provide my students with a set of radioactivity warmup questions. The first grouping of questions mirrors the work we completed the other day regarding nuclear decay modes (HS-PS1-8). The second grouping of questions promotes some synthetic thinking: how can one imagine a given nucleus turning into some second, target nucleus? The final question makes a link between this topic and the computational tasks of manipulating energy, wavelength, and frequency (HS-PS4-1).

Students work alone or with a neighbor as I wander around to check on progress and probe for understanding. As we are revisiting the computational aspects of the final question, I remind students to look back in their notes for similar, model problems.

After several minutes, I ask for students to voluntarily put answers on the board for others to view.

As the final question is different than the others and leads into the next segment of class, I separate the solutions into "part A" and "part B." This segment of class actually blends into the next segment - I use the final solution to discuss the wave mathematics of wavelengths, frequencies, and energies.

## Wave Mathematics Revisited

10 minutes

My intention during this portion of class is to re-introduce some of the computational aspects of wave relationships. I use the last warmup question as a vehicle to revisit these ideas. We take a look at the solution to that problem and locate a resource from a short while ago -  a problem set with formulas and an electromagnetic spectrum organized by frequency. In this short segment of class, the review of this one problem sets up our next assignment - a set of questions that present students the opportunity to demonstrate their understanding of the wave mathematics. I hand out the assignment and remind students that this is one of several options for the final segment of class. Students may engage in any one of the following activities:

- begin work on this new assignment due in one week

- finish collecting data for the recent Four Big Ideas investigation

- create graphs based on that data

- begin writing up the report of findings from the investigation.

## Self-Directed Time: Electromagnetics Assignments

45 minutes

I set aside some more time today for teams to collect data as part of a multi-day, multi-station exploration of electromagnetic phenomenon. As we near the end of our Four Big Ideas investigation teams naturally have different needs. I provide this "self-directed" time for teams and individuals to decide what to do: collect more data, create and analyze graphs for their upcoming reports, work the recently-assigned set of wave problems, or, perhaps, something I had not anticipated. One of our school's Learning Expectations is that all students become highly self-directed learners, so this time is a good opportunity to practice and demonstrate that.

Here, students begin to assemble; most teams need to collect at least a small amount of data so all students move to the back of the room and gather equipment and get started.

These students are trying to measure the separation of "bright spots" of a classic interference pattern. The lighting is set low so that this results of this station can be seen more distinctly.

Here is a terrific example of that interference pattern. by creating a large space between the double-slit barrier and the screen, the pattern can be easily seen and measured.

Here, some students are getting set up for one of the two induction stations: the fan is blowing on a small turbine which is spinning a magnet inside some coils and, as a result, generating some current. The computer in the background has a special file which converts the voltage reading from the turbine's terminals into an energy measurement (the integral of the power measured over a five-second window).

These two boys are exploring the photoelectric effect, looking for evidence that light behaves like a stream of particles. At this moment, they are using a blue light bulb and recording how the output of the photocell changes with distance form the bulb.

We continue in this mode until the end of class. By that time, some groups have completed their data collection and have moved on to the business of writing up their reports. By the end of class just two groups need data from one more station each.