# Wave Properties

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## Objective

Students will be able to manipulate information to write wave equations, sketch waves, and describe key wave characteristics.

#### Big Idea

Waves can be described verbally, graphically, and algebraically.

## Make a List!

15 minutes

To get students back to thinking about health risks and radiation (NGSS standard HS-PS4-4), I present my students with a multi-task opener today. First I ask them to make a list of things they've heard can be hazardous to their health. I encourage them to create the list without judgment as to whether or not they believe the health risk is real. I also encourage them to try to create as long a list as they can in two minutes.

When the two minutes are up, they turn and talk with a classmate, sharing their lists. Immediately after that, I collect thoughts from the group at the board, creating a much longer list than any single individual has made. My purpose here is to provide students who produced short lists a larger menu of options to choose from for the final segment of this opener.

The final task for students is to take their list and analyze it. They put a star next to 3 things that are LIKELY TRUE, underline 2 things that LIKELY FALSE, and circle one thing that are fairly SURE IS FALSE. While we do not process these choices now, I ask my students to ensure that they can retrieve this list at a later date. We use this list as part of an upcoming assignment.

## Wave Properties Presentation - Functions of Time

25 minutes

To transition into this segment of class, I remind students that we used the phrase "electromagnetic waves" the other day when we first spoke about radiation. We must develop a certain level of insight into waves if we're going to understand radiation. This insight is exactly what NGSS HS-PS4-1 calls for.

The skills students need are sketching waves, writing wave equations, and extracting key information (amplitude, period, and frequency) from either a graph or an equation. In other words, given an equation of a wave (or a sketch), students should be able to determine the amplitude and the period, and, given the amplitude and period students should be able to write the equation of the wave and sketch it. To that end, I present at the board while students take notes and respond to questions throughout this time. I start with a wave template that eventually fills out, to a richer drawing, to include a variety of wave ideas.  I demonstrate each of the aforementioned skills and solicit student ideas and questions along the way. When done, students have a wave equation template that identifies where the amplitude and period are embedded (Y = A*sin(2*pi*t/T)).

For the time being, I limit the discussion to waves as functions of time. We discuss waves as function of space later today. After the discussion runs its course, we transition to some practice problems.

## Practice with Wave Ideas

20 minutes

I provide students with a short set of practice problems to check for understanding (see part A and part B). Students work on these problems in their notebooks and are encouraged to collaborate and check in with me. I roam the room looking to assist where necessary. After a few minutes, I post the solution to the first wave practice problem on the Smartboard in order to assist those who may be struggling to get started.

The investment in this practice time is heightened by the upcoming one-question quiz. Students have an opportunity, at no risk, to get a high score on a 20-point single question quiz. As this is something we have done several times throughout the year, they are familiar with the zero-risk, high-reward possibility and, typically, engage fully in the practice problems. At the end of about 20 minutes or so, I ask students to cease collaboration and to try the one-question quiz.

## One-question Quiz

15 minutes

Having provided my students with a quarter-page piece of paper each, I reveal the one-question quiz on wave mathematics for students to attempt. Students work individually to address the question, though they may consult their notes. They also indicate the lowest score (out of 20 points) that they would accept. This odd arrangement is welcomed by students - this quiz, though unannounced before today, is a way that students can demonstrate their understanding of a new concept with zero risk. If they do well, I record the grade in my gradebook. If they do not meet their own standard, I don't count it. In my gradebook, I set the symbol "X' as an exemption grade:

My rationale for this structure is this: I really want a formative assessment of student understanding that builds an incentive for engagement yet introduces low anxiety about grades. I think with this structure I can accomplish all this within a few minutes of in-class time (the actual quiz) and out-of-class time (the assessment is very quick). A solution is provided for convenience.

## Functions of Space

10 minutes

As the quiz wraps up, I briefly introduce another way of looking at waves: as functions of space. Having created some comfort with waves that describe a change over time, I want my students to acknowledge and understand that waves also describe changes in space. The notes page for this segment is, naturally, quite similar to the previous instruction on temporal waves. This is both a benefit and an drawback.

The benefit is that there are no new forms of the equation to understand - the sine function is used again and is defined by just two parameters, as before. In addition, the skill set is exactly the same. Students can sketch the waves just as quickly as before and can extract information from the wave equation in the same ways using the same algebraic approaches. All of this allows us to, in a short time frame, discuss waves as a function of space.

The drawback is that such similarity can breed a casual link between the ideas of "period" and "wavelength." To an extent, this is appropriate as each defines the interval for a single cycle of a wave - its period (in time) or its wavelength (in space). But they are, of course, as different as one's age and one's height! Indeed, I ask my students how absurd it would be to receive the answer of "5 foot, 11 inches"  from someone whose age was requested!

I take some time to draw the distinction of the horizontal axes, assuring students that, in this class, if we mark that axis with an "x" it will mean distance and we'll indicate time with a "t." In addition, the use of the symbol lambda will be reserved for wavelength, while T will be used for period.

Though we will do more with these ideas later, I change gears and reserve the last few minutes of class for an exit ticket.

## Exit Ticket

10 minutes

In the final few minutes of class I show my students a question they need to answer individually. I remind them that they'll need to access their answer for an upcoming assignment. This exit ticket is a way for me to get students to consider wave properties, link those properties with the idea of energy, and set up a conversation in the future about the energetics of waves. Students write in their notebooks their best thoughts to the question: "What wave property would I alter if I wanted to change the energy of a wave . . . and why?"