# Wave Relationships

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## Objective

Students will be able to describe the qualitative relationships between frequency, wavelength and speed.

#### Big Idea

Students will use information from simulations to develop qualitative relationships for wave quantities.

## PhET Simulation: Wave on String

45 minutes

The goal of this class is for students to use a simulation to investigate how different properties affect each other in a transverse wave. Students are developing models and relationships between properties like amplitude, wavelength, frequency and wave speed that they will further investigate with a lab in the next lesson (SP2). By defining these relationships, students complete HS-PS4-1. The simulation helps students to identify the relationships by measuring the different properties of a transverse waves and analyzing data (SP5).

To begin class, I ask students to return to the packet (PhET Simulation Activity) that we started on in the previous class. I demonstrate how to start Part 2 again since we ended class with that. Then I ask them to work through Part 2 and create a graph. I allow students to create the graph any way the want, including through Plotly, as long as they have a sketch on their papers. Once they have graphed their data, they can see from the hyperbolic shape that frequency and wavelength are inversely proportional.

I give students about 10 minutes to complete Part 2 before I explain how to complete Parts 3 and 4 with the wave speed. Since it is a little more complicated, I show them that the need to pause and use the step button to measure a distance of 50 cm.

As seen in the picture above, I show students that they need to start at a peak of a wave and reset the timer. Then they can use the step button until the peak of the wave has reached 50 cm. Then they record the time and use the distance to find the speed of the wave. After I show students how to get the time and then determine the speed, I give them about 25 minutes to complete the remaining parts.

## Wave Relationship Discussion

10 minutes

After students have finished the simulation, I ask the class to discuss their results. To do this, I write Inversely Proportional, Directly Proportional and No Relationship on three whiteboards in the classroom. We go through each relationship that the students investigated during the simulation and I ask them to move to the part of the room with the whiteboard that says has the relationship that they found. Then I ask one student from each group to talk about what they found with the data to back up their conclusion. We repeat this process for each relationship.

The relationships that we discuss are:

1. Does amplitude affect wavelength?

- There is no relationship between amplitude and wavelength.

2. Does frequency affect wavelength?

- There is an inverse relationship between frequency and wavelength.

3. Does the frequency affect wave speed?

- There is no relationship between frequency and wave speed.

4.Does string tension affect wave speed?

- There is a direct relationship between string tension and wave speed.

5. Does damping affect wavelength?

- There is no relationship between damping and wavelength.

Through the discussion, I find that students generally find the correct relationships. This simulation lends itself well to these relationships when collecting data. If students don't get these relationships, we talk about what they got and it typically comes up that they had a numbers that were a little off but they correlated that to a relationship. For example, if looking at the frequency and wave speed a student's data may look like f=50 Hz & v=60 ms;  f=80 Hz & v=63 m/s; f=100 Hz & v=64 m/s. For some students, these numbers appear correlated when in fact the speed essentially remains constant.

## Wave Labeling Checkpoint

5 minutes

To end class, I have students take the Wave Labeling End of Discussion Checkpoint. I do this so I can see what they have gained from the simulation and what they know about the different parts of the wave before we move onto more applications of the relationships in the next few lessons. The students work individually on this checkpoint and I ask that they label at least one of each part (crest, rarefaction, wavelength, etc.) of the wave that is being asked about in #1 and #2. When students finish, they bring them up to me and I grade them before the next class. A student sample is shown below. This is a great way to end this activity because both the students and I can see how they are progressing with the content they have learned in the past few lessons.