Frequency, Pitch, and Amplitude: Developing Models
Lesson 2 of 7
Objective: Students will be able to develop models demonstrating the relationships between characteristic properties of waves.
Students at this point have just been introduced to wave properties. This lesson is designed to develop a deeper understanding of wave properties through the creation of models. I have found that this lesson typically takes two days. As students are building their foundational understandings in models and in wave properties, I find that this lesson in particular is a lesson not to rush through.
Waves can be a challenging topic for a middle school student. With many waves being "invisible", it can be a difficult concept for a student to relate to and explain. As a result, they have many misconceptions about wave behavior. In order to allow students to make connections, this lesson helps make wave properties visible as they create models to demonstrate property relationships (SP2 Developing and Using Models, CCC Patterns). The Next Generation Science Standards have identified an essential question that can drive student learning as, "What are the characteristic properties of waves and how can they be used?" This lesson focuses specifically on the following NGSS standards:
MS-PS4-1 Use mathematical representations that describes a simple model for waves that includes how the amplitude of a wave is related to the energy in the wave.
The disciplinary core idea PS4-A explains that a simple wave has a repeating pattern with a specific frequency, wavelength, and amplitude. In turn, creating relationships between these wave properties is critical for student understanding. Graphs and charts are a great method for representing patterns in data mathematically. With the use of slinkies, students can discover these relationships and gather data for developing their own graphs showing property relationships.
Have the students refer to their Unit Plan that includes the Essential Question, "What are the characteristic properties of waves and how are they used?" along with the "I can" statements/skills for the unit. In the previous lesson, the students worked to break down what the essential question means. As this is only the second day of the unit, take time to break the question down again to make sure that all students are connecting to what their focus is.
Here's how to break down the question. First read the EQ as a class. Then examine key words. For example, ask students what "characteristic", "properties", and "how are they used" might mean. Many middle school students have an especially difficult time verbalizing what a property is. Without this understanding, it will be challenging for them to connect to what they are supposed to be learning. The conversation may be very similar to the previous day's lesson; however, hopefully, it may go a little faster! A conversation may unfold something like this:
Teacher: What does the word characteristic mean? Your response does not have to be connected to science. In your everyday life when you hear that word, what does it mean to you?
Student: Something that describes something.
Teacher: Absolutely! One characteristic about me is that I love science. What does the word property mean to you? Again, your response does not have to be connected to science. In your everyday life when you hear the word property, what does it mean to you?
Student: Something you own, something that is yours.
Teacher: Absolutely! Now, I am wondering how a wave can own something. What is it that a wave can own?
Student: Like what type of wave it is or what it looks like.
Teacher: Hmmm....characteristic and property both seem like they mean similar things. They are both words that make us think of descriptions of things. I wonder why both words are in this Essential Question. (Pause....Wait time! Let the students think about why both words are needed.) Let me ask you this. I notice that in this question the word characteristic is used a little differently. It says, "characteristic properties". I wonder how the meaning of the word characteristic changes when it is put in front of another word like this. For example, what if I said, "What are the characteristic properties of a science teacher?" What does the word characteristic mean now?
Student: Typical or common.
Teacher: Ahh! That makes sense. So, what we are looking for here it seems is typical or common ways to describe waves. Maybe it is the things that waves might have in common.
Teacher: I am noticing that there is a second part to this EQ. It says, "...how can they be used". What do you think we should look for when making connections to that?
Student: Maybe...ways that humans might use them in the real world?
Teacher: Today we are going to continue to identify characteristic properties of waves. In addition, we are going to investigate the relationships between these properties.
Say, "Yesterday, we looked at the Skills 2 and 3 "I Can" statements. We identified that we needed to look at properties such as amplitude, frequency, wavelength, and pitch. What is important when looking at an "I Can" statement is to identify what you need to do with each of those properties. Look at these skills again, what is it that we should be able to do with these skills?"
Students should offer things like "find relationships", "provide evidence" and "create models".
Say, "Create models? Hmmm. What does that mean?"
Students may offer many things, but ultimately they come to the conclusion that a model is a visual representation of a concept.
Allow students to brainstorm ideas of what a model could mean. Students often come up with these ideas:
- Draw a diagram. (For more information about important elements of a diagram, you could look at this lesson.)
- Create a graph predicting how variables would affect each other.
- Write words in the shape of its definition. (Want an example of what this might look like? Go here!)
- Build a prototype.
- Make a demonstration.
To help guide your discussion it may be helpful to read the following article. In the article, Joseph Krajcik and Joi Merritt explain in the article "Engaging Students in Scientific Practices: What does constructing and revising models look like in the science classroom? Understanding A Framework for K−12 Science Education" that:
"Models provide scientists and engineers with tools for thinking, to visualize and make sense of phenomena and experience, or to develop possible solutions to design problems (NRC 2011). Models are external representations of mental concepts. Models can include diagrams, three-dimensional physical structures, computer simulations, mathematical formulations, and analogies."
Explain that today students will be creating models that represent relationships between some of the characteristic properties of waves. Explain that to practice this, they will be using a "Laser Light Show" to model the relationship between any characteristic properties of waves of their choosing. Explain how important evidence is in this activity. When students create their model, they must demonstrate it for you in order to explain the evidence that their model accurately shows of the relationship.
I provide the students with a "Laser Light Show" "contraption" to experiment with various properties of waves such as amplitude and pitch. Want a Laser Light Show Apparatus? Here is where I got them. If you don't have them, it is fine! Ask students to come up with their own ideas, provide them with slinkies, tuning forks, etc. The great thing about models is that the possibilities are endless! The key here is that when students show you their models that they can do three things:
- State the relationship.
- Produce an accurate model.
- Provide evidence their model demonstrates.
As students are experimenting with the Laser Show to identify relationships between characteristic properties of waves, I stop in and ask students, "Are you noticing any relationships between any characteristic properties of waves?". Without checking in, students can lose focus of their goal.
( I want to emphasize that this is hard to capture on film. I wanted to give you a visual of what the Laser Light Show Apparatus does; but it is just impossible to capture all of the awesomeness of this apparatus on video. They are so cool!)
Once each group has presented their models to you, tell them that they will be creating three more models to present to the class. Students have access to whistling tubes, slinkies, tuning forks, paper, pencils, or classroom materials of their choosing that they feel like would help them in their model. There are no specific materials that students have to use. Students create models of the following wave properties:
- The relationship between energy and amplitude.
- The relationship between frequency and pitch.
- The idea that pitch/frequency are independent of amplitude (they show no relationship).
Number 3 is definitely the most challenging. One misconception that students have is that amplitude changes frequency. They think that adding energy speeds up the frequency when in fact they are independent of each other (you can have a high amplitude, high frequency/pitch and a low amplitude, high frequency/pitch).
As students work, encourage them to practice what they are going to share to the class. They should discuss and plan which group members will demonstrate each model and which members will explain each model to the class. Emphasize that they must include evidence of the relationship in their explanation.
After each group presents, ask the students in the audience to pose any follow up questions they still have. I especially encourage students to ask about what evidence was shown of the relationships. I explain to the students that when students ask follow up questions, they are not being critical. We are simply engaging in science discourse. We are going to have a conversation about science. In our quest for understanding, we are all in it together!
Here are a few examples:
Energy vs. Amplitude
Frequency vs. Pitch
Amplitude vs Frequency/Pitch
To close, have students use their hands to demonstrate direct and inversely related wave properties. For a direct relationship, students would put two thumbs up indicating that as one variable increases, the other increases. For an inverse relationship, student put one thumb up and one thumb down to show that as one variable increases, the other decreases. I ask them to show the following:
- Frequency and Pitch (two thumbs up)
- Energy and Amplitude (two thumbs up)
- Frequency and Wavelength (one thumb up and the other thumb down)
- Wavelength and Pitch (one thumb up and the other thumb down)
I end with the toughest -- Amplitude and Frequency. (Students should do something to show that they are not proportionally related).