### Summary

In this lesson, students observe standing waves in strings, rods, pipes, and hoops through videos and teacher demonstrations. Students investigate the ‘particle in a box’ problem using a PhET simulation, which presents the electron as a wave with discrete wavelengths. Students investigate wave functions as orbitals in atoms. Students investigate and explain the spectral emission of hydrogen atoms.

### Essential Question(s)

Is light a wave or a particle? Is a particle a wave?

### Snapshot

**Engage**

Students complete the I Think/We Think instructional strategy about standing waves and observe a demonstration of a real standing wave on a string.

**Explore**

The students observe the teacher demonstrations about standing waves in strings, rods, pipes and hoops through videos.

**Explain**

Students investigate the ‘particle in a box’ problem using a PhET simulation, which presents the electron as a wave with discrete wavelengths.

**Extend**

Students investigate wave functions as orbitals in atoms through videos and readings. Students investigate and explain the spectral emission of hydrogen atoms using spectroscopes and lamps.

**Evaluate**

Students use the 3-2-1 instructional strategy to show what they have learned about wave properties in particles.

### Materials

Lesson Slides (attached)

Particle in a Box Student Handout (attached, one per student)

Wave Functions in Atoms Student Handout (attached, one per student)

Hydrogen Emission Lines Student Handout (attached, one per student)

Teacher’s Guide: Particle in a Box handout (attached, optional)

Teacher’s Guide: Wave Functions in Atoms handout (attached, optional)

Teacher’s Guide: Hydrogen Emission Lines handout (attached, optional)

Singing rods demonstration kit

**Materials Included in Kit:**Aluminum rod, ½" diameter, 24" long

Aluminum rod, ½" diameter, 18" long

Aluminum tube, ½" o.d., 24" long

Metal rod, ?" diameter, 24" long

Rosin bag, 2 oz

Sound tubes

**Materials Included in Kit:**Steel tube, 2" diameter, 17" long

Wire disks, 2¼" diameter, 20 mesh, 3

Whirly tube

Standing wave generator-

Adjustable strobe light

Science Notebooks

Computer or access to computer lab (1 per 2 students)

Spectroscopes or spectral slides

Hydrogen and helium lamps

Lamp power supply

### Engage

30 Minute(s)

Use the attached **Lesson slides** to present the lesson.

Display **slides 3-4 **to introduce the essential questions and learning objective to the class.

Display **slide 5**. Show the video called **What is a Standing Wave?** Answer a prompt about the video. Encourage students to jot down some notes and key points in their Science Notebooks while watching the video.

Once the video has finished, display **slide 6** and introduce the I Think/We Think instructional strategy. Have the students divide a page in their Science Notebooks into two columns. Instruct students to label the left side “I Think” and the right side “We Think.” On the left side under “I Think,” ask the students to write their independent response to the prompt: “Describe a Standing Wave.” Provide students with two minutes to write their answer. Inform them that they need to use the terms *node* and *antinode* in their description.

Have students find a partner. Ask them to share with their partners what they have written on their page and together come up with a new description. Ask them write down the new description on the right side under “We Think.” Remind them to use the terms *node* and *antinode* in their description. Give the pairs two-three minutes to discuss and write down their new description. Ask some of the students to volunteer and share what they have written.

Display **slide 7** and tell the students to watch a demonstration of a real standing wave on a string. Inform students that they are going to answer a prompt about the video, and they should jot down some notes and key points in their Science Notebooks while watching the video. Start the video **Modes on a String**.

Pause the video at 4:55 minutes. Ask the class to predict the next frequency that will produce a standing wave and determine how many nodes and antinodes the wave will have.

Pause the video at 5:52 minutes. Ask the class to predict the next frequency that will produce a standing wave and determine how many nodes and antinodes the wave will have.

Display** slide 8**. Explain to the class that they are to participate in another “I Think/We Think.” Ask them to create a new T-Chart on a clean sheet of paper in their Science Notebook. Have them label the left side “I Think” and the right side “We Think.”

On the left side under “I Think,” have the students independently write their response to the prompt: “How are standing waves dependent on frequency and why do only certain frequencies produce standing waves?” Give students two minutes to write their answers. After two minutes, ask students to find a partner. Ask them to share with one another what they have written on their paper and come up with a new response.

Ask the students to write down the new response on the right side under “We Think.” Give the students two-three minutes to discuss and write down their new description. Ask for volunteers to share what they have written.

### Explore

25 Minute(s)

Display **slide 9** and show students the video Flexural and Longitudinal Waves.

Pause the video at 55 seconds. Ask the students “Why was the instructor able to hold the rod only in certain places without destroying the wave?”

After a quick discussion about the question, start the video again and let it play until complete.

Display **slide 10**. You will perform a ‘Singing Rods’ demonstration. You will need at least one aluminum rod and some rosin. During the demonstration, hold the rods at two different node positions and then at any position away from the node. Ask the students why the rod stops ‘singing’ when you hold it away from the node.

Suggest they think about the first video where they could see the wave in the rod.

Display** slide 11 **and ask students the following questions:

Which wave picture(s) go with the demonstration based on where the rod was held?

What should the fourth wavelength be?

Call on a few students to answer the questions.

If you are unable to perform the Singing Rods demonstration, unhide **slide 12** and show the video “Singing Rods and Tubes.”

Display **slide 13 **and perform the Whirly tube demonstration. You will need one whirly tube. Hold the tube just above the wide end and whirl it slowly and then speed up until you hear the first tone. Spin the rod faster to create a second tone. Spin the rod even faster to create a third and then fourth tone.

Ask the students the following questions:

Why can only four tones be heard? Why does the tone instantly jump up instead of continuously increasing?

Where are the missing tones that the tube can’t produce?

Call on a few students to answer the question. If needed, guide the students to the answer that only certain standing waves can fit in the tube.

Display **slide 14.** Inform students that this image shows how some waves fit perfectly inside the tube. Any wavelengths that are in-between the lengths shown will not fit in the tube. Have students get out their Science Notebooks and draw the picture for the fourth mode.

Next, perform the sound tubes demonstration. You will need one sound tube. Explain to the class that this is another example of standing waves in tubes.

Perform a demonstration of standing waves with a “Stringin’ It” machine or other wave generator and a strobe light. Demonstrate at least three different wavelengths during the demonstration. Ask the students the following question: How many nodes and antinodes are in each of the standing waves generated?

If you do not have the materials to perform the Sound Wave or a Stringin’ It machine, demonstration, unhide **slides 15 and 16** and demonstrate these waves. Display **slide 17** and have students draw a picture of each standing wave. Instruct them to label all of the *nodes* and *antinodes*.

End Day 1.

### Explain

30 Minute(s)

Start here for Day 2. Remind students of the essential questions and the learning objective.

Inform the students that they will investigate something known as quantum states. Use **slide 18** to define wave functions. Have students record this definition in their Science Notebooks.

Display **slide 19.** Present the Schrodinger Equation to students. This equation predicts the wave function and the behavior of the quantum state. It is like Newton’s Second Law for Classical Motion. This equation factors time, mass, position, kinetic and potential energies.

Display **slide 20.** Show the video What is the Schrodinger Equation, Exactly?

Display **slide 21**. Present some unusual ideas about wave functions.

Display **slide 22. **Use the slide to explain the meaning or particle in a box.

Display **slide 23. **Use the slide to define probability densities and have students record this definition in their Science Notebooks.

Display **slide 24**. Introduce the Particle in a Box simulation. Pass out the attached **Particle in a Box** handout to each student. Place the students in pairs and have them share a computer to complete the handout. Have students navigate to the PhET simulation Quantum Bound State.

**Slides 25 - 28. ** These slides may be used in teacher discussion or presented if students can’t access the simulation.

**Slide 25. **Emphasize that the bottom graph is the wave function for the first mode of the standing wave.

**Slide 26. **Emphasize that the bottom graph is the wave function for the second mode of the standing wave.

**Slide 27. **Emphasize that the bottom graph is the wave function for the third mode of the standing wave.

**Slide 28. **Emphasize that this graph shows the probability densities for the first three standing waves. This graph comes from the square of the first three wave functions. The anti-nodes represent the most probable location of the electron in the box. The nodes represent positions where the electrons cannot exist.

### Extend

Display **slide 29**.** **Assign students a new partner and pass out the attached **Wave Functions** handout to each pair of students.

Have students read through Figure 2 of the handout. Then pause the activity.

Display **slide 30.** Show the Standing Wave in Vibrating Hoop video. Emphasize that circular standing waves exist and electrons in atoms can be thought of as standing waves.

Have students read through the rest of the handout. But do not have them answer the questions.

Display **slide 31**. Show Atomic Orbitals 3-D video. Emphasize that each dot in images represents a possible electron position in an atom.

Allow students to answer the handout questions. Take up the handouts to review or grade.

End Day 2 here.

Display **slide 32. ** Pass out spectroscopes or diffraction gradient slides to students. Tell students you are going to turn on a lamp that contains energized hydrogen atoms. Turn off all of the room lights. Turn on the lamp and allow students to view the light with their spectroscopes. Tell students you are replacing the hydrogen lamp with a helium lamp that contains excited helium atoms. Turn on the helium lamp and allow students to observe the light.

Display **slide 34**. Discuss questions with the class. Have students record responses in their Science Notebooks.

Display **slide 35. ** Pass out the attached **Hydrogen Emission Lines** handout to each pair of students. Pair up students and allow students time to read through the handout and answer the questions in their Science Notebook or on notebook paper. Collect the papers or Science notebooks to review when students are finished.

### Evaluate

Display **slide 36** and introduce the students to the 3-2-1 instructional strategy. Inform the students that they will use this strategy to assess what they have learned throughout this lesson. Students will answer the following in their Science Notebook or on a sheet of notebook paper.

3 -Statements showing what you learned about electrons having properties of waves.

2- Questions you have about electrons having properties of waves.

1- Thing you found most interesting about electrons having properties of waves.

### Resources

Arbor Scientific. (2009 February 23). Dramatically demonstrate nodes, Anti-Nodes & standing waves! | Singing rods | Video. YouTube. Arbor Scientific. https://www.youtube.com/watch?v=EYhwKve0MZU

K20 Center. (n.d.). 3-2-1. Strategies. https://learn.k20center.ou.edu/strategy/117

K20 Center. (n.d.). I think/We think. Strategies. https://learn.k20center.ou.edu/strategy/141

Koon Physics. (2020 December 24). Hydrogen discharge lamp. Video. YouTube. https://www.youtube.com/watch?v=JiKb9jcD0Xs

Martin, Geoff. (2015 August 28). Modes on a string. Video. YouTube. https://www.youtube.com/watch?v=cnH2ltfW48U

New Zealand Institute of Physics. (2022 May 30). Physics demonstration: Singing rods and tubes. Video. YouTube. https://www.youtube.com/watch?v=3zrtu6c71Xk

NPS Physics. (2016 June 9). Flexural and longitudinal waves - Singing rods demonstration. Video. YouTube. https://www.youtube.com/watch?v=sIw0Fh-fXIM

Physics Demos. (2016 August 20). Standing wave demo: Vibrating hoop. Video. YouTube. https://www.youtube.com/watch?v=df3oJPi9_mg

Sci Pills. (2020 February 26). Atomic orbitals 3D. Video YouTube. https://www.youtube.com/watch?v=Nr40fnfHccQ

Steve Spangler Science. (2017 January 25). Singing pipes - The Spangler effect. Video. YouTube. https://www.youtube.com/watch?v=LCEvzU9sh4Y

Steve Spangler Science. (2009 March 2). Sound hose - Whirly tube. Video. YouTube. https://www.youtube.com/watch?v=CuGnsW0ysrA

The Physics Classroom. (2023 January 5). What is a standing wave? Video. YouTube. https://www.youtube.com/watch?v=aTaT1orpHg8

3D Modeling & STEM. (2019 November 19). Amazing 3D standing wave motion. Video. YouTube. https://www.youtube.com/watch?v=vraQIQSW-Rc

University of Colorado-Boulder. (n.d.). Quantum bound states. PhET simulations. https://phet.colorado.edu/en/simulations/bound-states

Up and Atom. (2018 July 6). What is the Schrödinger equation, exactly? Video. YouTube. https://www.youtube.com/watch?v=QeUMFo8sODk