Harmonics and Standing Wave Patterns

The Standing Waves and Harmonics Video Tutorial explains how to construct standing wave diagrams for the various harmonics of a string or rope and explains how the frequencies and the wavelengths of the various harmonics are related to each other. Numerous examples, illustrations, and animations assist in the explanations.

The video lesson answers the following questions:

How do you draw the standing wave patterns for the various harmonics?
How are the frequencies and wavelengths for the various harmonics related?

Video

You can watch the video below, or click here to watch on YouTube (opens in a new tab).

To improve the effectiveness of the learning experience, The Physics Classroom has provided the following tools:

Additional and Related Learning Tools

Physics Interactives: Standing Wave Maker
Our interactive simulations allow you to playfully alter a variable and observe the result in the form of an animation. Ask a question and pursue the answer. This one challenges you to find "just the right frequency" to cause a rope to vibrate as a standing wave. Great tool! And follow it up with the Concept Checker (below).

Concept Checkers, Standing Waves
A Concept Checker provides a student with a quick assessment of understanding associated with a resource on our website. This one is intended to accompany the Standing Wave Maker simulation (above). Download the student activity sheet that goes with the simulation; work through the activity and then do the Concept Checker. It's a great way to further your learning.

Minds On Physics, Wave Motion Module, Mission WM7
This mission from our Minds On Physics program may be our most effective follow-up to the video. Give yourself the challenge and rise to the occassion. You got this!

Concept Builders, Waves and Sound Chapter: Name That Harmonic (Strings)
This Concept Builder is also a great fit to the video. You will be challenged to detemine the harmonic number based on a standing wave pattern, relate the frequency of one harmonic to that of another, and determine the wavelength of a wave from the pattern and the length of the string (or rope).

Physics Classroom Tutorial, Vibrations and Waves Chapter, Lesson 4 - Nodes and Antinodes
When you need to quickly review, brush up, and revisit the ideas in the video, turn to the Physics Classroom Tutorial page that accompanies the video. This page discusses how to recognize a harmonic number from the pattern of nodes and antinodes in a standing wave diagram.

Physics Classroom Tutorial, Vibrations and Waves Chapter, Lesson 4 - Standing Waves and Harmonics
This Tutorial pages discusses the standing wave diagrams and the mathematical relationships for the various harmonics of a vibrating rope (or string or wire).

Teacher Resources

Curriculum Corner: Wave Motion
Try our Curriculum Corner for a Think Sheet or a whole unit of Think Sheets and get your students thinking about waves. You will find a Think Sheet here on the topic of standing waves. If the video is homework; then these are awesome next day starters. This is free curriculum for the taking. And for a few extra bucks, you can obtain the source documents and purchase a license to place them and any deriviative from them on your course management pages; see the Solutions Guide.

Physics Interactives: Standing Wave Maker
Our interactive simulations allow a student to playfully alter a variable and observe the result in the form of an animation. This one on standing waves challenges students to find "just the right frequency" to cause a rope to vibrate as a standing wave. Using our student activity sheet, they will record data and look for patterns in the data, leading to an equation that relates the frequency of a harmonic to the harmonic number and the frequency of the fundamental. Don't miss the classroom-ready student activity sheet and the accompanying Concept Checker. When put together - simulation, student activity sheet, and Concept Checker - you have the skeleton of a highly engaging lesson plan.

Minds On Physics, Wave Motion Module, Mission WM7
This mission from our Minds On Physics program may be our most effective follow-up to the video. It's a great challenge for students and worth the class time to do.

Concept Builders, Waves and Sound Chapter: Name That Harmonic (Strings)
This Concept Builder is also a great fit to the video. Students will be challenged to detemine the harmonic number based on a standing wave pattern, to relate the frequency of one harmonic to that of another, and tp determine the wavelength of a wave from the pattern and the length of the string (or rope).

Physics Classroom Tutorial, Vibrations and Waves Chapter, Lesson 4 - Nodes and Antinodes
When students need to quickly review, brush up, and revisit the ideas in the video, point them towards the Physics Classroom Tutorial page that accompanies the video.. This page discusses how to recognize a harmonic number from the pattern of nodes and antinodes in a standing wave diagram.

Lesson Notes

Download (opens in a new tab) or view below

Slides

Do you like the slides we used? They are available in our low cost Teacher Presentation Pack, along with other updated materials used in our presentation.