Mathematics of Standing Waves
The Mathematics of Standing Waves Video Tutorial discusses the mathematic formulas associated with standing waves and an effective strategy to solving such problems. The use of the formulas and the strategy are then modeled to solve six example problems.
The video lesson answers the following questions:
- What are the formulas one needs to solve a standing wave problem?
- How does one solve a standing wave problem?
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
Calculator Pad: Vibrations and Waves Chapter, Problem Sets WM10 - WM14
Tap the link to navigate to the Calculator Pad section. Scroll down and try any one of Problem Sets WM10 - WM14. This will be perfect practices. The problems get harder as you continue futher. Click the help links for problem-specific help.
Minds On Physics, Wave Motion Module, Mission WM8
When you can complete a Minds On Physics mission, then you know you understand. Give it a try; use the help link (textbook icon, lower right) as needed. 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 - Standing Wave Mathematics
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 wave mathematics. 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.
Calculator Pad: Vibrations and Waves Chapter, Problem Sets WM10 - WM14
The Calculator Pad section presents students with a collection or set of problems on a discrete topic. Problems include random numbers and a Check Answer button. Students can attempt the problem as many times as needed and access problem-specific help. Problem Sets WM10 - WM14 are great follow-ups to this video.
Minds On Physics, Wave Motion Module, Mission WM8
When a student completes a Minds On Physics mission, then they probably understand; there's little to no faking it with this tool. Take some class time to get their minds on physics.
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.
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 - Standing Wave Mathematics
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 Tutorial pages discusses the standing wave diagrams and the mathematical relationships for the various harmonics of a vibrating rope (or string or wire).
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.