Mathematical Analysis of Closed-End Air Columns

The Closed-End Air Column Problems Video Tutorial demonstrates how to approach Physics word problems involving closed-end air columns. Mathematical formulas and relationships are reviewed and an effective problem-solving framework is presented. Then Mr. H proceeds to demonstrate the use of the formulas and framework using five examples.

The video lesson answers the following questions:

1. What are the formulas one needs to solve a problem involving an closed-end air column?
2. How does one solve an closed-end air column 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

The Calculator Pad, Sound Waves Chapter, Problem Sets SM19 - SM22
When you need practice with problem-solving and guidance on how to approach them, the go-to location is The Calculator Pad. You will find problems that you can solve and check with immediate feedback. And many of the problems are accompanied by an audio-guided solution. It's all free. It's all good. And it is going to be difficulty to find anything comparable.

Minds on Physics, Sound Waves and Music Module: Mission SM11 - Mathematics for Closed-End Air Columns
Need practice with the mathematics of closed-end air columns? Spend 10 minutes on this mission of Minds On Physics and raise your game to a higher level. When you get stuck, the Help button will be your friend. Give it a try!!

Concept Builders, Waves and Sound: Name That Harmonic (Closed-End Air Columns)
This Concept Builder will sharpen your skill at recognizing relationships between the standing wave patterns for an closed-end air column and the frequencies and wavelengths of the various harmonics.

Physics Tutorial, Sound Waves and Music Chapter: Closed-End Air Columns
Our video tutorials are motivated by the existing written tutorials on our website. This page was the motivation for the video.

Teacher Resources

Curriculum Corner, Sound: Resonance and Close-End Air Columns
Try our Curriculum Corner for a Think Sheet or a whole unit of Think Sheets and get your students thinking about closed-end air columns. You will find the video is closely correlated to the Think Sheet. 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 password-protected course management pages; see the Solutions Guide.

The Calculator Pad, Sound Waves Chapter, Problem Sets SM19 - SM22
When your students need practice with problem-solving and guidance on how to approach them, the go-to location is The Calculator Pad. You will find problems that can be solves and checked with immediate feedback. Many of the problems are accompanied by an audio-guided solution. The free version is awesome. The paid version is even awesome-er. With a low-cost Task Tracker subscription, you can customize the problem sets, write your own problems and problem sets, and track student progresss.

Minds on Physics, Sound Waves and Music Module: Mission SM11 - Mathematics for Closed-End Air Columns
Do your students need more practice with the mathematics of closed-end air columns? Have them spend 10 minutes on this mission of Minds On Physics and raise their game to a higher level. When they get stuck, the Help button will be their friend. If you have a Task Tracker subscription for MOPs, you can customize it to your liking, set up scoring rules, and retrieve student scores.

Minds on Physics, Sound Waves and Music Module: Mission SM10 - Harmonics for Closed-End Air Columns
There's nothing like a Minds On Physics mission for insuring understanding. This one pertains to resonance in closed-end air columns ... and brings great closure to the topic. Advise students to use the Help button when they get stuck.

Concept Builders, Waves and Sound: Name That Harmonic (Closed-End Air Columns)
This Concept Builder will sharpen student's skill at recognizing relationships between the standing wave patterns for closed-end air columns and the frequencies and wavelengths of the various harmonics. And it works well with Task Tracker.

Science Reasoning Center, Sound Waves: The Sound of Music
Looking for something different? This activity uses two tables to compare and contrast the frequency, wavelength and speeds of the various harmonics produced by open- and closed-end resonance columns. The frequency composition of a clarinet and a flute are compared to one another. Questions target a student's ability to select information from a complex data table or a graph, to identify the relationship among the variables wavelength, frequency, speed and harmonic number, to use such relationships to make comparisons of the sounds produced by two different air columns, and to combine information in a table with information in a graph in order to identify appropriate conclusions.

Physics Tutorial, Sound Waves and Music Chapter: Closed-End Air Columns
Our video tutorials are motivated by the existing written tutorials on our website. This specific page provides a great review of the video. Consider providing a link to this Tutorial page from your Course Management System.

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.