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### Standing Waves

• Standing waves are produced on a string if L = nλ/2, where L is the length of the string, λ is the wavelength, and n is a positive integer.
• In an air column open at both ends, standing waves occur if λ = 2L/n; in terms of frequency the condition is f = nv/2L.
• In an air column closed at one end, standing waves occur if λ = 4L/n, where n is an odd positive integer; in terms of frequency, the condition is f = nv/4L.

### Standing Waves

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Standing Wave on String 0:09
• Propagation Waves
• String with Both Ends Fixed
• Sine Wave
• Placing Two Nodes and Vibrating String
• Fundamental Frequency
• First Overtone
• Example 20:49
• Spring
• Hanging a Weight with a Pulley
• Air Columns 26:22
• Pipe Open at Both Ends
• Pipe Open at One End
• Example 41:56
• Container with Water
• Tuning Fork
• Resonance
• Length of Pipe Producing Wavelength
• Extra Example 1: String Sound Wave
• Extra Example 2: Block with Wire is Plucked
• Extra Example 3: Pipe Natural Frequencies