1. Announcements 2/22/11 Prayer Dispersion lab due tonight Labs 4 & 5 due Saturday I will have office hours today

2. Interference Path length a. a.Constructive b. b.Destructive Demo: Moire pattern transparencies Video: Two outdoor speakers Ripple Tank image: wikipedia

3. Reading Quiz In a standing wave, the points that have the maximum vibration are called: a. a.nodes b. b.antinodes

4. Standing Waves Demo: Rubber tubing Image from Wikipedia

5. Standing Waves Will occur whenever you have two waves (same frequency, wavelength) moving in opposite directions Math: A cos(kx -  t) + A cos(kx +  t)  From trig.: cos(a–b) + cos(a+b) = 2cos(a)cos(b) Can occur via refletions of a single wave! But timing (frequency) has to be just right for it to occur over & over again Web demo, revisited http://www.colorado.edu/physics/phet/simulations/stringwave/stringWave.swf http://www.colorado.edu/physics/phet/simulations/stringwave/stringWave.swf Image by Colton

6. Demos Video: http://stokes.byu.edu/standing_script_flash.htmlhttp://stokes.byu.edu/standing_script_flash.html Demo: “Ladies belt” Videos: Bowling ball, goblet, [Tacoma Narrows bridge] Demo: Trumpet “Resonance”

7. Standing Wave Patterns Back to Ladies belt demo a. a.What kinds of patterns do you get? b. b.“node” vs “antinode” Harmonics

8. Standing waves on a string: “Closed-Closed” For stable patterns: L = _______ What are the frequencies? Relative to the fundamental frequency? L L  L 

9. Standing waves in air: “Open-Open” Quick writing: draw what you think the second harmonic should look like For stable patterns: L = _______ What are the frequencies? Relative to the fundamental frequency? Demo: Trumpet, again Open end L  Example: organ pipe

10. Standing waves in air: “Open-Closed” Quick writing: draw what you think the second, third, and fourth harmonics should look like For stable patterns: L = _______ What are the frequencies? Relative to the fundamental frequency? Why wasn’t trumpet in this category? Open end Closed end L 

11. Standing Waves in 2D Again, from Wikipedia Advertisement for Physics 318!

12. Standing Waves in 3D From Colton and Wienkes, Rev. Sci. Instr., 2009 a. a.Light waves, frequency = 10 GHz (microwaves) Advertisement for Physics 641! Do they exist? Class poll

13. Final Demo Flame standing waves