Announcements 10/15/10 Prayer Long list of HW changes/corrections/clarifications, see email Dispersion lab due tomorrow. Labs 4 & 5 starting tomorrow Term.

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Announcements 10/15/10 Prayer Long list of HW changes/corrections/clarifications, see Dispersion lab due tomorrow. Labs 4 & 5 starting tomorrow Term project proposal due a week from tomorrow, ed to me directly, text in body of & figures (if needed) as attachments. a. a.Syllabus: “The term project is an opportunity for you to propose and conduct a simple experiment or to theoretically, mathematically, or computationally investigate an aspect of the course in more depth.” b. b.Groups of 2 are OK. Groups of 3 only with permission. c. c.At least 15 hours of work (per person, if in a group). d. d.Guidelines/Grading info: fall10/project/guidelines.htm fall10/project/guidelines.htm e. e.Ideas: fall10/project/ideas.htm fall10/project/ideas.htm f. f.Some actual projects: fall10/project/actualprojects.htm fall10/project/actualprojects.htm

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

Standing Waves Demo: Rubber tubing Web demo, revisited Image from Wikipedia

Standing Waves Will occur whenever you have two waves (same frequency) moving in opposite directions a. a. Math: A cos(kx -  t) + A cos(kx +  t)  From trig.: cos(a–b) + cos(a+b) = 2cos(a)cos(b) Can occur with a single wave, if it reflects, provided… 1. vibration frequency is right, i.e. 2. reflection happens just right

Demos Video: Demo: “Ladies belt” Videos: Bowling ball, goblet, [Tacoma Narrows bridge] Demo: Trumpet “Resonance”

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

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

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

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 =_____

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

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

Demos PVC pipe vs. Spectrum Lab (skipped for now) Flame standing waves