Announcements 9/28/12 Prayer About that exam… a. a.In Testing Center, Saturday morning until Thursday evening b. b.No textbook, no notes c. c.See website for list of equations that I give you d. d.I’ll give you all constants/conversion factors/materials parameters you need (except for super easy ones, like 100 cm = 1 m) e. e.You can use your own calculator, but you’re on your honor not to store extra stuff in calc. memory f. f.18 multiple choice, 3 short descriptive answer, 6 worked problems, 1 extra credit (no partial credit on the e.c.) g. g.No time limit, but “time goal” is 2 hours avg (took me 39 mins, not including extra credit)

The equations I give you:

What to study? I’d recommend in roughly this order: a. a.Homework b. b.Class notes c. c.Old exams d. d.Book problems & optional HW problems More on the exam xkcd Some more specifics about the exam…

Waves Skipping: Oscillations, Ch. 15 a. a.If you don’t recall “simple harmonic motion”, please review on your own. Starting next lecture: Some sections from Physics Phor Phynatics, Dr. Durfee’s book Starting lecture after that: Complex numbers a. a.Clicker: Have you seen: e ix = cosx + isinx ? A = “have seen” B = “not” C = “maybe, but I can’t remember”

From warmup Extra time on? a. a.(nothing in particular) Other comments? a. a.This material starts the new unit, so it's not on the exam, right? b. b.Is the homework that's due today as time consuming as it looks? c. c.Can you get a standing longitudinal wave?

Wave intro: some math What do these functions look like? a. a.f(x) = x 2 b. b.f(x) = (x – 1) 2 Think: What would be an equation for a parabola that moves 1 m to the right every second? What will this function look like at 0 s? at 1 s? at 2 s? a. a.f(x) = (2x – 6t) 2 b. b.What is its “velocity”?

Sinusoidal waves Nothing special about parabolas… What does f(x) = cos(x – vt) look like at t = 0? at t = a little later? Add in “amplitude” Add in “phase” How to change spatial period? What if you want wave to move right-to-left instead of left-to-right? “Wave function”

Wave properties Definition: oscillating disturbance that transfers energy (but not mass). Direction of travel Direction of oscillation: transverse vs longitudinal Medium Examples… a. a.Water b. b.Earthquake (P & S) c. c.Sound d. d.Light e. e.Rubber tubing (demo) f. f.Slinky (demo) Wikipedia: “S-wave”

Did you say “Slinky”? The handing out of the slinkies

From warmup In a long line of people waiting to buy tickets, the first person leaves and a pulse of motion occurs as people step forward to fill the gap. As each person steps forward, the gap moves through the line. Is the propagation of the gap longitudinal or transverse? Explain. a. a.It is longitudinal because the gap travels parallel to the direction the people move. Think about "the wave" at a BYU football game. People stand up and raise their arms as the wave arrives at their location and the resultant pulse moves around the stadium. Is this wave transverse or longitudinal? a. a.Transverse because the people move up which is perpendicular to the direction the wave is traveling.

From warmup Do transverse waves occur in air? Explain why or why not. a. a.No because there is nothing that would cause air to go up and down [wave is horizontal]. Sound is a longitudinal wave b. b.They are not propagated by air. however, an electromagnetic wave may move through the air.

Web demo

Wave properties, cont. Web demo: Stokes’ “Traveling Sine Wave” Wavelength a. a.meters/wave Period T a. a.seconds/wave Frequency ( f = 1/T ) a. a.waves/second Speed v a. a.m/s v = f

Wavefunction Let’s call it “s(x)” for now (because “f” is used for frequency) What are the units of s? What does s really represent? a. a.For transverse waves… b. b.For longitudinal waves… What does s(x) represent?

The (Linear 1D) Wave Equation Why is it called the wave equation? a. a.Because traveling waves are solutions of the equation! Any function that has “x-vt” will work! …or “x+vt” What’s that funny symbol? C = v 2

k and  What’s the difference between these: General form of cosine wave: …sometimes written as: k = “wavevector”;  = “angular frequency”  = _______