Announcements 2/7/11 Prayer About that exam…

a. In Testing Center, Tues (tomorrow) until a week from Tues; late fee after 5 pm on last day

b. Can bring handwritten 3x5 card (both sides)c. I will give you all constants/conversion

factors/ materials parameters you need– See first page of last year’s exam

d. Can use your own calculator (but storing extra stuff in calc. memory violates spirit if not letter of the law)

e. Time goal: 2 hours avg (took me 33 mins)

What to study? Well, especially…a. Homeworkb. Class notesc. Old examsd. Book

Some more specifics about the exam

More on the exam

Foxtrot

Waves

Skipping: Oscillations, Ch. 15 Today: Basic wave info Starting Wednesday: Some sections from

Physics Phor Phynatics, Dr. Durfee’s book Starting Friday: Complex numbers

a. Clicker: Have you seen: eix = cosx + isinx ?

A = “have seen”B = “not”C = “maybe, but I can’t remember”

Reading quiz

Which of the following phenomena can NOT exhibit a combination of transverse and longitudinal waves?

a. sound waves in airb. surface water wavesc. waves in the earth generated by an

earthquake

Wave intro: some math

What do these functions look like?a. f(x) = x2

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. f(x) = (x – 5t)2

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” What if you want wave to move right-to-

left? “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. Waterb. Earthquake (P & S)c. Soundd. Lighte. Rubber tubing (demo)f. Slinky (demo)

Wikipedia: “S-wave”

Did you say “Slinky”?

The handing out of the slinkiesa. We have about 36b. There are 40 students registered for

the class

Web demo http://

paws.kettering.edu/~drussell/Demos/waves/wavemotion.html

Wave properties, cont.

Web demo: Stokes’ “Traveling Sine Wave”http://

stokes.byu.edu/sinewave_script_flash.html

Wavelength a. meters/wave

Period Ta. seconds/wave

Frequency ( f = 1/T )a. waves/second

Speed va. m/s

v = f

Worked Problem

AM1320 KFAN broadcasts the Utah Jazz games at a frequency of 1320 kHz. (Check out www.jazzfanz.com .) Radio waves travel at the speed of light, 3  108 m/s. (a) What is the wavelength of the AM1320 radio waves? (b) What is the period?

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. For transverse waves…b. For longitudinal waves…

What does s(x) represent?

The (Linear 1D) Wave Equation

Why is it called the wave equation?a. Because traveling waves are solutions of the

equation!

2 2

2 2

s sC

t x

2 2

2 2

2

sin( ) sin( )

sin( )

cos( ) cos( )

cos( )

s sA x vt A x vt v

x tAv x vt

s sA x vt Av x vt v

x t

Av x vt

2C v

Any function that has “x-vt” will work! …or “x+vt”

cos( )s A x vt

What’s that funny symbol?

k and

What’s the difference between these:

General form of cosine wave:

…sometimes written as:

k = “wavevector”; = “angular frequency”

cos( 5 )s x t

cos(2( 5 ))s x t

cos( ( ) )s A k x vt

cos( )s A kx t

= _______