announcements 2/7/11 prayer about that exam… a. a.in testing center, tues (tomorrow) until a week...
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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)
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What to study? Well, especially…a. Homeworkb. Class notesc. Old examsd. Book
Some more specifics about the exam
More on the exam
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Foxtrot
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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”
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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
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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”?
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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”
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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”
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Did you say “Slinky”?
The handing out of the slinkiesa. We have about 36b. There are 40 students registered for
the class
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Web demo http://
paws.kettering.edu/~drussell/Demos/waves/wavemotion.html
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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
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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?
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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?
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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?
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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
= _______