Announcements 9/30/11
Prayer
 About that exam…
a. Review session this afternoon, 4 pm, room C460
b. In Testing Center, Saturday morning until
Thursday evening
c. No textbook, no notes
d. I will give you a list of equations (but not all
equations!), and all constants/conversion
factors/materials parameters you need
e. Can use your own calculator, but you’re on your
honor not to store extra stuff in calc. memory
f. No time limit, but “time goal” is 2 hours avg
(took me 33 mins)
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More on the exam
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What to study? I’d recommend in this order:
a. Homework
b. Class notes
Chris office hours
c. Old exams
today: 3-4 pm
d. Book
Some more specifics about the exam…
xkcd
Waves
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Skipping: Oscillations, Ch. 15
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. 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 do NOT
exhibit a combination of transverse and
longitudinal waves?
a. sound waves in air
b. surface water waves
c. waves in the earth generated by an
earthquake
Wave intro: some math
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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) = (2x – 6t)2
b. What is its “velocity”?
Sinusoidal waves
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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
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Definition: oscillating disturbance that transfers
energy (but not mass).
Direction of travel
Direction of oscillation: transverse vs longitudinal
Medium
Examples…
a. Water
b. Earthquake (P & S)
c. Sound
d. Light
e. Rubber tubing (demo)
f. Slinky (demo)
Wikipedia: “S-wave”
Did you say “Slinky”?
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The handing out of the slinkies
a. We have about 35
b. There are 34 students registered for the
class
Web demo
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http://paws.kettering.edu/~drussell/Demos/waves/wavemotion.html
Wave properties, cont.
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Web demo: Stokes’ “Traveling Sine Wave”
http://stokes.byu.edu/sinewave_script_flash.html
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Wavelength l
a. meters/wave
Period T
a. seconds/wave
Frequency ( f = 1/T )
a. waves/second
Speed v
v=f
a. m/s
l
Wavefunction
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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
2s
2s
C 2
2
t
x
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C = v2
What’s that
funny symbol?
Why is it called the wave equation?
a. Because traveling waves are solutions of the equation!
s  A cos( x  vt )
Any function that has
“x-vt” will work! …or “x+vt”
s
  A sin( x  vt )
x
s
  A sin( x  vt )  v 
t
  Av sin( x  vt )
2s
  A cos( x  vt )
2
x
2s
  Av cos( x  vt )  v 
2
t
  Av 2 cos( x  vt )
k and w
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What’s the difference between these:
s  cos( x  5t )
s  cos(2( x  5t ))
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General form of cosine wave:
s  A cos(k ( x  vt )   )
…sometimes written as:
w = _______
s  A cos(kx  wt   )
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k = “wavevector”; w = “angular frequency”