Announcements 9/28/12
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Prayer
About that exam…
a. In Testing Center, Saturday morning until Thursday
evening
b. No textbook, no notes
c. See website for list of equations that I give you
d. I’ll give you all constants/conversion factors/materials
parameters you need (except for super easy ones, like
100 cm = 1 m)
e. You can use your own calculator, but you’re on your
honor not to store extra stuff in calc. memory
f. 18 multiple choice, 3 short descriptive answer, 6 worked
problems, 1 extra credit (no partial credit on the e.c.)
g. No time limit, but “time goal” is 2 hours avg (took me 39
mins, not including extra credit)
The equations I give you:
More on the exam
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What to study? I’d recommend in roughly this
order:
a. Homework
b. Class notes
c. Old exams
d. Book problems & optional HW problems
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”
From warmup
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Extra time on?
a. (nothing in particular)
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Other comments?
a. This material starts the new unit, so it's not on
the exam, right?
b. Is the homework that's due today as time
consuming as it looks?
c. Can you get a standing longitudinal wave?
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
From warmup
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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. It is longitudinal because the gap travels parallel to the
direction the people move.
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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. Transverse because the people move up which is
perpendicular to the direction the wave is traveling.
From warmup
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Do transverse waves occur in air? Explain why or why
not.
a. No because there is nothing that would cause air to
go up and down [wave is horizontal]. Sound is a
longitudinal wave
b. They are not propagated by air. however, an
electromagnetic wave may move through the air.
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”