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)
More on the exam


What to study? Well, especially…
a. Homework
b. Class notes
c. Old exams
d. Book
Some more specifics about 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 air
b. surface water waves
c. 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. Water
b. Earthquake (P & S)
c. Sound
d. Light
e. Rubber tubing (demo)
f. Slinky (demo)
Wikipedia: “S-wave”
Did you say “Slinky”?

The handing out of the slinkies
a. We have about 36
b. 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 l
a. meters/wave
Period T
a. seconds/wave
Frequency ( f = 1/T )
a. waves/second
Speed v
v=f
a. m/s
l
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
2s
2s
C 2
2
t
x

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

What’s the difference between these:
s  cos( x  5t )
s  cos(2( x  5t ))

General form of cosine wave:
s  A cos(k ( x  vt )   )
…sometimes written as:
w = _______
s  A cos(kx  wt   )

k = “wavevector”; w = “angular frequency”