Transcript lecture 19 - superposition, standing waves

Announcements 10/10/12
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Prayer
Term projects: Proposals due a week from Saturday,
emailed to me with your proposal in body of email.
Groups of 2 are encouraged. Groups of 3 with permission.
Just send one email per group, but CC your partners on
the email.
Syllabus: “The term project is an opportunity for you to
propose and conduct a simple experiment or to
theoretically, mathematically, or computationally
investigate an aspect of the course in more depth.”
Guidelines: “At least 15 hours of work per person (not
including time spent at the hardware store, etc.)”
http://www.physics.byu.edu/faculty/colton/courses/phy123resources/project/guidelines.htm
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Some ideas to get you thinking:
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Some actual projects:
http://www.physics.byu.edu/faculty/colton/courses/phy123resources/project/ideas.htm
http://www.physics.byu.edu/faculty/colton/courses/phy123resources/project/actualprojects.
htm
From warmup
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Extra time on?
a. First warmup question
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Other comments?
a. Do we have a strobe light with an adjustable
frequency? They can make a lot of really cool
demos for this stuff when combined with standing
waves on a string.
b. Can we have answer ranges on the next exam, or
at least a comic, or perhaps a comical answer
range?
Close to
Home
Interference (same wavelength waves)
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Path length differences
a. Constructive
b. Destructive
 Video: Two outdoor speakers
(1:16)
 Demo: Moire pattern
transparencies
 Demo: Hearing test
 Demo: 2-speaker interference
Ripple Tank
image: wikipedia
From warmup
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A wave carries energy. When two waves
destructively interfere, however, their
amplitudes cancel out. Where has the energy
gone? (Consider waves on a rope for simplicity.)
a. In the moment the waves cancel each other
out, the individual bits of the rope are still in
motion. The wave energy is 100% transverse
kinetic energy at that moment.
From warmup
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In a standing wave, what is the difference
between the nodes and the antinodes?
a. The nodes are the places where destructive
interference continually occurs--the rope
looks like it is not moving. The antinodes are
the places where constructive interference
occurs the most--the rope moves from the
max positive displacement to the max
negative.
Standing Waves
Image from Wikipedia
Image by Colton
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Will occur whenever you have two waves (same frequency,
wavelength) moving in opposite directions
Math: A cos(kx - wt) + A cos(kx + wt)
 From trig.: cos(a–b) + cos(a+b) = 2cos(a)cos(b)
Standing Waves, cont.
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Video (on your own time):
http://stokes.byu.edu/teaching_resources/standing_script_fl
ash.html (1:48)
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Can occur via reflections of a single wave! But timing
(frequency) has to be just right for it to occur over & over
again
Demo: rubber tubing
Web demo, revisited
http://www.colorado.edu/physics/phet/simulations/stringwa
ve/stringWave.swf
Demo: “Ladies belt”
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Standing Wave Patterns
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Back to rubber tubing demo
a. What kinds of patterns do you get?
b. “node” vs “antinode”
Harmonics: allowed frequencies
Standing waves on a string: “Closed-Closed”
L =_____
L=_____
L =_____
L
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For stable patterns: L = _______
What are the frequencies?
Relative to the fundamental frequency?