describing waves traveling disturbances § 14.1–14.2
TRANSCRIPT
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Describing Waves
traveling disturbances
§ 14.1–14.2
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What’s a Wave?
• Oscillation– object moves cyclically
• Wave– medium moves cyclically– disturbance travels, medium does not
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Group Whiteboard Work
2. A wave generator produces 10 pulses each second. The pulses travel at 300 cm/s.
a. What is the period of the waves?
b. What is the wavelength of the waves?
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Wave Pulse
• Why does the pulse move?
• What determines its speed?
• What happens inside the medium?
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Points to Ponder
The particles of the string change their motion as the wave travels. What force accelerates them?
a cb
d
What are the velocity and acceleration of the string particles at the following positions? Why?
a. middle (leading edge)b. crest
c. middle (trailing edge)d. trough
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Types of Waves
• Motion of the medium is perpendicular to the direction the wave travels: transverse wave (example: string wave)
• Motion of the medium is parallel to the direction the wave travels: longitudinal wave (examples: sound wave, slinky wave)
• Animation
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Wave Speed
• Speed of disturbance traveling through the medium
• Generally not the speed of the oscillating medium itself!
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Periodic Waves
repeat in time and space
§ 15.2
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• Wavelength: crest-crest distance• Trough: low point
• Period: crest-crest-timing
Features of a Wave
• Crest: high point
crest
trough
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Periodic Wave Parameters
• Angular frequency = (rad/s)
• Cycle frequency f = /2 (cycle/s)
• Repeat time = period T = 1/f (s/cycle)
• Repeat distance = wavelength (m/cycle)
• Angular wavenumber k = 2/ (rad/m)
• Wave speed v = /T = f = /k (m/s)
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Poll Question
Doubling the frequency of a wave while keeping its speed constant will cause its wavelength to
A. increase.B. decrease.C. stay the same.
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Poll Question
Doubling the frequency of a wave while keeping its wavelength constant will cause its speed to
A. increase.B. decrease.C. stay the same.
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Poll Question
Doubling the wavelength of a wave while keeping its speed constant will cause its period to
A. increase.B. decrease.C. stay the same.
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Propagation Speed
in a rope
§ 14.2
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Purely transverse wave
In a rope, string, or spring:
•Speed increases with tension F
•Speed decreases with density
v = F/
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Wave Functions
oscillations extended
§ 14.3
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Think Question
• The waves travel to the right.
In which direction is A moving right now?A. A is momentarily stationary.
B. Upward. C. Downward.
A B
• A and B are points on the medium.
CD
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Poll Question
• The waves travel to the right. • A and B are points on the medium.
In which direction is B moving right now?A. B is momentarily stationary.
B. Upward. C. Downward.
A B
CD
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Think Question
• The waves travel to the right. • A and B are points on the medium.
In which direction is C moving right now?A. C is momentarily stationary.
B. Upward. C. Downward.
A B
CD
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Think Question
• The waves travel to the right. • A and B are points on the medium.
In which direction is D moving right now?A. D is momentarily stationary.
B. Upward. C. Downward.
A B
CD
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Formula Description
Displacements y of A and B with time
A B
y(xA,t) = A cos(t)
y(xA+/4,t) = A cos(t–2/4)
yA yB
ty
+A
−A
generalize to any x
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Formula Description
y(xA,t) = A cos(t)
y(xA+/4,t) = A cos(t–2/4)
y(x,t) = A cos(t–kx)
same as
y(x,t) = A cos(kx–t)
where
–k(/4) = –2/4
k = 2/
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Parameters
= 2/T = angular frequency (rad/s)
k = 2/ = wave number (rad/m)
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Graphing y (x,t)
Each tells only part of the story!
y(x = 0)
y(t = 0)
x
t
T
snapshot of the wave at one time
displacement of the medium at one place
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3D Graph
x
t
cresttrough
T
slope = v
Displacement-position-time
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Traveling the Other Way
x
t
cresttrough
T
slope = v
Displacement-position-time