Oscillations%20and%20Waves

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Oscillations and Waves

• Physics 100 Chapt 8

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Equilibrium (Fnet 0)
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Examples of unstable Equilibrium
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Examples of Stable equilibrium
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Destabilizing forces
N
Fnet 0
W
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Destabilizing forces
N
Fnet away from equil
W
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Destabilizing forces
Fnet away from equil
N
W
destabilizing forces always push the system
further away from equilibrium
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restoring forces
N
Fnet 0
W
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restoring forces
N
Fnet toward equil.
W
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restoring forces
N
Fnet toward equil.
W
Restoring forces always push the system back
toward equilibrium
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Pendulum
N
W
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Mass on a spring
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Displacement vs time
Displaced systems oscillate around stable equil.
points
amplitude
Equil. point
period (T)
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Simple harmonic motion
Pure Sine-like curve
T
Equil. point
T period time for 1 complete oscillation
1/T
f frequency of oscillations/time
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Masses on springs
Animations courtesy of Dr. Dan Russell, Kettering
University
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Not all oscillations are nice Sine curves
A
Equil. point
T
f1/T
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Natural frequency
f (1/2p)?k/m
f (1/2p)?g/l
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Driven oscillators
natural freq. f0
f 0.4f0
f 1.1f0
f 1.6f0
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Resonance (ff0)
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Waves
Animations courtesy of Dr. Dan Russell, Kettering
University
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Wave in a string
Animations courtesy of Dr. Dan Russell, Kettering
University
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Pulsed Sound Wave
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Harmonic sound wave
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Harmonic sound wave
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Harmonic wave
Wave speed v
Shake end of string up down with SHM period T
wavelength l
l T
distance time
wavelength period
Wave speed v

fl

Vfl or fV/ l
but 1/Tf
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Reflection (from a fixed end)
Animations courtesy of Dr. Dan Russell, Kettering
University
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Reflection (from a loose end)
Animations courtesy of Dr. Dan Russell, Kettering
University
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Adding waves
pulsed waves
Animations courtesy of Dr. Dan Russell, Kettering
University
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Adding waves
Two waves in same direction with slightly
different frequencies
Wave 1
Wave 2
resultant wave
Beats
Animations courtesy of Dr. Dan Russell, Kettering
University
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Adding waves
harmonic waves in opposite directions
incident wave
reflected wave
resultant wave
(standing wave)
Animations courtesy of Dr. Dan Russell, Kettering
University
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Confined waves
Only waves with wavelengths that just fit in
survive (all others cancel themselves out)
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Allowed frequencies
l 2L
f0V/l V/2L
Fundamental tone
f1V/l V/L2f0
lL
1st overtone
l(2/3)L
f2V/lV/(2/3)L3f0
2nd overtone
lL/2
f3V/lV/(1/2)L4f0
3rd overtone
l(2/5)L
f4V/lV/(2/5)L5f0
4th overtone
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Ukuleles, etc
l0 L/2 f0 V/2L
l1 L f1 V/L 2f0
l2 2L/3 f2 3f0
L
l3 L/2 f3 4f0
Etc
(V depends on the Tension thickness Of the
string)
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Doppler effect
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Sound wave stationary source
Wavelength same in all directions
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Sound wave moving source
Wavelength in forward direction is shorter
(frequency is higher)
Wavelength in backward direction is longer
(frequency is higher)
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Waves from a stationary source
Wavelength same in all directions
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Waves from a moving source
v
Wavelength in backward direction is longer
(frequency is higher)
Wavelength in forward direction is shorter
(frequency is higher)
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surf
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Folsom prison blues
long wavelengths
Short wavelengths
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Confined waves