Oscillations and Waves

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Oscillations and Waves

• Micro-world Macro-world Lect 5

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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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Two wave sources
constructive interference
destructive interference
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Confined waves
Only waves with wavelengths that just fit in
survive (all others cancel themselves out)
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Confined waves
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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 2L 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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Vocal Range Fundamental Pitch
1175 Hz
880 Hz
587 Hz
523 Hz
392 Hz
329 Hz
196 Hz
165 Hz
147 Hz
131 Hz
98 Hz
82 Hz
Tenor C2 C5
SopranoG3 D6
Mezzo-SopranoE3 A5
?
?
Baritone G2 G4
Bass E2 E4
ContraltoD3 D5
Thanks to Kristine Ayson
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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 lower)
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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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Visible light
Short wavelengths
Long wavelengths
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receding source ? red-shifted
approaching source ? blue-shifted
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Edwin Hubble
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More distant galaxies have bigger red shifts
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The universe is expanding!!
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(No Transcript)
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Use red- blue-shifts to study orbital motion of
stars in galaxies
receding red-shifted
approaching blue-shifted
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A typical galactic rotation curve
NGC 6503
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Large planets create red-shiftsand blue shifts
in the light of their star
Use this to detect planets measure their
orbital frequency
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Planetary motion induced stellar velocity