oscillations and waves
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Oscillations and Waves
Micro-world Macro-world Lect 5
Equilibrium (Fnet = 0)
Examples of unstable Equilibrium
Examples of Stable equilibrium
Destabilizing forces
W
N Fnet = 0
Destabilizing forces
W
N Fnet = away from equil
Destabilizing forces
W
NFnet = away from equil
destabilizing forces always push thesystem further away from equilibrium
W
N
Fnet = 0
restoring forces
W
N
Fnet = toward equil.
restoring forces
W
NFnet = toward equil.
restoring forces
Restoring forces always pushthe system back toward equilibrium
Pendulum
N
W
Mass on a spring
Displacement vs time
amplitude
period (=T)
Displaced systems oscillatearound stable equil. points
Equil. point
Simple harmonic motion
Equil. point
T
T= period = time for 1 complete oscillation
f = frequency = # of oscillations/time = 1/T
Pure Sine-like curve
Masses on springs
Animations courtesy of Dr. Dan Russell, Kettering University
Not all oscillations are nice Sine curves
A
TEquil. point
f=1/T
Natural frequency
f= (1/2)g/l f= (1/2)k/m
Driven oscillators
f = 0.4f0 f = 1.1f0 f = 1.6f0
natural freq. = f0
Resonance (f=f0)
Waves
Animations courtesy of Dr. Dan Russell, Kettering University
Wave in a string
Animations courtesy of Dr. Dan Russell, Kettering University
Pulsed Sound Wave
Harmonic sound wave
Harmonic sound wave
Harmonic wavewavelength
=Wave speed
=v
Wave speed = v =distancetime
wavelengthperiod= =
T
= f
but 1/T=fV=for f=V/
Shake end ofstring up & down
with SHM period = T
Reflection (from a fixed end)
Animations courtesy of Dr. Dan Russell, Kettering University
Reflection (from a loose end)
Animations courtesy of Dr. Dan Russell, Kettering University
Adding waves
pulsed waves
Animations courtesy of Dr. Dan Russell, Kettering University
Adding waves
Wave 1
Wave 2
resultant wave
Two waves in same direction with
slightly different frequencies
“Beats”
Animations courtesy of Dr. Dan Russell, Kettering University
Adding waves
harmonic waves in opposite directions
incident wave
reflected wave
resultant wave
(standing wave)
Animations courtesy of Dr. Dan Russell, Kettering University
Two wave sources
destructive
interference
const
ruct
ive
inte
rfere
nce
Confined waves
Only waves with wavelengths that just fit in survive(all others cancel themselves out)
Confined waves
Allowed frequencies
=(2/3)L
f0=V/ = V/2L
f1=V/ = V/L=2f0
= 2L
=L
=(2/5)L
=L/2
f2=V/=V/(2/3)L=3f0
f3=V/=V/(1/2)L=4f0
f4=V/=V/(2/5)L=5f0
Fundamental tone
1st overtone
3rd overtone
4th overtone
2nd overtone
Ukuleles, etc
L
0 = 2L; f0 = V/2L
1= L; f1 = V/L =2f0
2= 2L/3; f2 = 3f0
3= L/2; f3 = 4f0
Etc…
(V depends on theTension & thickness
Of the string)
Vocal Range – Fundamental Pitch
♩♩
♩♩ ♩♩
♩♩
♩♩
♩♩ ♩♩
♩♩
♩♩
♩♩
♩♩
♩♩
Bass Bass EE22 – E – E44
BaritonBaritone Ge G22 – –
GG44
Tenor Tenor CC22 – C – C55
ContralContraltoDtoD33 – –
DD55
Mezzo-Mezzo-SopranSopranoEoE33 – A – A55
SopranSopranoGoG33 – D – D66
♂♂:: ♀♀::
82 Hz82 Hz
329 329 HzHz
98 Hz98 Hz
392 392 HzHz
131 131 HzHz
523 523 HzHz
147 147 HzHz
587 587 HzHz
165 165 HzHz
880 880 HzHz
196 196 HzHz
1175 1175 HzHz
Thanks to Kristine Ayson
Doppler effect
Wavelength same in all directions
Sound wave stationary source
Wavelength in backward direction is longer (frequency is
lower)
Wavelength in forward direction is shorter (frequency
is higher)
Sound wave moving source
Waves from a stationary source
Wavelength same in all directions
Waves from a moving source
Wavelength in forward direction is shorter (frequency
is higher)
Wavelength in backward direction is longer (frequency is
higher)
v
Visible light
Long wavelengthsShort wavelengths
receding source red-shifted
approaching source blue-shifted
Edwin Hubble
More distant galaxies have bigger red shifts
The universe is expanding!!
Use red- & blue-shifts to study orbital motion of stars in galaxies
receding
red-shifted
approaching
blue-shifted
A typical galactic rotation curve
NGC 6503
Large planets create red-shiftsand blue shifts in the light of their star
Use this to detect planets & measure their orbital frequency
Planetary motion induced stellar velocity
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