Oscillations and Waves
Physics 100 Chapt 8
Equilibrium (Fnet = 0)
Examples of unstable Equilibrium
Examples of Stable equilibrium
Destabilizing forces
NF = 0
net
W
Destabilizing forces
N
Fnet = away from equil
W
Destabilizing forces
Fnet = away from equil
N
W
destabilizing forces always push the
system further away from equilibrium
restoring forces
N
Fnet = 0
restoring forces
N
Fnet = toward equil.
restoring forces
Fnet
N
= toward equil.
Restoring forces always push
the system back toward equilibrium
Pendulum
N
W
Mass on a spring
Displacement vs time
Displaced systems oscillate
around stable equil. points
amplitude
Equil. point
period
(=T)
Simple harmonic motion
Pure Sine-like curve
T
Equil. point
T= period = time for 1 complete oscillation
f = frequency = # of oscillations/time = 1/T
Masses on springs
Animations courtesy of Dr. Dan Russell, Kettering University
Not all oscillations are nice Sine
curves
A
Equil. point
T
f=1/T
Natural frequency
f= (1/2p)g/l
f= (1/2p)k/m
Driven oscillators
natural freq. = f0
f = 0.4f0
f = 1.1f0
f = 1.6f0
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 wave
Shake end of
string up & down
with SHM period = T
Wave speed
Wave speed
wavelength
=v
=l
distance
time
=v=
=
V=fl or f=V/ l
wavelength
period
l
= = fl
T
but 1/T=f
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
Two waves in same direction with
slightly different frequencies
Wave 1
Wave 2
resultant wave
“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
Confined waves
Only waves with wavelengths that just fit
(all others cancel themselves out)
in survive
Allowed frequencies
l= 2L
f0=V/l = V/2L
Fundamental tone
l=L
l=(2/3)L
f1=V/l = V/L=2f0
1st overtone
f2=V/l=V/(2/3)L=3f0
2nd overtone
l=L/2
f3=V/l=V/(1/2)L=4f0
3rd overtone
l=(2/5)L
f4=V/l=V/(2/5)L=5f0
4th overtone
Ukuleles, etc
L
l0 = L/2; f0 = V/2L
l1= L; f1 = V/L =2f0
l2= 2L/3; f2 = 3f0
l3= L/2; f3 = 4f0
Etc…
(V depends on the
Tension & thickness
Of the string)
Doppler effect
Sound wave stationary source
Wavelength same in all directions
Sound wave moving source
Wavelength in forward
direction is shorter
(frequency is higher)
Wavelength in backward
direction is longer
(frequency is higher)
Waves from a stationary source
Wavelength same in all directions
Waves from a moving source
v
Wavelength in forward
direction is shorter
(frequency is higher)
Wavelength in backward
direction is longer
(frequency is higher)
surf
Folsom prison blues
Confined waves