frequency how many cycles per time, usually per second

1
Periodic motion Notes
Define the words frequency and period in
relation to time
Period How long it takes to make a full cycle.
Examples 2 minutes/ 1 time around the track
20 seconds/ 1 turn on
merry-go-round
Frequency How many cycles per time, usually per
second.
Examples 30 laps/hour 5 waves/second
5 Hz (times per/second)
2
Waves and Vibration
Define Amplitude
Amplitude A is maximum displacement from rest
or equilibrium (more difficult for rotational
objects like pendulums.
3
Waves and Vibration
What is a wave?.
Examples? Wave like - Waving hand, pendulum,
swing, mass on a spring. Waves - Sound waves,
visible light waves, radio waves, microwaves,
water waves, sine waves, cosine waves, telephone
chord waves, stadium waves, earthquake waves,
waves on a string, and slinky waves
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Oscillations and Pendulums
5
Simple periodic Motion Oscillations and Pendulums
The following pendulum is at rest.
The forces are in equilibrium so we can say the
pendulum is a state of equilibrium.
Ftension
Fgrav
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Oscillations and Pendulums
1) When pulled at an angle, the tension in the
rope decreases it is not directly opposing
gravity
Ftension
2) Gravity is split up, partly pulling against
tension, but partly pulling the pendulum toward
equilibrium
Fgrav
3) Gravity will attempt to restore the pendulum
to equilibrium.
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Restoring force for pendulums
This restoring force can be found using the
following equation Fnet mg sin q
Ftension
If the angle is less than 10o (0.17 radians) it
can be approximated through the following
equation Fnet (mg/L)s
Fgrav
This force tries to restore the pendelum back to
rest
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Period of a Pendulum

• Not dependent on Mass
• Not dependent on displacement (angle)
• Is dependent on length

9
Period of a Pendulum T vs l
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Period of a Pendulum T2 vs l
11
Equations and Pendulums
1 g
v
v
L
2p

T
2p L
g
frequency T Period L Length of Pendulum g
9.8 m/s2
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Equations and Pendulums
Find period of a pendulum that has a length of
1.00 meters.
v
1.00 m
2p
T
9.8m/s2
T
13
Periodic Motion and Springs
Find length of a pendulum that will give you at
period of 1.0s.
( )
2
1 s
9.8 m/s2
L
2p
L
14
Periodic Motion and Masses on Springs
15
Periodic Motion and Springs (Restoring Force)
Assume the block is on an air track (frictionless)
No net Force
The Restoring Force is the force of the spring on
the block
Restoring Forces
Fnet -k x

• Because force is always toward center
• k is spring constant for individual spring (N/m)
• x is distance from equilibrium (meters)

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What can be determined from this graph of a
spring undergoing oscillating motion?
19
Periodic Motion and Springs (14.3 Velocity)
vmax
2pf A
Max Velocity
vmax 2pA
T
No Velocity
A Amplitude (meters) f frequency (hz) T
Period (seconds)
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Periodic Motion and Springs (14.3 Position at
some time)
x(t) A cos (2 p f t)
A Amplitude (meters) f frequency (hz) t
the time you want to know where its at
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Periodic Motion and Springs (14.4 Period and
Frequency)
T Period m mass of object k spring constant
1 k
v

2p m
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Periodic Motion and Springs (14.4 Energy)
B
A
Etotal K Us
K ½ mv2
Energy is Kinetic Only
Us ½ kx2
Energy is Spring Potential only
What is the distance from equilibrium at A
what does this mean for the amount of potential
energy?
What is the velocity at B what does this mean
for the amount of kinetic energy?
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Periodic Motion and Springs (14.4 Energy)
A mass on a spring undergoes SHM. If the
amplitude is 0.08m and the spring constant is 200
N/m, how much energy is in the system?
Etotal K Us
At the amplitude, the velocity of the mass is
zero. So zero Kinetic Energy At max displacement,
Energy is all potential.
½ mv2 ½ kx2
½ 200N/m(0.08m)2
0.64 J
24
Periodic Motion and Springs (14.4 Energy)
How much kinetic energy is there when the mass
has moved to 0.04 m?
Etotal K Us
0.64J Us K
0.64J ½ kx2 K
0.64J 0.16J K
0.48J K _at_ 0.04m
25
Waves and Vibration
In your journal, list examples of waves.
Share/compare your answers with one or two people
sitting to your left and right.
If you had to describe a wave to a 6 year old,
what would you say? List/bullet your ideas.
Share/compare your answers with one or two people
sitting to your left and right.
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Waves and Vibration
Observe the wave demonstration at the front.
Write down 4 observations about the wave.
Make an additional observation about the motion
of the wave.
What do you notice about the motion of the sticks?
Infer from the previous chapters When you watch
a wave move what is actually moving? how it
moving?
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Vibration Review / Intro to Waves
Period How long it takes to make a full cycle.
Examples 2 minutes/ 1 once around the track
20 seconds/ turn on
merry-go-round 0.001 seconds
per wave crest
Frequency How many cycles per time, usually per
second.

• Examples 30 laps/hour
• 5 waves/second
• 5 Hz (times per/second)

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Types of Waves 14.1
Mechanical
Energy flows only if Medium is present. (Air,
Water, steel, etc) Example Sound, Water wave,
Earthquake Speed is determined by properties of
material (density, temperature)
Does not need a medium moves better through a
vacuum (space). Example Light (visible, radio,
microwave Speed is always 3x108 m/s in a vacuum
travels slower in a medium like air or water
Electromagnetic
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What can waves look like?
Examples?
30
Waves and Vibration
Parts of a wave
31
Waves and Vibration
Parts of a wave
32
Waves and Vibration
Parts of a wave
33
Other concepts

• Waves are the transfer of energy
• The Medium vibrates and returns to its original
  position (it doesnt travel with the wave)
• The speed of a wave is dependent on properties of
  the medium, not the wave.
• (not amplitude, not frequency, not wavelength)

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Waves in a string 14.2
V wave velocity (m/s) T Tension Force
(Newtons) m Linear Density (kg/m)
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Waves in a string 14.2
A spiders web is made of silk and has a linear
density of 7.5 x 10-6 kg/m. If the silk has a
tension of 0.3 N, what is the speed of waves in
silk?
v
Ts
vstring
m
200 m/s
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Waves in a string 14.2
If a fly lands 20 cm away, how long until the
spider finds out?
x
V
t
.001 seconds or 1 millisecond (1ms)
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Waves Equation
Wave speed frequency x wavelength
v f x ?
Ex) A transverse wave is found to have a vertical
distance of 4 cm from a trough to a crest, a
frequency of 12 Hz, and a horizontal distance of
5 cm from a crest to the nearest trough.
Determine the, period, wavelength and speed of
such a wave.
Period 1/12th second Wavelength 0.1 m
v f x ? 12 hz x 0.1 m 1.2 m/s
39
Slow and Fast Waves
Sound _at_ 20oC 343 m/s
Light in a vacuum 300,000,000 m/s
Sound Mechanical Wave requires a medium
Light Electromagnetic Wave only travels in a
vacuum is impeded by matter (air, water)
Review Prefixes Giga (G) 1 billion
1,000,000,000 Mega (M)1 million
1,000,000 Kilo (k)1 thousand 1,000 Milli
(m) 1/1000 or 0.001 Micro (µ) 1 / 1,000,000
or 0.000,001 Nano (n) 1 / 1,000,000,000 or
0.000,000,001
40
Sound
Origin
Vibrations. Examples tuning fork guitar string
Pitch
Pitch refers to the frequency. High
frequency high pitch
Type of wave
Longitudinal and mechanical, speed is about 343
m/s in air
41
Sound
Requires a medium (anything made of matter) to
propagate the wave. Can sound travel in outer
space?
Rarefaction
Compression
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Speed Properties
44
Sound as a pressure wave
45
Speed Properties
46
Doppler Effect
A change in the apparent frequency of sound due
to the motion of the source or the receiver.
Imagine a loud car or siren as it passes you on
the street. The pitch suddenly drops just as the
object moves by.
47
Doppler Effect
48
Non-moving wave source
Doppler Effect wave frequency and length is
distorted in front and behind
49
Doppler Effect
(speed of sound speed of observer) (speed of
sound speed of source)
Perceived frequency actual frequency
(v vob) (v - vs )
fo refers to the original or actual frequency
emitted
f fo
Vob is () if the observer moves toward the
source Vob is (-) if the observer moves away from
the source Vs is () if the source moves toward
the observer Vs is (-) if the source moves away
from the observer
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(v vo ) (v - vs )
Doppler Effect
f fo
Sitting on a beach at Coney Island one
afternoon, Kim finds herself beneath the flight
path of the airplanes leaving Kennedy Airport.
What frequency will Kim hear as a jet, who
engines emit sound at a frequency of 1000 Hz,
flies toward her at a speed of 100 m/s?
(340 m/s 0 m/s ) (340 m/s - 100 m/s )
f 1000 Hz
f 1417 Hz
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(v vo ) (v - vs )
Doppler Effect
f fo
A sparrow chases a crow with a speed of 4.0 m/s,
while chirping at a frequency of 850 Hz. What
frequency of sound does the crow hear as he flies
away from the sparrow with a speed of 3.0 m/s?
(340 m/s -3.0 m/s ) (340 m/s - 4.0 m/s
)
f 850 Hz
f 852.5 Hz
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Source of wave traveling at speed of wave.
(Traveling at the speed of sound)
Source traveling faster than the speed of wave.
(Traveling faster than speed of sound)
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Electromagnetic Spectrum (Light)
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Loudness
Power area
Intensity
Loudness is measured in W/m2
Typical Sound wave spreads out in a spherical
pattern
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Loudness
Typical Sound wave spreads out in a spherical
pattern
The rate of decrease happens at rate of
1/r2 Example If loudness is 1 at meter Its ¼
intensity at 2 meters And 1/9 intensity at 3
meters
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Loudness
Typical Sound wave spreads out in a spherical
pattern
Power area
Intensity
Psource 4pr2
I
57
J s
Power W
W m2
20 dB 1.0 x 10-10
J s
1.0 x 10-10
1m2
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Waves and Vibration
In your journal, list examples of waves.
Share/compare your answers with one or two people
sitting to your left and right.
If you had to describe a wave to a 6 year old,
what would you say? List/bullet your ideas.
Share/compare your answers with one or two people
sitting to your left and right.
59
Superposition
60
Superposition

• When two or more waves are present in the same
  space, the displacement of the medium at that
  point is the sum of the displacements

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Superposition
62
Superposition
63
Superposition
64
Superposition(Standing Waves)
65
Superposition
66
Superposition
67
Traveling vs. Standing Waves
Standing waves - Waves that look like they
arent moving forward, just back and forth, or up
and down.
In a Standing wave, some parts dont move (B) -
nodes. Areas of greatest movement (A) are called
antinodes.
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Standing Waves
69
Standing Waves
Formation Standing waves result as waves
interfere with each other, many times from a wave
bouncing off a boundary.
70
Standing Waves
There are 5 nodes and 4 antinodes in the above
picture.
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Standing Waves
Each node is spaced at l/2, so a wavelength is
twice the distance between two nodes.
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Standing Waves
Nearly all objects vibrate if hit, plucked, or
are otherwise disturbed. They tend to vibrate at
certain frequencies depending on size, tension,
and material
Natural Frequency The frequency or frequencies
that an object tends to vibrate at.
73
Standing Waves in Strings
The frequency with which a string vibrates
depends on the number of antinodes, wave speed,
and length of string.
n v 2L
( of antinodes) (wave speed) 2 ( length)
or f
Frequency
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Standing Waves in Strings
Fundamental frequency. N 1
First overtone. N 2
2nd overtone. N 3
75
Standing Waves in Strings
Fundamental frequency. N 1
First overtone. N 2
2nd overtone. N 3
76
Standing Waves in Strings
77
Standing Waves in Pipes
Fundamental frequency. N 1
First overtone. N 2
2nd overtone. N 3
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Speed of Sound
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