Periodic Motion Motion that repeats in a regular cycle is
called periodic motion. The revolution of a planet about its sun is
an example of periodic motion. The highly reproducible period (T)
of a planet is also called its year. Mechanical devices on earth
can be designed to have periodic motion. These devices are useful
timers. They are called oscillators.
Slide 4
Periodic Motion Motion that repeats in a regular cycle is
called periodic motion or simple harmonic motion. Pendulum - Mass
on a spring Pendulum Mass on a spring
Slide 5
Simple Pendulum Simple harmonic motion can be demonstrated by
the swing of a pendulum. A simple pendulum consists of a massive
object, called the bob, suspended by a string or light rod of
length L.
http://www.science-animations.com/support-files/energy.swf
http://www.wiley.com/college/halliday/0470469080/simulations/fig08_07/fig08_07.html
Slide 6
Forces on Pendulum L x At the left and right positions, the net
force and acceleration are maximum, and the velocity is zero. At
the middle position in the figure, the net force and acceleration
are zero, and the velocity is maximum
Slide 7
SHM - Pendulum L x You can see that the net force is a
restoring force; that is, it is opposite the direction of the
displacement of the bob and is trying to restore the bob to its
equilibrium position.
Slide 8
GPE max GPE zero KE 0 KE max KE 0 F net and a max F net and a
zero F net and a max v zero v max v zero http://www.science-
animations.com/support- files/energy.swf Pendulum
Slide 9
Simple Harmonic Motion Requres a RESTORING FORCE - force that
restores object to its equilibrium position that is directly
proportional to the displacement of the object Period (T): time it
takes the object to complete one cycle of motion. Units - seconds
Frequency (f): number of cycles in one second. Units - seconds -1
or Hertz Amplitude (A) : maximum distance that the object moves
from the equilibrium position Units - meters
Slide 10
Experimentally determine what T depends on before derive an
expression
Slide 11
Slide 12
Experimental Design Purpose? Determine relationship between two
different variables Controlled Experiments Manipulate only one
variable in an experiment Observe its effect on a second variable
Hold ALL other variables in the experiment CONSTANT
Slide 13
Variables Any factor that might affect the behavior of an
experiment. Independent Variables Factor that is changed or
manipulated during the experiments Always plotted on the x-axis
Time is usually the independent variable Dependent Variables Factor
that depends on the independent variable Always plotted on the
y-axis
Slide 14
Collecting and Recording Data At least 6 data points are
necessary for a good graph. Independent variable should cover a
range of at least 10 fold if possible (eg. 0.2 to 2.0 m) Raw data
is recorded in a data table immediately as it is collected in the
lab. Data Table Construct data table before collecting the data
Independent variable in leftmost column of data table Every column
is labeled with the variable name being measured AND the units in
parentheses Values in table do not have units. Same number of
decimal places in each column
Slide 15
Graphing Data Purpose Determine relationship between two
variables Plot data as scatter graphs (do not connect the data
points) Graphs Always include Title (in WORDS) DEPENDENT vs.
INDEPENDENT variable Label each axis with the variable and the
UNITS Recognize common relationships in graphs Connect the data
points with a line or curve of best fit to show the relationship
between variables
Slide 16
Graphing Data Force Applied vs. Mass Direct Relationship Title
(words) Axes labeled with variable symbols (not words) and units
F=2m Dependent variable Independent variable
Slide 17
Simple Harmonic Motion for a Pendulum independent of mass
independent of amplitude Dependent on g (gravitational
strength)
Slide 18
Example Problem On a planet with an unknown value of g, the
period of a 0.75 m long pendulum is 1.8 sec. What is g for this
planet?
Slide 19
Resonance Resonance is a special form of simple harmonic motion
in which the additions of small amounts of force at specific times
in the motion of an object cause a larger and larger displacement.
Resonance from wind, combined with the design of the bridge
supports, may have caused the original Tacoma Narrows Bridge to
collapse. London Millenium bridge Tacoma Narrows Bridge Tacoma
Narrows Bridge2 https://www.youtube.com/watch?v=JiM6AtNLXX4 glass
shattering montage
Slide 20
Waves Disturbance that travels through a medium from one
location to another location.
Slide 21
Waves Disturbance that carries energy through matter and space.
A wave transports energy NOT matter Waves travel through matter or
space Newtons laws of motion & conservation of energy govern
the motion of waves
Slide 22
Mechanical Waves Mechanical waves require a medium to travel
through Water Air Ropes Travel through the medium, but do not carry
the medium away Electromagnetic Waves Electromagnetic waves do NOT
require a medium to travel through
Slide 23
X-rays Sound waves Light waves ripples Earthquake or seismic
waves Microwaves Radio waves Surfing wave Stadium wave Ultrasound
waves What type of wave??? ME or EM EM ME EM
Slide 24
Transverse Waves Wave that vibrates perpendicular to the
direction of the waves motion. Crest highest point on the wave
Wavelength shortest distance between two identical points on a wave
Amplitude maximum distance from equilibrium (related to energy of
the wave Trough lowest point on the wave
Slide 25
Wave that vibrates parallel to the direction of the waves
motion. Example: Vibrate a slinky back and forth Sound travels as
longitudinal waves Longitudinal Waves
Slide 26
Transverse Waves Direction of travel Disturbance Direction of
travel Disturbance
Slide 27
Measurements of a Wave Amplitude depends on source, not on
speed or medium Period/Frequency - depend on source, not on speed
or medium Speed depends only on medium (not on amp or frequency)
Wavelength depends only on medium Phase
http://tdflashzone.net23.net/we b_flash/wavemotion_v3.swf
Slide 28
Measuring a wave
Slide 29
Measuring a wave AMPLITUDE 2xs amp 4xs energy
Slide 30
Period & Frequency Frequency number of waves per second
Measured in Hertz (Hz) Period time it takes to complete one cycle
Measured in seconds (s) http://tdflashzone.net23.net/we
b_flash/wavemotion_v3.swf
Slide 31
Period & Frequency The frequency of a wave is equal to the
reciprocal of the period. Both the period and the frequency of a
wave depend only on its source. They do not depend on the waves
speed or the medium.
Slide 32
Measuring a wave Wavelength, large Wavelength medium Wavelength
small Wavelength
Slide 33
Measuring a wave -speed Speed of wave depends on the properties
of the medium it travels in eg. Wave speed in a string depends on
tension and strings mass/length eg. Wave speed in water depends on
depth and g
Slide 34
Transverse WaveLongitudinal Wave A transverse wave is one that
vibrates perpendicular to the direction of the waves motion. 2) A
quick shake of a rope sends transverse waves in both directions. 3)
Waves obtained in threads and ropes are transverse waves. A
longitudinal wave is one in which the particle displacement is in
the same direction as, or parallel to, the direction of the waves
motion. 2) The squeeze and release of a coiled-spring toy sends out
longitudinal wave pulses in both directions. 3) Waves obtained in
springs and sounds are longitudinal waves.
Slide 35
DO NOW a.What is the speed of the wave? b.What is the
wavelength of the wave? c.What is the period of the wave? d.If the
frequency was changed to 442 Hz, what would be the new wavelength
and period? A sound wave has a frequency of 192 Hz and travels the
length of a football field, 91.4 m, in 0.271 s. 337 m/s 1.76 m
0.0052 s Same medium so same v (337m/s) New T=0.0023s, new
=0.76m
Slide 36
The time required for the sound waves (v = 340 m/s) to travel
from the tuning fork to point A is ____. The wavelength of the
sound is ______ 0.059 s 0.664 m
Slide 37
a. one-ninthb. one-third c. the same asd. three times larger
than Two waves are traveling through the same container of nitrogen
gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of
4.5 m. The speed of wave B must be ________ the speed of wave A.
Same medium so same v
Slide 38
The water waves below are traveling along the surface of the
ocean at a speed of 2.5 m/s and splashing periodically against
Wilbert's perch. Each adjacent crest is 5 meters apart. The crests
splash Wilbert's feet upon reaching his perch. How much time passes
between each successive drenching? Answer and explain using
complete sentences.
Slide 39
Suppose I wiggle a slinky back and forth, and count that 6
waves pass a point in seconds. What would the frequency be? f = 6
waves/2 sec = 3 waves/sec = 3 Hz
Slide 40
Slide 41
Sound Waves Sound is a type of wave. Longitudinal As the bell
shown in the figure moves back and forth, the edge of the bell
strikes particles in the air.
Slide 42
When the edge moves forward, air particles are driven forward
Air particles bounce with greater velocity Greater pressure When
the edge moves backward, air particles are no longer driven forward
Air particles bounce with lower velocity Lower pressure
Slide 43
This results in alternating regions of slightly high and
slightly low pressure. The collisions among air particles cause the
pressure variations to move away in all directions. These pressure
variations are transmitted through matter as sound waves.
Slide 44
All Sound is Caused By Vibration of Something- Example - Sound
Field radiated by a Tuning Fork
http://www.betavakken.nl/natuurkunde/Applets/Golven%20en%20straling/Geluid/activity.swf
Slide 45
Properties of Sound Speed Pitch frequency of sound Loudness
amplitude of sound Quality or timbre
Slide 46
Pitch A measure of how high or low a sound is A measure of how
high or low a sound is Pitch depends on the frequency of a sound
wave Pitch depends on the frequency of a sound wave - Low pitch -
Low frequency - Longer wavelength - High pitch - High frequency -
Shorter wavelength Louder (larger Amp) Softer (Smaller Amp) Phet
sound and speaker sim
Slide 47
Slide 48
Measurements of a Wave Amplitude depends on source, not on
speed or medium Period/Frequency - depend on source, not on speed
or medium Speed depends only on medium (not on amp or frequency)
Wavelength depends only on medium Phase
http://tdflashzone.net23.net/web _flash/wavemotion_v3.swf
Slide 49
Wave Behavior (all waves) When the wave encounters the boundary
of the medium in which it is traveling, it often reflects back into
the medium. In other instances, some or all of the wave passes
through the boundary into another medium often changing direction -
refraction. Many properties of wave behavior result from the fact
that two or more waves can exist at the same time in the same
medium (unlike particles).
Slide 50
Waves at Boundaries wave speed depends on the medium Incident
Wave - wave that strikes the boundary Transmitted or Refracted Wave
wave that transmits to the new medium Reflected Wave returning wave
on the original medium
Slide 51
Reflection of Waves Occurs when a wave strikes a medium
boundary and bounces back into original medium. Completely
reflected waves have the same energy and speed as original
wave.
Slide 52
Reflection from fixed boundary Reflects back - same speed
-Inverted - same amp
Slide 53
Reflection from free boundary Reflects back - same speed -
upright
Slide 54
Refraction of Waves Transmission of wave from one medium to
another. Refracted waves may change speed and wavelength.
Refraction is almost always accompanied by some reflection.
Refracted waves do not change frequency.
Slide 55
No boundary Rigid boundaryFree Boundary Low to high density
boundary High to Low density boundary When a wave encounters a
boundary which is neither rigid (hard) nor free (soft) but instead
somewhere in between, part of the wave is reflected from the
boundary and part of the wave is transmitted across the
boundary.
Slide 56
Reflection and Transmission of Waves slower Same speed
same
Slide 57
Reflection and Transmission of Waves Same speed faster High to
Low density boundary
Slide 58
Reflection and Transmission of Waves Reflected wave Same speed
Refracted wave slower High to Low density boundary MORE dense LESS
dense
Slide 59
Reflection and Transmission of Waves Refracted wave faster High
to Low density boundary MORE dense LESS dense Reflected wave Same
speed
Slide 60
Reflection and Transmission of Waves ReflectedTransmitted Speed
( )*samefaster waveformupright amplitudesmallerlarger MORE dense
LESS dense ReflectedTransmitted Speed ( )*sameslower
waveforminvertedupright amplitudelargersmaller *Transmitted waves
DO NOT change frequency
Slide 61
DO NOW The speed of sound in water is 1498 m/s. A sonar signal
is sent straight down from a ship at a point just below the waters
surface, and 1.80 s later, the reflected signal is detected. How
deep is the water? 1348.2m = 0.84 mile
Slide 62
DO NOW 0.1m 1m/s 0.1m v reflected v transmitted 2cm TOP: An
incident pulse is traveling at a speed of 1 m/s in a string (blue)
to which a 2 nd string of a different density (red) is attached.
BOTTOM: Part of the wave is reflected at the boundary and part is
transmitted. a)What is the amplitude of the incident pulse? b)What
are the wavelengths of the incident, reflected and transmitted
pulses? c)What are the frequencies of the incident, reflected and
transmitted pulses? d)What are the speeds of the reflected and
transmitted pulses? e)Which string is denser, the blue or the red
one? 4 cm i =0.8m, r =0.8m, t =0.4m 1.25hz v r =1m/s, v t =0.5m/s
Red
Slide 63
Superposition of Waves When two or more waves pass a particular
point in a medium simultaneously, the resulting displacement at
that point in the medium is the sum of the displacements due to
each individual wave. The waves interfere with each other.
http://www.cabrillo.edu/~jmccullough/Applets/Flash/Fluids,%20Oscillati
ons%20and%20Waves/StandingWaveExplanation.swf
Slide 64
Wave Interference Destructive Interference wave displacements
in opposite direction Constructive Interference wave displacements
in same direction Antinode Node
http://zonalandeducation.com/mstm/physics/waves/int
erference/waveInterference1/WaveInterference1.html
Slide 65
Principle of Superposition The displacement of a medium caused
by two or more waves is the algebraic sum of the displacements
caused by the individual waves. In other words, two or more waves
can combine to form a new wave - interference. Constructive
interference result in a new wave with greater amplitude.
Destructive interference result in a new wave with lesser
amplitude.
Standing Waves A standing wave is a wave which is reflected
back and forth between fixed ends (off a string or pipe, for
example). Reflection may be fixed or open-ended. Superposition of
the wave upon itself results in a pattern of constructive and
destructive interference and an enhanced wave.
https://www.youtube.com/watch?v=-n1d1rycvj4
https://www.youtube.com/watch?v=-gr7KmTOrx0
Slide 69
Standing Waves Wave that appears to be standing still. Standing
wave is the interference of two traveling waves (with equal f and
), moving in opposite directions. Nodes are at the ends of the
rope. Antinodes are in the middle.
Slide 70
Standing Waves If you double the frequency of the vibration,
you can produce one more node and one more antinode in the rope.
Further increases in frequency produce even more nodes and
antinodes. http://www.walter-fendt.de/ph14e/stwaverefl.htm
Slide 71
Resonance Resonance is a special form of simple harmonic motion
in which the additions of small amounts of force at specific times
in the motion of an object cause a larger and larger displacement.
Resonance from wind, combined with the design of the bridge
supports, may have caused the original Tacoma Narrows Bridge to
collapse. London Millenium bridge Tacoma Narrows Bridge Tacoma
Narrows Bridge2 https://www.youtube.com/watch?v=JiM6AtNLXX4 glass
shattering montage
Slide 72
Slide 73
Standing Waves Nodes Poinst of complete destructive
interference Do not move Antinodes Poinst of complete constructive
interference Largest amplitude points of the standing wave Incident
wave Reflected wave
Slide 74
Fixed end Standing Waves (violin string) First Harmonic
Standing Wave Pattern Third Harmonic Standing Wave Pattern 1 st
harmonic L= v/f 1 2 nd harmonic (one octave higher) L= v/f 2 3 rd
harmonic L= 3/2 3/2 v/f 3
http://zonalandeducation.com/mstm/physics/waves/standingWav
es/standingWaves1/StandingWaves1.html If a guitar string is simply
plucked, the fundamental frequency dominates. The first harmonic
can be produced by touching the string lightly in the middle when
plucking it. Touching the string lightly one-third the length of
the string from one end will produce the second harmonic
Slide 75
Harmonic # of Nodes # of Antinodes PatternResonant Frequency
1st21 L = 1 /2 = v/2f 1 2nd32 L = 2 = v/f 2 f 2 =2f 1 3rd43 L = 3 3
/2 = 3v/2f 3 f 3 = 3f 1 4th54 L = 2 4 = 2v/f 4 f 4 = 4f 1 5th65 L =
5 5 /2 = 5v/2f 5 f 5 = 5f 1 6th76 L = 6 6 /2= 3v/f 6 f 6 = 6f 1
nthn + 1n -- L = n n /2= nv/2f n f n = nf 1 Standing Waves First
Harmonic Standing Wave Pattern Second Harmonic Standing Wave
Pattern Third Harmonic Standing Wave Pattern
http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html
guitar strings
Slide 76
Example: If a violin string vibrates at 440 Hz as its
fundamental frequency, what are the frequencies of the first four
harmonics
Slide 77
Example: Violin A 0.32 m long violin string is tuned to play A
above middle C at 440 Hz What is the wavelength of the fundamental
string vibration? 1 st harmonic L=
Slide 78
Wind Instruments Sound is generated by vibrations, so when air
is blown into one end of a pipe or tube and then bounces off of the
sides, the air vibrates. When the air inside the tube vibrates at
the same frequency, or in resonance, with the vibration of your
lips, a sound is produced.
Slide 79
Wind Instruments The vibrating reed or lip produces sound waves
with many frequencies. This sound wave of alternate high- and low-
pressure variations moves down the air column. When the wave
reaches the end of the column, it is reflected back up the column
and can set up standing waves.
Slide 80
Resonance in an Open Pipe Ends must be same - both ends are
pressure nodes (displacement antinodes) Harmonics increase by 1: 1
st, 2 nd, 3 rd, 4 th, 5 th, etc. 1 st Harmonic L = /2 2 nd Harmonic
L = 3 rd Harmonic L = 3 /2 n th Harmonic L = n n /2 Pressure nodes
sound wave in pipes Pressure nodes
Slide 81
Resonance in a Closed Pipe Ends must be opposite: open nodes,
closed-antinodes Harmonics increase by 2 (only odd harmonics). 1 st
Harmonic L = /4 = v/4f 1 3 nd Harmonic L = 3 /4 = 3v/4f 3 f 3 = 3f
1 5 th Harmonic L = 5 /4 = 5v/4f 5 f 5 =5f 1 n th Harmonic (odd
only) L = n n /4 = nv/4f n f n = nf 1 Pressure node Pressure
antinode http://zonalandeducation.com/mstm/physics/waves/standin
gWaves/standingWaves3/StandingWaves3.html
Slide 82
Closed Pipes Ends are opposite Odd Harmonics Open Pipes
http://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html Shakuhachi
Ends same Every Harmonic Pan Pipes Clarinet Trumpet Flute Sax
Slide 83
Do Now For an open tube with a length of 0.3 m, a) What is the
fundamental resonant frequency? b) What is the frequency of the 2
nd harmonic? The speed of sound waves in the tube is 343 m/s OPEN
PIPE 1 st Harmonic f1 = 572 Hz 2 nd Harmonic f 2 = 1143 Hz (= 2f 1
) 1 st 2 nd 3 rd
Slide 84
Do Now Closed PIPE For closed tube with a length of 2 m, a)
What is the fundamental resonant frequency? b) What is the
frequency of the 3 rd harmonic? The speed of sound waves in the
tube is 343 m/s 1 st Harmonic f1 = 42.88 Hz 2 nd Harmonic f 3 =
128.6 Hz (= 3f 1 ) 1 st 3 rd
Slide 85
Determine the length of a closed-end air column that produces a
fundamental frequency (1st harmonic) of 480 Hz. The speed of waves
in air is known to be 340 m/s. Draw a diagram to help you solve. 1
st Harmonic v = 340 m/s f = 480 Hz L
Slide 86
The lead instrumentalist of a band uses a test tube (closed-
end air column) with a 17.2 cm air column. The speed of sound in
the test tube is 340 m/sec. Find the frequency of the first
harmonic played by the instrument. 1 st Harmonic L=0.172m f1=494
Hz
Slide 87
Doppler Effect
Slide 88
Stationary Sound source emitting sound with frequency f s I
hear f s
Slide 89
Doppler Effect Sound source moving with v s emitting sound with
frequency f s I detect lower pitch f O < f s I detect higher
pitch f O >f s
Slide 90
Breaking the Sound Barrier Sound source moving at the speed of
sound (Mach 1) emitting sound with frequency f s I detect lower
pitch f o < f s OW, I hear sonic BOOM
Slide 91
Supersonic Sound source moving faster than the speed of sound
(Mach 1.4) emitting sound with frequency f s I detect lower pitch f
o < f s OW, I hear sonic BOOM
http://www.youtube.com/watch?feature=player_detailpage&v=-d9A2oq1N38
The Doppler effect occurs in all wave motion, both mechanical
and electromagnetic. Astronomers observe light from distant
galaxies and use the Doppler effect to measure their speeds and
infer their distances. Radar detectors use the Doppler effect to
measure the speed of baseballs and automobiles. Physicians can
detect the speed of a moving heart wall in a fetus by means of
Doppler effect in an ultrasound.
Slide 94
Doppler Effect A trumpet player sounds C above middle C (524
Hz) while traveling in a convertible at 24.6 m/s. If the car is
coming toward you, what frequency would you hear? Assume that the
temperature is 20C. F s = 524 Hz v s = 24.6 m/s
Slide 95
Doppler Effect A trumpet player sounds C above middle C (524
Hz) while traveling in a convertible at 24.6 m/s. Once the car
passes and is going away from you, what frequency would you hear?
The speed of sound is 343 m/s. F s = 524 Hz v s = 24.6 m/s
Slide 96
One foggy morning, Benny is driving his speed boat toward a
lighthouse as the fog horn blows with a frequency of 180.0 Hz. As
he approaches, he hears a frequency of 188 Hz. What speed is Kenny
traveling to hear this change in frequency? The speed of sound in
air is 343 m/s. Givens: f s = 180Hz f O = 188 Hz v = 343 m/s v s =
0
