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Transcript of VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as...
![Page 1: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/1.jpg)
VIBRATIONS AND WAVES
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Hooke's LawOne of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law.
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The idea behind Hooke's The idea behind Hooke's Law:Law:
Any object that is initially Any object that is initially displaced slightly from a displaced slightly from a stable equilibrium point stable equilibrium point will oscillate about its will oscillate about its equilibrium position. It equilibrium position. It will, in general, experience will, in general, experience a restoring force that a restoring force that depends on the depends on the displacement x from displacement x from equilibrium. equilibrium.
![Page 4: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/4.jpg)
Harmonic Motion Oscillator
http://www.kettering.edu/~drussell/Demos/SHO/mass.html
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Energy Conversion
http://www.kettering.edu/~drussell/Demos/SHO/mass.html
![Page 6: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/6.jpg)
Harmonic Motion
![Page 7: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/7.jpg)
Simple Harmonic Motion (SHM)
• Motion that occurs when the restoring force acting on an object is proportional to the object’s displacement from its resting position
• Harmonic part if SHM means the motion repeats itself
• Objects at the end of springs move in SHM when they are displaced from their rest position and bounce up and down on the spring, or oscillate.
![Page 8: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/8.jpg)
Sine Curve• To and fro vibration motion of swinging
pendulum in small arc is called SHM
![Page 9: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/9.jpg)
Sine Curve
![Page 10: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/10.jpg)
Sine Curve
• Pictorial representation of a wave
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Simple Tire Swing
![Page 12: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/12.jpg)
Harmonic motion in a Bottle…making a bottle “sing”
http://arts.ucsc.edu/ems/music/tech_background/TE-12/teces_12.htmlhttp://arts.ucsc.edu/ems/music/tech_background/TE-12/teces_12.html
Flow of air across bottle top, pulls air out of bottle reducing mass of Flow of air across bottle top, pulls air out of bottle reducing mass of air in bottle which reduces pressure within bottle. The low pressure air in bottle which reduces pressure within bottle. The low pressure pulls air back into bottle causing oscillations. pulls air back into bottle causing oscillations.
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VIBRATION OF A PENDULUM
• What does the period (T) depend upon?
• Length of the pendulum (l).• Acceleration due to gravity (g).• Period does not depend upon
the bob mass.
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Pendulum
When oscillations are
small, the motion is called
simple harmonic motion (shm)
and can be described by a
simple sine curve.
T l g2
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Vibrations and Waves
• Waves transmit energy and information.
–Sound and Light are examples of waves.
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There are two ways to transmit information/energy
in our universe:
Particle Motion
and
Wave Motion Wave Simulation: http://phet.colorado.edu/simulations/sims.php?sim=Wave_Interference
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Mechanical Waves
• Requires a medium• Ex. Water waves, sound• Two different material objects cannot be in the
same place at the same time…however mechanical waves displace matter to transfer energy and thus can be in the same place at the same time.
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Electromagnetic Waves
•Do not require a medium (can move through empty space, a vacuum)
•Ex. Radio waves, light waves, microwaves
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WAVES
•Transfer energy not matter from one place to another
•Disturbance that moves through space or through a medium (material)
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Wave Pulse
• Single Disturbance
http://www.colorado.edu/physics/phys4830/phys4830_fa01/lab/n0911.htm
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Wave Train (Continuous Wave)
• Series of pulses at regular intervals
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Sine Curve
AmplitudeA
Wavelength
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Picture of a Transverse Wavel
WavelengthWavelength
ll
A - AmplitudeA - Amplitude
AA
CrestCrest
TroughTrough
2. WAVE DESCRIPTION
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TRANSVERSE WAVESParticles vibrate perpendicular to
the wave motionTransverse waves can be polarized
string musical instruments
ripples on water
electromagnetic waves e.g. Light waves, x-rays, radio waves
![Page 25: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/25.jpg)
Picture of a Transverse Wave
CrestCrest
TroughTrough
WavelengthWavelength
AA
A - AmplitudeA - Amplitude
![Page 26: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/26.jpg)
Transverse Wave
http://dev.physicslab.org/Document.aspx?http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xmldoctype=3&filename=WavesSound_IntroductionWaves.xml
![Page 27: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/27.jpg)
Transverse Wave
• Particles vibrate perpendicular to the direction the wave travels
• Ex. Vibrating string of musical instrument, radio waves
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Longitudinal Wave
• Particles vibrate parallel to the direction of wave travel
• Ex. Sound
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Longitudinal Wave
• Compression- (similar to crests) – particles close together (high density)
• Rarefactions (similar to troughs)- particles spread out or rarefied (low density)
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LONGITUDINAL WAVESParticles vibrate parallel to the motion
of the waves
Ex: Sound Waves
http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xmlhttp://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xml
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Rarefactions are regions of low density.
Compressions (condensations) are regions of high density.
is the length of one rarefaction plus one compression
Animated comparison of transverse & longitudinal waves: http://members.aol.com/nicholashl/waves/movingwaves.html
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Time required to make one vibration.
• Time required to generate one wave
• Time required for the wave to travel one
wavelength.
Period (T)
![Page 33: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/33.jpg)
Frequency (f)
The number of vibrations per unit of
time made by the vibrating source.
Units -cycles/sec or hertz (Hz)
![Page 34: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/34.jpg)
Examples of Frequency
• What is the frequency of the second hand of a clock?
Frequency = 1cycle/60 secFrequency = 1cycle/60 sec Period = 60 secPeriod = 60 sec
What is the frequency of US Presidential What is the frequency of US Presidential elections?elections?
Frequency = 1 election/4 yrsFrequency = 1 election/4 yrs Period = 4 yrsPeriod = 4 yrs
FrequencyPeriod
1
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WAVE MOTION• Energy is transported by particles or waves. A wave
is a disturbance transmitted through a medium.
• Exception: light does not require a medium.
• A disturbance moves through the medium. Causing
elements of the medium vibrate.
– Example: ripples on water
![Page 36: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/36.jpg)
WAVE MOTION
• Medium is disturbed, energy is imparted to it
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WAVE SPEED
The average speed is defined as
time
distancev
![Page 38: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/38.jpg)
For a wave, if the distance traveled is a
wavelength (), then the time to travel
this distance is the period (T). Thus
Tv
fv or
![Page 39: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/39.jpg)
is true for all waves.
Note:
v is dictated by the medium
f is dictated by the source.
fv
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Surface Water Waves
http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xmlhttp://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xml
![Page 41: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/41.jpg)
SuperpositionTwo or more waves overlapping in
some way
The overlapping causes interference
Animation courtesy of Dr. Dan Russell, Kettering University
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Wave Interactions• Because waves are not matter but rather
displacement of matter, two waves can occupy the same space at the same time
• Combination of two overlapping waves is called superposition (causes interference)
![Page 43: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/43.jpg)
Superposition Principle
• Displacement of a medium (material) caused by 2 or more waves is the sum of the displacements of the individual waves at each point
• Holds true for all types of waves
![Page 44: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/44.jpg)
Interference
• Interference is a characteristic of all waves.
• Result of superposition of 2 or more waves
• Constructive- (crest meets crest or trough meets trough) amplitudes added
• Destructive- (crest meets trough) amplitudes subtract
![Page 45: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/45.jpg)
Interference Pattern
The pattern formed by superposition of different sets of waves that produce mutual reinforcement in some places and cancellation in others.
![Page 46: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/46.jpg)
Constructive Interference
Reinforcement
†
Maximum
In phase displacement
![Page 47: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/47.jpg)
ConstructiveConstructive
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Constructive Interference
• When the crest of one wave overlaps the crest of another
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Destructive- Crests and Troughs overlap
CANCELLATIONCANCELLATION
Zero Zero DisplacementDisplacement
![Page 50: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/50.jpg)
Destructive: crests & troughs overlap
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Interference –Destructive
• When the crest of one wave overlaps the trough of another
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Destructive Interference
![Page 53: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/53.jpg)
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Standing Waves• When two sets of waves of equal amplitude
and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is “standing still.”
![Page 55: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/55.jpg)
Standing Wave
V
V
V
V
Standing Wave
Incident Wave
Reflected Wave
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Standing Waves
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Standing Waves
• Result of interference and reflection
• When 2 sets of waves of equal amplitude and λ pass through each other in opposite directions, the waves are steadily in and out of phase with each other.
• Consists of nodes (0 amplitude) and antinodes (max. amplitude)
• Wave looks as if it is standing still
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Standing Waves
• Nodes- point in standing wave that undergoes complete deconstructive interference and is therefore stationary (no vibration)
• Antinode- a point in a standing wave (1/2way between 2 nodes) at which the largest amplitude occurs (maximum vibration)
Waves on a String: http://phet.colorado.edu/simulations/sims.php?sim=Wave_on_a_String
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Standing Waves
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Standing Waves
• Since the two identical waves travel in opposite directions, the net energy flow is zero; the energy is “standing” in the loops
![Page 61: VIBRATIONS AND WAVES Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That.](https://reader036.fdocuments.us/reader036/viewer/2022081519/56649e125503460f94afe34e/html5/thumbnails/61.jpg)
Standing Wave Harmonics
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There is no vibration at a node.• There is maximum vibration at an
antinode.
ll
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Standing Waves on a StringA string that's held very A string that's held very tightly at both ends can only tightly at both ends can only vibrate at very particular vibrate at very particular
wavelengths.wavelengths.
It can vibrate in halves, It can vibrate in halves, with a node at the middle of with a node at the middle of the string as well as each the string as well as each end, or in thirds, fourths, end, or in thirds, fourths, and so on. and so on.
Any wavelength that doesn't Any wavelength that doesn't have a node at each end of have a node at each end of the string, can't make a the string, can't make a standing wave on the string.standing wave on the string.
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Sound
• Travels as a longitudinal wave
• sounds audible to humans range from 20 - 20,000 Hz
• as f increases, pitch rises
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• Pitch refers to how f is observed
• speed of sound depends on medium and temperature
• speed of sound in air @ 0 ºC is 331 m/s…it increases by 0.59 m/s for every 1 ºC increase
Sound Simulation: http://phet.colorado.edu/simulations/sims.php?sim=Sound
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ORIGIN OF SOUND
• Sound Waves are produced by a vibrating object
• Are longitudinal, mechanical waves
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A noise is a jumble of sound waves.
A tone is a very regular set of waves, all the same size and same distance apart distance
apart.
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Approximate Speeds of Sound in Various Mediums
• 0º C air = 331 m/s
• 25º C Saltwater = 1533 m/s
• 25º C Freshwater = 1493 m/s
• Steel = 5790 m/s
• Iron = 5130 m/s
• Rubber = 1600 m/s
• Diamond = 12,000 m/s
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SOUND FREQUENCY• Determines pitch
– frequency and pitch are directly related
• 20-20,000 Hz are audible to avg. person
• < 20 Hz are infrasonic
• > 20,000 Hz are ultrasonic
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ULTRASONIC WAVES
• A) sonar showing Hamilton schooner, sunk in Lake Ontario during War of 1812 lies under 91 m of water
• B) Bats (as well as dolphins) use echolocation
• C) ultrasonic waves travel through tissue get reflected by tumors or amniotic fluid
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Applications of Sound
SONAR: How deep is the water; where are the fish?
Ultrasound is sound at a frequency whichis outside of the range of human hearing
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What is the Mosquito Ring tone?
• High pitched ring tone that most adults cannot hear
• “teen buzz”
• originally designed as a repellant
• Mosquito ringtone is 17 kHz (that’s 17,000 Hz for those of you who forgot what a kilo is)
• The highest note on a piano is only 4 kHz
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Hearing Range by Age
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
18-21 yrs 30-39 yrs 40-49yrs 50-59 yrs
Hearing
Range
kHz
2-16 kHz 2-14
kHz 2-12 kHz 2-11
kHz
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Frequencies
• http://www.opti.dyndns.org/~dng/SOUND/ReferenceSound/refsound.html
• http://www.freemosquitoringtone.org/
Ringtones
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• Beats• When two sound waves of different frequency approach your ear,
the alternating constructive and destructive interference causes the sound to be alternatively soft and loud - a phenomenon which is called "beating" or producing beats. The beat frequency is equal to the absolute value of the difference in frequency of the two waves. Arising from simple interference, the applications of beats are extremely far ranging.
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/beat.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/sound/beat.html
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Pulsating Loudness due to Difference in Frequencies
• beat frequency or the different between the two frequencies beat frequency = |f2 - f1|
• beat pitch at which those beats are heard is the average of the two frequencies beat pitch = ½(f2+f1)
http://library.thinkquest.org/C005705/English/sound/sound3.htm
Examples of Beat Frequencies: http://www.school-for-champions.com/science/sound_beat.htm
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Practice
• Suppose you sound two tuning forks simultaneously: one fork has a frequency of 256 hz and the other has a frequency of 260 hz.
a) How many beats would be heard each second?
b) What is the pitch of these beats?
Try to determine the unknown frequencies: http://www.hazelwood.k12.mo.us/~grichert/explore/dswmedia/tonebeat.htm
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DOPPLER EFFECT• Refers to the change in frequency when
there is relative motion between an observer of waves and the source of the waves
Source moving with vsource < vsound ( Mach 0.7 )
Source moving with vsource = vsound ( Mach 1 - breaking the sound barrier )
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DOG IN WATER
Dog treads water (no velocity)
Dog swims to the right
Dog swims at same speed as water waves he is creating
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Doppler Effect
• A change in frequency due to a change in motion of either the vibration source or the observer
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Red & Blue Shifts
• Light from moving objects will appear to have different wavelengths depending on the relative motion of the source and the observer.
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Explain the following Bumper Sticker viewed on the back of a
passing car:
If this sticker appears blue you are driving too
fast!
http://www.artunderthesun.com/page3.htm
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• Objects in motion compress the light waves in front of them making them appear more blue (blue shift), the light waves behind are stretched out and appear more red (red shift).
http://cse.ssl.berkeley.edu/bmendez/ay10/2002/notes/lec8.html
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Reflection
• Turning back of a wave at the boundary of a new medium
• ex. Light off a mirror; sound echo
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Law of Reflection
• States that the angle of incidence equals the angle of reflection
• Өi = Өr
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Refraction• Bending of a wave path as it enters a new
medium at an angle
• Caused by difference in speed of wave in new medium
• Fast to slow- bends towards the normal
• Slow to fast- bends away from normal
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More on Refraction
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Drawing the Refracted Wave
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Refraction • Bending of waves due to change in speed as it passes through a new medium
• During World War I drivers returning to the rear from the front encountered alternating regions of intense artillery sound/ no sound caused by refraction,then reflection, then refraction, etc.
• On some evenings the whistle of trains miles away can be heard; however the train whistle is not heard during the day.
Sound speed is greater in warm air.
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Diffraction
• Spreading of waves around edges or through an opening of a boundary
• Is greatest when size of opening is smaller than wavelength of wave passing through
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Diffraction
A wave spreads out (noticeable diffraction) when the size of the slit is comparable to or smaller than the wavelength
A wave goes straight when the size of the slit is much larger than the wavelength
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Interference & Diffraction
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Resonance
• Condition that exists when the frequency of an applied force is the same as the natural frequency of vibration of an object or system
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What is the Natural Frequency?
• The frequency at which an elastic object naturally vibrates when hit, struck, or somehow disturbed.
• At this frequency, a forced vibration occurs with minimal energy.
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Natural Frequency...
• The natural frequency of an object depends on its ...– elasticity– size– shape
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Resonance
• If a singer produces a note at the same frequency as the resonant frequency of say a wine glass, they can set up vibrations in the glass itself. If they sing loud enough, they will produce larger vibrations and can shatter the glass!
http://www.scienceyear.com/outthere/index.html?page=/outthere/sound_check/http://www.scienceyear.com/outthere/index.html?page=/outthere/sound_check/sound_music.htmlsound_music.html
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Natural Frequency
• Examples– Mass on a Spring– Ringing Small and Large Bells– Xylophone – Rubbing the rim of a Glass
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What is Forced Vibrations?
• The tendency of one object to force another adjoining object into vibrational motion is referred to as a forced vibration
• During forced vibration sound is intensified because a larger surface area is available to vibrate air molecules.
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• http://mmem.spschools.org/grade3science/3.sound/musicvsnoise.html
http://upload.wikimedia.org/wikibooks/en/e/e3/TuningFork.gif
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Speed of Sound in Various Mediums
Medium Velocity of sound at 0C(m/s)
Air 331
Oxygen 460
Alcohol 1213
Water 1435
Copper 3560
Iron 5130
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Speed of Sound at Various Temperatures
Temperature (C) Velocity of sound (m/s) 0 331
20 344
100 386
500 553
1000 700
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Forced Vibrations...
Few examples:– Holding a tuning fork against a table– Vibration of factory floor from heavy
machinery
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What is Resonance?
• This occurs when the frequency of forced vibrations on an object matches the objects natural frequency.
• Results in an increase in amplitude that can destroy the object that is vibrating
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Examples of Resonance
• swinging your legs in a swing
• breaking a glass using sound
• a tuning fork exciting a guitar string
• a truck driving on a rough road
Video of glass shattering: http://www.wellesley.edu/Physics/Rberg/glassdemo.html
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SINGING IN THE SHOWER
• An experiment you can do is to stand in the shower (they reflect sound well) and start singing while changing the pitch slowly. At certain pitches the sound will suddenly amplify, because the sound waves fit an even number of times between the walls.
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Tacoma Narrows Bridge
• Why did the Tacoma Narrows Bridge fall?
Video of bridge: Video of bridge: http://www.archive.org/stream/SF121/SF121_256kb.mp4
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Tacoma Narrows Bridge• Collapsed Nov 7, 1940• The failure of the
bridge occurred when a never-before-seen twisting mode occurred. This is called a torsional mode whereby when the left side of the roadway went down, the right side would rise, and vice-versa, with the centerline of the road remaining still.
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• The original bridge was a suspended plate girder type that caught the wind, rather than allowing it to pass through.
• The wind produced a force in resonance with the natural frequency of the bridge.
• Increasing the amplitude until the bridge collapsed.
• What one student did after he learned of the Tocoma Bridge colapse: http://video.popularmechanics.com/services/player/bcpid1214137061?bctid=1233395616
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• http://www.answers.com/topic/tacoma-narrows-bridge
Current Tocoma Narrows Bridge
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• The MRI machine applies an RF (radio frequency) pulse that is specific only to hydrogen.
• The pulse causes the protons in that area to absorb the energy required to make them spin.
• The RF pulse forces them to spin at a particular frequency of resonance, in a particular direction.
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Amplitude vs. Frequency
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Resonance is all around us…
• …from a simple mass on a spring to Nuclear Magnetic Resonance…
• …from a “singing” glass to the collapse of the Tacoma Narrows Bridge.
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•
Shock WaveThe cone-shaped wave made by an object moving at supersonic speed through a fluid.
The source is moving faster than the wave speed, which is the speed of sound!
(Super-sonic speed)
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SHOCK WAVES
• There are two booms, one from the front of the flying object and one from the back.
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If the plane breaks the sound barrier and flies faster If the plane breaks the sound barrier and flies faster than the speed of sound, it produces a sonic boom than the speed of sound, it produces a sonic boom when it flies past. The boom is the "wake" of the when it flies past. The boom is the "wake" of the plane's sound waves.plane's sound waves.
http://hyperphysics.phy-astr.gsu.edu/Hbase/sound/soubar.html#c1
Source moving with vsource > vsound (Mach 1.4 - supersonic)
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Shock Wave
The temperature in the low pressure regions must drop, leading to condensation of the water vapor present: Ideal Gas Law
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Shock wave and Sonic Booms
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Sonic Boom
The loud sound resulting from the incidence of a shock wave.
This is the result of the pile up of many wave fronts which produces a sonic boom
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- slower than the speed of sound
Subsonic
• Supersonic - faster than the speed of sound
• Mach Number =speed of sound
speed of object