chapter 19 vibrations and waves there are two ways to transmit information and energy in our...
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Chapter 19Chapter 19
Vibrations and Vibrations and Waves Waves
There are two ways to transmit information and energy in our universe:
Particle Motionand
Wave Motion
Vibration - Wiggle in time
Wiggle in space Wave -
Light and SoundBoth are vibrations of
different kinds.
1. VIBRATION OF A 1. VIBRATION OF A PENDULUMPENDULUM
Demo - MetronomeDemo - Metronome
Demo - Bowling ball pendulumDemo - Bowling ball pendulum
Video – Three Bowling BallsVideo – Three Bowling Balls
Video – Swinging ExamplesVideo – Swinging Examples
Demo - Pendulum with extra massDemo - Pendulum with extra mass
Time to swing depends on the length but not the mass of the pendulum. Time to swing depends on the length but not the mass of the pendulum.
T is the period, the time for one vibration.
l is the length of the pendulum. g is the acceleration due to gravity. Galileo discovered this. Period (T ) is independent of the
mass of the bob.
g2πT l
Period of a PendulumPeriod of a Pendulum
Pendulum Uses:Pendulum Uses:
Timing
Oil prospecting
Walking
When the oscillation is small, the motion is called simple harmonic motion and can be described by a simple sine curve.
2.2. WAVE DESCRIPTIONWAVE DESCRIPTION
Frequency ( f ) is the number of
vibrations per unit of time made by the
vibrating source.
Units - cycles per second
1/s
Hertz (Hz)
Picture of a Transverse Picture of a Transverse WaveWave
Crest
Trough
Wavelength
A
A - Amplitude
Baseline
Distance between adjacent crests in a
transverse wave
Distance a wave travels during one vibration
- meters or feet
Wavelength (Wavelength ())
Units
The period (T ) of a vibration is the time required to make one vibration.
The period (T ) of a wave is the time required to generate one wave.
It is also the time required for the wave to travel one wavelength.
secvibration/21
FrequencyFrequency PeriodPeriod
ionsec/ vibrat21
ionsec/ vibrat31
ionsec/ vibrat41
ionsec/ vibrat2
ionsec/ vibrat1
/ secvibrations3
secvibration/1
/ secvibrations4
/ secvibrations2
FrequencyPeriod 1
f1T
In symbolic formIn symbolic form
oror
3.3. WAVE MOTIONWAVE MOTION
Energy is transported by
particles or waves.
A wave is a disturbance transmitted
through a medium.
Exception: light does not require a
medium.
Demo – Waves on a ropeDemo – Waves on a rope
A disturbance moves through
the medium.
Elements of the medium vibrate.
Examples: ripples on water
wheat waves
4.4. WAVE SPEEDWAVE SPEED
The average speed of anything is defined as
timedistance
v
T1
v
For a wave, if the distance traveled is a
wavelength (), then the time to travel
this distance is the period (T ). Then
Tv
or
fv Therefore
fT1
Remember that
is true for all waves.
Demo - Complete Bell Wave MachineDemo - Complete Bell Wave Machine Note: v is dictated by the medium.
(must change medium to change v) f is dictated by the source. (must change the source to change
f )
fv
5.5. TRANSVERSE WAVESTRANSVERSE WAVES
Video - Slinky Transverse WavesVideo - Slinky Transverse Waves
Examples: string musical instruments ripples on water electromagnetic waves
Demo – Human Waves (Include Demo – Human Waves (Include Standing)Standing)
6.6. LONGITUDINAL WAVESLONGITUDINAL WAVES
Video - Slinky Longitudinal WavesVideo - Slinky Longitudinal Waves
ParametersRarefactions are regions of low density.Compressions (condensations) are
regions of high density.is the distance between successive
rarefactions or successive compressions.
Demo - SlinkyDemo - Slinky
Example: sound in air
Rarefactions
Compressions
7.7. INTERFERENCEINTERFERENCE
Video - Superposition of WavesVideo - Superposition of Waves
Slide - Interference - Interference
InterferenceInterference
Constructive interference occurs Constructive interference occurs when waves are in phase, that is when waves are in phase, that is when crests are superimposed and when crests are superimposed and troughs are superimposed. troughs are superimposed.
Destructive interference occurs Destructive interference occurs when waves are out of phase, that is when waves are out of phase, that is when crests are superimposed with when crests are superimposed with troughs.troughs.
Interference is a Interference is a characteristic of all waves.characteristic of all waves.
Standing WavesStanding 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.” It is a changing interference pattern.
Demo - Rope and strobeDemo - Rope and strobe
There is no vibration at a node.There is maximum vibration at an antinode. is twice the distance between successive
nodes or successive antinotes.
Video - Drumhead VibrationsVideo - Drumhead Vibrations
Demo - Organ pipe and tuning forkDemo - Organ pipe and tuning fork
Demo – Standing waves in sheet Demo – Standing waves in sheet
metalmetal
Another example: musical
instruments
8.8. DOPPLER EFFECTDOPPLER EFFECT
Refers to the change in frequency when
there is relative motion between an observer
of waves and the source of the waves
Video - Doppler Effect in AirVideo - Doppler Effect in Air
Video - Doppler Effect in a Ripple TankVideo - Doppler Effect in a Ripple Tank
URL– Doppler Movie (htm)URL– Doppler Movie (htm)
Demo – Doppler RocketDemo – Doppler Rocket
When a source of waves and an When a source of waves and an observer of waves are getting closer observer of waves are getting closer together, the observer of the waves together, the observer of the waves observes a frequency for the waves observes a frequency for the waves that is higher than the emitted that is higher than the emitted frequency.frequency.
When a source of waves and an When a source of waves and an observer of waves are getting observer of waves are getting farther apart, the observer of the farther apart, the observer of the waves observe a frequency for the waves observe a frequency for the waves that is lower than the emitted waves that is lower than the emitted frequency.frequency.
All waves exhibit the Doppler effect.
A particularly interesting example is
used by astronomers to determine if
light emitting objects (such as stars)
are getting closer to us or farther
away.
On average most stars are moving
farther away, and their light spectra
are “red shifted.”
Red ShiftRed Shift
Lab Absorption Spectrum of Element XLab Absorption Spectrum of Element X
Star Absorption Spectrum of Element XStar Absorption Spectrum of Element X
Star is moving away from us.Star is moving away from us.
Red ShiftedRed Shifted
Police use the Doppler effect to
catch speeding motorists.
Radar bounced off a spinning
planet can exhibit a Doppler effect
and lead to a determination of the
spin rate of the planet.
This was used to discover that
Venus has a retrograde spin.
Planet Spinning Under Cloud Cover
9.9. BOW WAVESBOW WAVES
Waves in front of moving object pile up.
Wave Barrier
x x x x x xx
“Bow” Wave
x x x x x x x
The familiar bow wave generated by a speedboat knifing through the water is a non-periodic wave produced by the overlapping of many periodic circular waves. It has a constant shape.
10. SHOCK WAVES10. SHOCK WAVES Just as circular waves move out
from a swimming bug, spherical waves move out from a flying object. If the object flies faster than the waves, the result is a cone-shaped shock wave.
Demo - Cone of WavesDemo - Cone of Waves There are two booms, one from the
front of the flying object and one from the back.
Demo – Crack whipDemo – Crack whip
Video – Sonic Booms OnlineVideo – Sonic Booms Online
Video - FB-111 Sonic BoomVideo - FB-111 Sonic Boom
Video – F-14 Sonic BoomVideo – F-14 Sonic Boom
URL – More Boom URL – More Boom
Word Doc - Sonic BoomWord Doc - Sonic Boom
The boom is not produced just when the flying
object “breaks” through the sound barrier.
- faster than the speed of sound
- slower than the speed of soundSubsonic
Supersonic
Mach Number =speed of sound
speed of object