Vibrations and Waves

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Chapter 18

• Vibrations and Waves

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Simple Harmonic Motion

• to-and-fro vibratory motion
• results in sine curves
• Examples
• Metronome

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Simple Harmonic Motion

• to-and-fro vibratory motion
• results in sine curves
• Examples
• mass on a spring

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Simple Harmonic Motion

• to-and-fro vibratory motion
• results in sine curves
• Examples
• pendulum

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Pendulums

• The period does not depend on the amount of mass.
• The period does depend on the length of the
  pendulum.

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Wave Comparisons

• Water Waves
• Sound Waves
• Light Waves
• Waves
• Medium
• Wave Speed
• What if you go faster?
• Human Perception

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Vibrations and Waves
Wiggles in Time
Wiggles in Space

• Oar in Water
• Wings of a Bee
• Electrons in an Light Bulb

Water Waves Sound Waves Light Waves
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Wave Description

• Period - the time required for one vibration
• measured in seconds
• Frequency - number of vibrations / unit time
• measured in Hertz

Bowling Ball Demo
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Wave Description
Bowling Ball Demo
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• If you double the frequency of a vibrating
  object, what happens to the period?
• a) the period doubles
• b) the period stays the same
• c) the period is cut in half
• d) not enough information is given

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• What is the frequency in vibrations per second of
  a 60-Hz wave in cycle per second?
• Answer 60 cycles per second
• What is its period (seconds)?
• Answer 1/60 second

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Sine Curves

• Amplitude - distance from the baseline to the
  crest of a wave
• Wavelength - the distance from the top of one
  crest to the top of the next one

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Example Wave
2 ½ meters
Antinode
20 cm
Amplitude 10 cm
Wavelength 1 m
Number of Nodes 6
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Wave Motion

• medium - the stuff that carries the wave

Waves
Medium
water waves
water
rope
waves on a rope
people
stadium waves
sound
air
light
space (vacuum)
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Wave Speed

• Speed with which waves pass by a particular point
• e.g. the speed of a surfer
• Depends only on the type of medium
• Wave Speed Frequency ? Wavelength
• m/s cycles/s x
  meters/cycle

Waves on a Rope
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• If a water wave oscillated up and down three
  times each second and the distance between wave
  crest is 2 m, what is its frequency in Hertz?
• Answer 3 Hz
• What is its period (seconds)?
• Answer 1/3 second
• What is its wavelength (meters)?
• Answer 2 m
• What is its wave speed (m/s)?
• Answer 6 m/s

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Transverse Waves

• Side to side vibration in a direction
  perpendicular to the wave's motion
• Examples
• water waves
• waves on a rope
• string musical instruments

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Longitudinal Waves

• back and forth vibration in a direction parallel
  to the wave's motion
• Examples
• slinky waves
• sound waves

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http//www.kettering.edu/drussell/Demos/waves/wav
emotion.html
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• The distance from trough to trough on a periodic
  wave is called its...
• a) frequency.
• b) period.
• c) wavelength.
• d) amplitude.

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• Changing which of the following significantly
  affects the period of a pendulum?
• a) mass
• b) amplitude
• c) length
• d) angle

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• Dipping a finger in water faster and faster
  causes the wavelength of the spreading waves to
• a) increase
• b) decrease
• c) stay the same
• d) not enough information is given

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INTERFERENCE

• Constructive or destructive interference results
  when waves add.
• Standing Waves - wave pattern produced from
  interfering waves
• Examples
• Rope Waves
• Guitar Strings
• Bell Wave Machine
• Organ Pipe

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http//www.kettering.edu/drussell/Demos/superposi
tion/superposition.html
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DOPPLER EFFECT

• the change in frequency due to motion of the
  source
• "Wheeeeeeeeeeee.Oooooooooooooo
• Coming towards you higher frequency
• Going away from you lower frequency
• Examples
• moving cars and trains
• rotating whistle

• Doppler with Water

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Subsonic

• - slower than the speed of sound

• Supersonic

- faster than the speed of sound
speed of object
Mach Number

speed of sound

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Shock Wave
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Doppler Shift Gives Radial Velocity
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• A train whistle at rest has a frequency of
  3000 Hertz. If you are standing still and
  observe the frequency to be 3010 Hertz, then you
  can conclude that...
• a) the train is moving away from you.
• b) the train is moving toward you
• c) the sound from the whistle has echoed
• d) not enough information is given

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• Dipping a finger in water faster and faster
  causes the wavelength of the spreading waves to
• a) increase
• b) decrease
• c) stay the same
• d) not enough information is given

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• The distance from trough to trough on a periodic
  wave is called its...
• a) frequency.
• b) period.
• c) wavelength.
• d) amplitude.

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