Intro to Waves

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Intro to Waves
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What is a wave?

• Take a moment to answer this question with the
  person at your table.
• As a group, create a definition and give an
  example of a wave.
• (Be a bit more original than an ocean wave.
• I know you can think of a better example)

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• a wave
• is a rhythmic disturbance that carries energy
  through matter or space

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Mechanical Waves

• require a medium
• medium the matter through which a wave travels
• examples water, air, anything made of matter

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• waves transfer energy from one point to another
  with little or no permanent displacement to the
  particles in the medium

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Two Types of Mechanical Waves

• Transverse Waves
• Longitudinal Waves

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Transverse Waves

• waves that propagate (or move) perpendicular to
  the direction of travel

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crest

• the point on the medium that exhibits the maximum
  amount of positive or upward displacement from
  the rest position

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trough

• the point on the medium that exhibits the maximum
  amount of negative or downward displacement from
  the rest position

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amplitude

• the maximum displacement of a particle on the
  medium from its equilibrium position

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wavelength

• the length of one wave is measured from a point
  on one wave to the same point on the next wave
• trough to trough
• crest to crest
• midpoint to midpoint

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Anatomy of a Transverse Wave

• Label the following parts of a transverse wave in
  your notes
• equilibrium
• crest
• trough
• amplitude
• wavelength

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Longitudinal Waves

• waves that propagate (or move) parallel to the
  direction of motion

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compression

• a point on a medium through which a longitudinal
  wave is traveling that has the maximum density

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rarefaction

• a point on a medium through which a longitudinal
  wave is traveling that has the minimum density

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Anatomy of a Longitudinal Wave

• Label the following parts of a longitudinal wave
  in your notes
• compression
• rarefaction
• wavelength

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Describing a Wave

• frequency the number of vibrations an object
  makes in a unit of time (generally one second)
• the unit of frequency is Hz
• period the time needed to complete one vibration
  (measured in seconds)

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• The Sears Tower sways back and forth at a
  frequency of about .1 Hz.
• What is the period of vibration?

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Speed Review

• an objects speed is described by the distance
  traveled in a specific amount of time (generally
  measured in m/s)

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Wave Speed

• v ? ? f
• wave speed wavelength ? frequency

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• A wave with a frequency of 60.0 Hz travels
  through vulcanized rubber with a wavelength of
  0.90 m.
• What is the speed of this wave?

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• The lowest pitch that the average human can hear
  has a frequency of 20.0 Hz.
• If sound with this frequency travels through air
  with a speed of 343 m/s, what is its wavelength?

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• A ship anchored at sea is rocked by waves that
  have crests 14 m apart. The waves travel at 7.0
  m/s.
• How often do the wave crests
• reach the ship?

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• Earthquakes generate shock waves that travel
  through Earths interior to other parts of the
  world. The fastest of these waves are
  longitudinal waves, like sound waves, and are
  called primary waves, or just p-waves. A p-wave
  has a very low frequency, typically around 0.050
  Hz.
• If the speed of a p-wave with this frequency is
  8.0 km/s, what is its wavelength?

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• A dolphin can typically hear sounds with
  frequencies up to 150 kHz.
• What is the speed of sound in water if a wave
  with this frequency has a wavelength of .01 m?

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• Sonar is a device that uses reflected sound waves
  to measure underwater depths. There is a sonar
  signal that has a frequency of 288 Hz. If the
  speed of sound in water is 1.45x103 m/s,
• what is the wavelength of
• the sonar signal?

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• Cicadas produce a buzzing sound that has a
  wavelength in air of 2.69 m. If the speed of
  sound in air is 343 m/s,
• what is the frequency of the sound produced by a
  cicada?
• What is its period?

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• A hiker shouts toward a vertical cliff 685 m
  away. The echo is heard 4 s later.
• What is the speed of sound of the hikers voice
  in air?
• The wavelength of the sound is .75 m. What is its
  frequency?
• What is the period of the wave?

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Wave Behavior

• What happens when a ball is thrown against a
  wall?
• Predict what would happen if a wave encounters a
  rigid boundary?

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• When a wave pulse is sent down a medium connected
  to a rigid wall,
• the energy transmitted
• is reflected.
• The reflected wave
• is inverted due to
• Newtons Third Law of
• Motion.

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• Predict what would happen if two waves were in
  the same place on a medium.
• Principle of Superposition
• the displacement of a medium caused by two or
  more waves is the algebraic sum of the
  displacements of the individual waves
• two or more waves can combine to form a new wave
• the result of the superposition of two or more
  waves is called interference

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Two Types of Interference

1. Constructive
2. Destructive

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Constructive Interference

• occurs when wave displacements are in the same
  direction
• the two waves pass through each other without
  changing their shapes or sizes
• the resultant pulse at the overlap of the two
  waves is the algebraic sum

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Constructive Interference
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Destructive Interference

• the superposition of waves with equal but
  opposite amplitudes
• when the pulses meet at the same location, the
  displacement of the medium is zero
• just as constructive interference, the waves pass
  through one another unchanged

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Destructive Interference
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Standing Waves

• a wave pattern that remains in a constant
  position
• the result of reflection and wave interference
• characterized by two fixed points on the wave

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Tacoma Narrows Bridge

• In an effort to save money, corners were cut in
  the design of the bridge thus compromising its
  stability
• On November 7, 1940 the Tacoma Narrows suspension
  bridge collapsed due to 42 mph wind induced
  vibrations.

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