Chapter 25: Vibrations and Waves

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Chapter 25 Vibrations and Waves
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Sine and Cosine
Period 2p
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Period

• The period (measured in seconds) of a wave tells
  you how long it takes for the wave to make one
  complete cycle.
• If a wave makes one complete cycle in 4 seconds,
  what is the period of the wave?
• T _____ seconds
• The period of a pendulum tells you how long it
  takes for the pendulum to make one complete
  cycle. The pendulum will make one complete cycle
  when it returns to the position where it started.

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• If you have two pendulums with different masses
  1.) What do you notice about the periods of the
  pendulums with different masses? Do they have
  the same period? Different periods? (In other
  words, does it take the same amount of time for
  each pendulum to make one full cycle? Do they
  make one full cycle in different amounts of
  time?)
• If you have two pendulums with different lengths
  2.) What do you notice about the periods of the
  pendulums with different lengths? Do they have
  the same period? Different periods? (In other
  words, does it take the same amount of time for
  each pendulum to make one full cycle? Do they
  make one full cycle in different amounts of
  time?)

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Vibration

• A vibration occurs when the particles in an
  object move back and forth in the opposite
  direction of equilibrium (resting position)
• A swinging pendulum is an example of a vibration.
  When a pendulum swings back and forth, it is
  moving away from its equilibrium position.
• When a guitar string is plucked, the string moves
  up and down in opposite directions from its rest
  position, causing vibrations in the string.
• When an earthquake occurs, the particles of earth
  move away from their resting position, resulting
  in vibrations.

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Simple Harmonic Motion

• The actual motion of the vibration is called
  simple harmonic motion.
• A pendulums motion is called simple harmonic
  motion a plucked guitar strings motion is
  called simple harmonic motion the motion of
  waves created by a slinky moving up and down is
  called simple harmonic motion.
• The motion of almost any vibration is called
  simple harmonic motion.

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Waves

• Vibrations result in waves water waves, light
  waves, sound waves, etc.
• Crest
• Trough
• Wavelength
• Amplitude

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Parts of a wave

• The wavelength is the distance from the top of
  one wave to the next.
• The top of the wave is called a crest, the bottom
  of a wave is called the trough.
• The crest is a high point the trough is a low
  point.
• The amplitude is the distance from the midpoint
  of the wave to the crest (or trough) of a wave.
  The amplitude equals the maximum displacement
  from the equilibrium (or rest) position.

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• The period is the time it takes for a wave to
  make one complete cycle.
• The frequency of a wave describes how frequently
  the wave occurs (usually in one second).
• Frequency is measured in hertz (Hz)
• If a pendulum can make 2 complete cycles in one
  second, then its frequency is 2 Hz.
• If the pendulum makes two complete cycles in one
  second, how many seconds does it take for the
  pendulum to make only one complete cycle? (What
  is the pendulums period?)

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• If the pendulum makes four complete cycles in one
  second, how many seconds does it take for the
  pendulum to make one complete cycle?
• If the pendulum makes 10 complete cycles in one
  second, how many seconds does it take for the
  pendulum to make one complete cycle?
• What do you notice about the frequency and period
  of the pendulum?

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Frequency and Period

• The frequency and period are inverses of each
  other. This is true for the frequency and period
  of all waves.
• f (frequency) 1
• T (period)
• T 1
• f

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• 1.) A pendulum makes 3 cycles in one second.
  What is the frequency of the pendulum? What is
  the period?
• 2.) A wave takes 6 seconds to complete one full
  cycle. What is the period of the wave? What is
  the frequency?
• 3.) A water wave vibrates up and down two times
  each second. What is the frequency of the wave?
  What is the period?

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• 1.) The Sears Building in Chicago sways back and
  forth at a frequency of 0.1 Hz. What is its
  period of vibration?
• 2.) A wave makes one complete cycle in 5 seconds.
  How many cycles does it complete in 1 second?
  How many cycles does it complete in 25 seconds?

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Do Now 3/4/09

• 1.) What is the difference between the period of
  a wave and the frequency of a wave?
• 2.) Draw a wave. Label the following parts on
  the wave amplitude, wavelength, crest, trough.

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• Vibrations pass through a medium
• A medium is the material or the object that
  experiences the disturbance of a vibration.
• When you shake a rope on one end, the vibration
  passes through the entire rope (the rope is the
  medium).
• Light and sound waves reach us by passing through
  the air (air is the medium).

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Do Now 3/5/09

• 1.) A water wave vibrates up and down two times
  each second and the distance between wave crests
  is 3 meters.
• (a) What is the frequency of the wave?
• (b) What is the wavelength?
• 2.) A wave makes one complete cycle in 4 seconds.
  How many cycles does it complete in 1 second?
• 3.) Pendulum A has a length of 20 cm. Pendulum B
  has a length of 35 cm. Which pendulum has a
  longer period? Explain.

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• If a train of freight cars, each 10 m long,
  rolls by you at the rate of 2 cars each second,
  what is the speed of the train?
• Remember speed distance/time

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• Imagine that you fix your eyes at a stationary
  point on the surface of water and observe that
  two crests pass that stationary point each
  second. You also notice that the wavelength is 3
  meters. What is the speed of the wave in meters
  per second? (In other words, how many meters pass
  by each second?)

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Wave Speed

• Wave speed frequency x wavelength
• In equation form v f?
• ? Greek letter Lamda represents wavelength
• Wave speed is measured in m/s
• If the frequency of a sound wave is 160 Hz and
  the wavelength is 2.13 m, what is the wave speed?

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• 1.) If the frequency of a sound wave is 264 Hz
  and the wavelength is 1.29 m, what is the wave
  speed?
• 2.) If the frequency of a sound wave is 396 Hz
  and the wavelength is 0.86 m, what is the wave
  speed?

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Do Now 3/6/09

• 1.) If a water wave vibrates up and down 2 times
  each second and the distance between wave crests
  is 1.5 m, what is the frequency of the wave? What
  is the wavelength? What is its speed?
• 2.) What is the wavelength of a 340 Hz sound wave
  when the speed of sound in air is 340 m/s?
• 3.) Does the following wave have a low frequency
  or high frequency? Does it have a short
  wavelength or a long wavelength?

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Types of Waves

• Transverse Waves occur when the motion of the
  medium (such as a rope) is perpendicular to the
  direction in which the wave travels.
• The rope moves up and down in a vertical
  direction, but the wave is moving horizontally
  down the rope.
• Longitudinal Waves occur when the medium moves in
  the same direction in which the wave travels. The
  medium moves along the direction of the wave
  instead of perpendicular to it.

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Journal 3/6/09

• 1.) What type of wave is associated with sound
  waves? Transverse or longitudinal?
• 2.) Did Bill Nye clear up any confusion you had
  about waves? Did he help you understand certain
  concepts that you were unsure about before you
  watched the video? If so, what concepts?

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Do Now 3/9/09

• 1.) If a water wave vibrates up and down three
  times each second and the distance between wave
  crests is 4 meters, what is the frequency of the
  wave? What is the wavelength? What is its
  speed?
• 2.) What is the difference between transverse
  waves and longitudinal waves?

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Constructive Interference

• When the crest of one wave interferes with the
  crest of another, their individual effects add
  together.
• The result of two crests interfering is a wave of
  increased amplitude.

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Constructive Interference

• When the trough of one wave interferes with the
  trough of another, their individual effects add
  together.
• The result of two troughs interfering is a wave
  of increased amplitude.

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Destructive Interference

• When the crest of one wave interferes with the
  trough of another wave, their individual effects
  are reduced.
• The high part (which is the crest) of one wave
  fills in the low part (which is the trough) of
  the other wave. The crest and the trough cancel
  out.

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Destructive Interference

• The crest and trough do not always cancel out.
• When the crest and trough meet, the amplitude can
  be reduced.

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Standing Waves

• An original wave (called the incidental wave) and
  the reflected wave form a standing wave.

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Nodes and Antinodes

• The parts of the wave that remain stationary
  (that dont move) are called nodes.
• The positions on a standing wave with the largest
  amplitudes are called antinodes. Antinodes occur
  halfway between two nodes.

ANTINODES
NODES
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Do Now 3/6/09

• 1.) While watching ocean waves at the dock of the
  bay, you notice that 10 waves pass beneath you in
  30 seconds. You also notice that the crests of
  two waves are 5 m apart. What are the period,
  frequency, wavelength, and speed of the ocean
  waves?
• 2.) Decide whether each
• labeled position in the
• following diagram is a
• position where constructive
• or destructive interference
• occurs.

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Doppler Effect

• When a fire engine gets close to you, you
  experience the waves more frequently, which is
  why the sound is so loud. But as it moves away
  from you, you encounter its waves less
  frequently, so the sound becomes much softer,
  until finally you dont hear the sirens at all.
• When a source moves towards you, you experience a
  change in a waves frequency, not a change in a
  waves speed.