Vibrations and Waves

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Chapter 25

• Vibrations and Waves

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Vibrations Waves

• Vibrationan oscillation or repeating back and
  forth motion
• Cannot exist in one instance needs time to move
  back and forth
• Wavea disturbance that repeats regularly in
  space and time and that is transmitted
  progressively from one place to the next with no
  actual transport of matter
• Cannot exist in one place
• Light and sound

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Vibration of a Pendulum

• Suspend a mass on a string let it swing back and
  fortha simple pendulum
• Pendulums swing back and forth with
  regularitythey are used to control the motion of
  clocks
• The time a pendulum takes to swing back and forth
  does not depend on mass
• Depends on length of pendulum and gravity
• Period (T)the time it takes to swing one time
  back and forth (on cycle)
• A long pendulum has a longer period than a
  shorter pendulum
• A pendulum on the moon has a shorter period than
  one on earth

T period L length (in meters) g
acceleration due to gravity
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Simple Pendulum

• What is the period of a 3.98 m long pendulum?
• A desktop toy pendulum swings back and forth once
  every 1.0 s. How long is this pendulum?

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Wave Description

• Simple Harmonic Motion (SHM)vibration about an
  equilibrium position in which a restoring force
  is proportional to the displacement from
  equilibrium
• Traces a sine curve
• Hookes Law (F kx) a mass on a spring is an
  example of simple harmonic motion

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Wave Description

• Cresthigh point
• Troughlow point
• Amplitudethe distance from the midpoint to the
  crest or trough (max displacement from
  equilibrium)
• Wavelengththe distance from the top of one crest
  to the top of the next one (or just the distance
  between successive identical parts of the wave)

crest
trough
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Wave Description

• Frequencyhow often a vibration occurs the
  number of back and forth vibrations in a given
  time (usually 1 second)
• A complete back and forth vibration is one cycle
• If three vibrations occur in 1 secondthe
  frequency is three cycles per second
• Unit of frequency is the hertz (Hz)
• A frequency of three cycles per second is 3 hertz
• AM radio waves are broadcast in kilohertz (103
  Hz)
• An AM station at 940 kHz on the radio dial
  broadcasts radio waves that have a frequency of
  940,000 vibrations per second
• FM radio waves are broadcast in megahertz (106
  Hz)
• An FM station at 96.7 on the radio dial
  broadcasts radio waves at 96,700,000 vibrations
  per second
• These radio frequencies are the frequencies at
  which electrons are forced to vibrate in the
  antenna of a radio stations tower
• Radar and microwave ovens operate at gigahertz
  (1012 Hz)

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Period Frequency

• The source of all waves is something that
  vibrates.
• The frequency of the vibrating source and the
  frequency of the wave it produces are the same.
• Frequency and period are inverses of each other
• If something makes 4 vibrations per second, it
  has a frequency of 4 Hz. It takes ¼ second to
  complete one cycle, so it has a period of ¼ s

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Wave Properties

• Does the time required to swing to and fro on a
  playground swing longer or shorter when you stand
  rather than sit?
• When you stand, the pendulum is effectively
  shorter, because the center of mass of the
  pendulum (you) is raised and closer to the pivot.
  So period is less it takes a shorter time.
• A weight suspended from a spring is seen to bob
  up and down over a distance of 20 cm, twice each
  second. What is its frequency? Its period? Its
  amplitude?
• Frequency 2 per second 2 Hz
• Period 1/frequency ½ s
• Amplitude distance from equil to max
  displacement i.e. ½ the peak-to-peak distance,
  i.e. 10cm

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Wave Motion

• Most of the information we need gets to us as a
  wave
• Sound waves, light waves, radio waves
• As a wave travels there is no transfer of matter
  between the two points
• The key point is that the medium (matter that
  wave is in) does not get propagated as the wave
  moves rather, it is the disturbance that
  propagates
• Water wave drop stone in a pond. See expanding
  circles
• Water is not transported with the circles
  rather, at any point, it moves up and down as
  wave passes by. (Can see this with a leaf on
  waters surface)
• Again, the medium returns to where it started
  after wave has gone by.
• Via waves, energy can be transferred from a
  source to a receiver without the transfer of
  matter between the two points (light waves, sound
  waves, microwaves)

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Wave Speed

• Speed depends on the medium of travel
• Sound waves moves about 4 times faster in water
  than they do in air
• Can find the speed (distance/time) of a wave by
  finding the wavelength and frequency

The wavelength is 1 m and 1 wave passes each
secondthe speed of the wave is 1 m/s
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Wave Speed

• Wave speed wavelength x frequency
• v ?f
• Works for all waves
• In California, Clay is surfing on a wave the
  propels him toward the beach with a speed of 5.0
  m/s. The wave crests are each 20. m apart.
• What is the frequency of the water wave?
• What is the period?
• Find the wavelength for B97? (radio waves are
  electromagnetic waves that travel at the speed of
  light 3.00 x 108 m/s)

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Transverse Waves

• Transverse wavewhen the motion of the waves is
  at right angles to the direction in which the
  wave is moving
• Transverse waves include water waves, waves on a
  stringed musical instrument, light, radio waves,
  microwaves

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Longitudinal Waves

• Longitudinal waveparticles move along (parallel
  to) the direction of the wave
• Longitudinal waves include sound waves. Air
  molecules vibrate to and fro.
• Can also be thought of as a pressure wave.
• http//physicsclassroom.com/mmedia/waves/lw.gif

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Interference

• Waves can superpose ( overlap), and form an
  interference pattern
• This property distinguishes waves from particles
• Can result in
• Increasing wave effects
• Decreasing wave effects
• Neutralizing (canceling) wave effects
• Constructive Interferencethe waves overlap and
  crests match up with crests troughs match up
  with troughs
• Results in a wave with an increased amplitude
• Destructive Interferencethe waves overlap and
  crests match up with troughs
• Results in a wave with a decreased amplitude
• Can cancel the wave effect

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Interference

• Interference is easy to see in water waves

Gray area is where the crest of one wave overlaps
the trough of the other. These are regions of
zero amplitude (and are out of phase) The dark
and light striped areas are where crests overlap
crests and troughs over lap troughs (and are in
phase)
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Standing Waves

• Standing wavewhen forward and backward going
  waves interfere such that parts of the medium are
  always stationary
• Tie rope to a wall and shake. Wave going to wall
  gets completely reflected. Shake in such a way
  that set up a standing wave
• Musical instruments that are plucked, bowed or
  struck, organs
• Pitch comes from length of string or air column
• Can be transverse or longitudinal

Standing waves are a result of interference
between the incident (original) wave and the
reflected wave.
Node a point of zero displacement (from
equilibrium) Antinode a point of maximum
displacement (from equilibrium)
http//physicsclassroom.com/mmedia/waves/swf.gif
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The Doppler Effect

• Doppler Effect--when the frequency changes due to
  motion of the wave source or the receiver

• Now consider if bug moves to the right at speed wave speed.
• Centers of the circular waves move in direction
  of bugs motion.

• Consider first stationary source (bug treading
  water with bobbing feet)
• waves are circular because distance between
  crests (wavelength) is same in all directions.

Effect is that crests bunch at point B, spread
out at point A. Since bug maintains same bobbing
frequency, then point B sees waves coming more
frequently B observes higher frequency and
shorter wavelength. (shorter time between
crests) Similarly, A observes lower frequency and
longer wavelength. (longer time between crests)
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The Doppler Effect

• Water waves spread on the surface
• Sound and light waves are three dimensional
• Doppler effect is why a siren or horn of a car
  has a higher-than-normal pitch as it approaches
  you, and a lower-than-normal pitch as it leaves
• Note dont confuse pitch(frequency) with
  loudness(amplitude)
• Police speed radar operate on the Doppler effect!
• Electromagnetic radar waves bounce off moving
  cars to a computer built in the radar system that
  calculates the speed of the moving car.
• The Doppler effect also occurs in light.
• Blue shiftan increase in frequency (approaching
  source)
• Red shifta decrease in frequency (receding
  source)
• Doppler radar uses the doppler effect for
  electromagnetic waves to predict the weather.
• The Doppler shift for light is used to help
  astronomers discover new planets and binary
  stars.
• Echocardiography - a medical test using
  ultrasound and Doppler techniques to visualize
  the structure of the heart.

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Doppler Effect Questions

• When an ambulance with its siren on passes you,
  what quantities do you measure a change in
  Frequency, Wavelength, Wave speed, Amplitude?
• Frequency (pitch) and wavelength.
• Wave speed stays the same
• Amplitude (loudness) eventually decreases
• (2) Is there a Doppler effect when the source of
  sound is stationary, and instead the listener is
  moving? If so, in what direction should listener
  move to hear a higher frequency?
• There is a shift in frequency, because there is
  relative motion between the source and receiver.
  If you move toward a stationary sound source,
  you meet wave crests more frequently, so receiver
  a higher frequency.
• (3) Is there a Doppler effect when you (the
  receiver) are moving in a car at the same speed
  and direction as a honking car?
• No no relative velocity between source and
  receiver.

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Doppler Effect Questions

• Perceived frequency actual frequency (speed of
  sound speed of observer)/(speed of sound
  speed of source)
• Sitting on the beach at Coney Island one
  afternoon, Sunny finds herself beneath the flight
  path of airplanes leaving Kennedy Airport. What
  frequency will Sunny hear as a jet, whose engines
  emit sound at a frequency of 1000. Hz, flies
  towards her at a speed of 100.0 m/s?
• What frequency will Sunny observe as the jet
  travels away from her at the same speed?

vo is () if the observer moves toward the
source vo is (-) if the observer moves away from
the source vs is () if the source moves towards
the observer vs is (-) if the source moves away
from the observer
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Bow Waves

• When speed of source is as fast as the wave
  speed, waves pile up instead of moving ahead of
  the source
• they superpose on top right in front.
• Now, if the source moves faster than wave speed,
  waves overlap at the edges as shown
• Overlapping circles form a V
• Called a bow wave
• can see when a boat speeds through water
• Idea of sound barrier
• Once thought that jets couldnt go faster than
  the speed of soundthe piling up of waves created
  a sound barrier
• Overlapping wave crests disrupt air flow over the
  wings making it harder to control the plan
• A jet can easily travel faster than the speed of
  sound if it has enough power

http//www.kettering.edu/drussell/Demos/doppler/d
oppler1.gif
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Shock Waves

• Shock wavesproduced by the overlapping of
  spheres form a cone.
• essentially is a bow wave in 3-dimensions
• A supersonic aircraft moves faster than speed of
  sound so generates a shock sound wave.
• An observer hears a sonic boom (sharp crack like
  sound) when the shell reaches him from
  superposition of crests.

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Shock Waves

• Observer A and C hear nothing (only roar of
  engines). Observer B is now hearing the sonic
  boom that C has already heard, and that A has not
  yet heard.

• A sonic boom is the audible component of a shock
  wave in air. The term is commonly used to refer
  to the air shocks caused by the supersonic flight
  of military aircraft or passenger transports such
  as Concorde (Mach 2.03, no longer flying) and the
  Space Shuttle (Mach 27, has only flown once since
  the 2003 crash). Sonic booms generate enormous
  amounts of sound energy, sounding much like an
  explosion typically the shock front may approach
  100 megawatts per square meter, and may exceed
  200 decibels.

• Similarly, get a water boom from bow waves
• a duck can be doused when the bow wave goes by.