Waves

1
Waves
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Periodic Motion

• We are surrounded by oscillations motions that
  repeat themselves
• Understanding periodic motion is essential for
  the study of waves, sound, alternating electric
  currents, light, etc.
• How many of you play an instrument?
• An object in periodic motion experiences
  restoring forces that bring it back toward an
  equilibrium position
• Those same forces cause the object to overshoot
  the equilibrium position
• Think of a block oscillating on a spring or a
  pendulum swinging back and forth past its
  equilibrium position Demonstrate

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How does a wave vary in position and velocity
with time? - Full body Demonstrate - PVA
graphs
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Wave Motion

• The wave is another basic model used to describe
  the physical world (the particle is another
  example)
• Any wave is characterized as some sort of
  disturbance that travels away from its source
• Periodic waves are result of oscillations
• For example, sound waves produced by vibrating
  string
• On the same order as size of source

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Definitions of a Waves

• A wave is a traveling disturbance that carries
  energy through space and matter without
  transferring mass.
• Transverse Wave A wave in which the disturbance
  occurs perpendicular to the direction of travel
  (Light).
• Longitudinal Wave A wave in which the
  disturbance occurs parallel to the line of travel
  of the wave (Sound).
• Surface Wave A wave that has charact-eristics of
  both transverse and longitudinal waves (Ocean
  Waves).
• Wave types

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Types of Waves

• Mechanical Waves Require a material medium such
  as air, water, steel of a spring or the fabric of
  a rope.
• Electromagnetic Waves Light and radio waves that
  can travel in the absence of a medium.

Medium the material through which the wave
travels.
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Mechanical waves

• For now, we will concentrate on mechanical waves
  traveling through a material medium
• The wave is the propagation of the disturbance
  they do not carry the medium with it
• All waves carry momentum and energy

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Types of Waves

• In solids, both transverse and longitudinal waves
  can exist
• Transverse waves result from shear disturbance
• Longitudinal waves result from compressional
  disturbance
• Only longitudinal waves propagate in fluids (they
  can be compressed but do not sustain shear
  stresses)
• Transverse waves can travel along surface of
  liquid, though (due to gravity or surface
  tension)
• Sound waves are longitudinal
• Each small volume of air vibrates back and forth
  along direction of travel of the wave
• Earthquakes generate both longitudinal (48 km/s
  P waves) and transverse (25 km/s S waves)
  seismic waves (Quicktime)
• Also surface waves which have both components

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Questions

• Which kind of wave is sound? (3)
• Which kind of wave are the ripples on a pond? (3)
• Which kind of wave is light? (2)
• Which kind of wave can exist in a vacuum? (2)
• Which kind of waves carry momentum and energy?

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Transverse Wave Characteristics

• Crest The high point of a wave.
• Trough The low point of a wave.
• Amplitude Maximum displacement from its position
  of equilibrium (undisturbed position).

John Wiley Sons
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Transverse Wave Characteristics (cont.)

• Frequency(f) The number of oscillations the wave
  makes in one second (Hertz
  1/seconds).
• Wavelength(?) The minimum distance at which the
  wave repeats the same pattern ( 1 cycle).
  Measured in meters.
• Velocity (v) speed of the wave (m/s).
• v f?
• Period (T) Time it takes for the wave to
  complete one cycle (seconds).
• T 1/f

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v f?
The Inverse Relationships

• The speed of a wave is determined by the medium
  in which it travels.
• Since velocity is constant for a given medium,
  the frequency and wavelength must be inversely
  proportional.
• As one increases, the other decreases

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The Inverse RelationshipsT 1/f

• Similar to the inverse relationship for frequency
  and wavelength, a similar relationship exists for
  frequency and the period.

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Speed of Waves
Waves have a speed!
Dependent on

• Medium
• Temperature
• Pressure
• Frequency (wavelength)

What about light?

• Medium
• Wavelength (frequency)
• (temperature)
• (pressure)

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Speed of Waves

• The relationship between wave speed, wavelength,
  and frequency is simple
• For a given temperature, pressure, material, etc.

v fl,
where v is the speed, f is the frequency, and
lambda is the wavelength.
What is v for sound?
What is v for light?
What is v for a Slinky?
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Speed of Waves
Medium Speed (m/sec) Frequency Wavelength
Sound 340 261
Light 300,000,000 700E-9
Ocean Wave 25 1
Tsunami 260
Earthquake P 2
Earthquake Surface 0.5
Guitar String 425 1m

http//www.pbs.org/wgbh/nova/earth/japan-killer-qu
ake.html
17
Waves at Fixed Boundaries

• A wave incident upon a fixed boundary will have
  its energy reflected back in the opposite
  direction. Note that the wave pulse is inverted
  after reflecting off the boundary.
• Example of Waves at Fixed Boundaries

www.electron4.phys.utk.edu
18
Interference

• Interference occurs whenever two waves occupy the
  same space at the same time.
• Law of Linear Superposition When two or more
  waves are present at the same time at the same
  place, the resultant disturbance is equal to the
  sum of the disturbances from the individual waves.

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Constructive Wave Interference
www.electron4.phys.utk.edu
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Destructive Wave Interference
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Standing Waves

• Standing Wave An interference pattern resulting
  from two or more waves moving in opposite
  directions with the same frequency and amplitude
  such that they develop a consistent repeating
  pattern of constructive and destructive
  interference.
• Node The part of a standing wave where
  interference is destructive at all times (180o
  out of phase) .
• Antinode The part of the wave where interference
  is maximized constructively.
• Standing Wave

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Continuous Waves

• When a wave impacts a boundary, some of the
  energy is reflected, while some passes through.
• The wave that passes through is called a
  transmitted wave.
• A wave that is transmitted through a boundary
  will lose some of its energy.
• Electromagnetic radiation will both slow down and
  have a shorter wavelength when going into a
  denser media.
• Sound will increase in speed when transitioning
  into a denser media.
• Speed of Light in different mediums

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Continuous Waves Higher Speed to Lower Speed

• Note the differences in wavelength and amplitude
  between of the wave in the two different mediums

Incident Reflected Wave
Transmitted Wave
Displacement
Lower speed Shorter wavelength
Higher speed Longer wavelength
Note This phenomena is seen with light traveling
from air to water.
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Waves at Boundaries

• Examples of Waves at Boundaries
• Wave Types (Cutnell Johnson)
• Waves - Colorado.edu
• Other Examples

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Key Ideas

• Waves transfer energy without transferring
  matter.
• Longitudinal waves like that of sound require a
  medium.
• Transverse waves such as electro-magnetic
  radiation do not require a medium.
• In transverse waves, displacement is
  perpendicular to the direction of the wave while
  in longitudinal waves, the displacement is in the
  same direction.

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Key Ideas

• Waves travel at different speeds in different
  mediums.
• Light slows down when going from air to a liquid
  or solid.
• Sound speeds up when going from air to a liquid
  or solid.
• Waves can interfere with one another resulting in
  constructive or destructive interference.

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Continuous Waves Lower Speed to Higher Speed

• Note the differences in wavelength and amplitude
  between of the wave in the two different mediums

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• Affects of sound waves
• Shatter glass!
• Transmit energy!

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http//www.youtube.com/watch?vw-qKlCy0T-g
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Wave Videos Reflection off a sea wall
http//www.youtube.com/watch?vPevRZAxDxZw Big
wave at beach http//www.weather.com/blog/weathe
r/8_21326.html https//www.youtube.com/watch?vQdo
TdG_VNV4featureplayer_embeddedat131 Tacoma
narrows bridge http//video.search.yahoo.com/sea
rch/video_yltA2KLqIGXaSdPEn0AIxT7w8QF?ptacoman
arrowsbridgeb21tnr20 http//www.google.com/u
rl?satrctjqesrcssourcewebcd14cadrjau
act8ved0CJEBEBYwDQurlhttp3A2F2Fwww.joe.ie
2Fnews2Fcurrent-affairs2Fvideo-these-huge-waves-
forced-pedestrians-to-flee-the-footpath-in-tramore
-this-morning2FeiYrZVU5GrFJCnsATLxYDYDwusgAFQ
jCNEee0VBKDWk-FqbGCzim6T6AgEF0gsig2WGLREQeIb59Hy
B3EiTcpJA

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Review of Springs

• Classic example of periodic motion
• Spring exerts restoring force on block
• k spring constant (a measure of
  spring stiffness)
• Slinky has k 1 N/m auto
  suspensions have k 105 N/m
• Movie of vertical spring
• Elastic potential energy stored in spring
• Uel 0 when x 0 (spring relaxed)
• Uel is gt 0 always
• We do not have freedom to pick where x 0
• Uel conserves mechanical energy

(Hookes Law)
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Shock Absorbers

• Shock absorbers provide a
  damping of the oscillations
• A piston moves through a viscous
  fluid like oil
• The piston has holes in it, which
  creates a (reduced) viscous
  force on the piston, regardless of the direction
  it moves (up or down)
• Viscous force reduces amplitude of oscillations
  smoothly after car hits bump in road
• When oil leaks out of the shock absorber, the
  damping is insufficient to prevent oscillations
• Shock absorber is example of an
  underdamped oscillator (see also
  critically damped and overdamped)

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Properties of Waves

• Superposition principle The overlap of 2 or more
  waves (having small amplitude) results in a wave
  that is a point-by-point summation of each
  individual wave

(constructive interference)
(destructive interference)
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Properties of Waves

• Traveling waves can both reflect and transmit
  across a boundary between 2 media
• Reflected wave pulse is inverted (not inverted)
  if wave reaches a boundary that is fixed (free to
  move)