Waves

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Waves Energy Transfer

• Physics 11

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Introduction to Waves

• Chapter 11 (11-1, 11-7, 11-8)

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Waves are all about Periodic Motion.

• Periodic motion is motion that repeats after a
  certain period of time.
• This time is appropriately known as the period,
  T.

Crest
Trough
Time
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Frequency

• This is the number of oscillations per second.
• It is related to the Period
• Frequency is measured in Hertz (Hz)
• If you hear Hertz, think per second

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Quick Example

• A pendulum has a period of 0.25s, what is its
  frequency?
• 4Hz so think 4 per second
• This makes sense, because if it takes ¼ of a
  second to make one oscillation, it will do 4 in
  one second.

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Common places to use Frequency

• Computer processors
• the Pentium 4 operates at 3.8 GHz
• (calculations per second)
• Digital music and video
• The audio file was encoded at 128 kHz
• Heart rate
• his heart rate was 80bpm
• Beats per minute (1/time)

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Amplitude

• The Amplitude, A, of a wave describes how much
  the wave deviates from its equilibrium/average
  position
• (math class, the sinusoidal axis)

Time
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Types of Waves
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Sound Waves
-a longitudinal wave
Light (EM) Waves
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Mechanical Waves

• So far we have only dealt with things that
  oscillate in time.
• Waves can exist in substances too
• Disturbances of this sort are referred to as
  Mechanical Waves
• Water waves
• Sound waves
• Waves in springs

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You may be wondering about Light..

• Light is a wave too, but it doesnt travel though
  any stuff
• Originally they thought it must go through
  something, and they called this stuff ether
• They looked for evidence of this ether, but were
  unable to find evidence of it.
• Michelson-Morley Experiment
• Not mechanical in the sense the other
  disturbances are.
• has many of the same properties

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Electromagnetic (EM) Waves ( 22-5, 24-4)

• Those that consist of oscillating electric and
  magnetic fields that move at the speed of light
  or c through space
• Examples visible light, radio and x-rays
• Do not require a medium for transmission

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Electromagnetic (EM) Waves

• Frequencies of EM waves are displayed on the EM
  spectrum

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Electromagnetic (EM) Waves

• visible light of different wavelengths perceived
  as colors (R-O-Y-G-B-I-V)

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Electromagnetic (EM) Waves

• Individual wavelengths can be observed using a
  diffraction grating

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Matter Waves

• Wave-like behavior of particles, such as
  electrons
• Use quantum mechanics to describe it

Electron diffraction pattern
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Properties of Waves

• Period T, still exists
• The period is how long it takes a for one spot
  along the wave to see a crest after it saw the
  last one
• Frequency, f, still defined the same way
• Wavelength, ?, a new quantity.
• Distance from crest to crest (or trough to
  trough)

?,
T
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Do waves move?

• There is nothing physical that moves from one
  point to another
• The disturbance does travel
• The Universal Wave Equation

?,
T
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Practice Questions

1. A metronome beats 54 times over a 55 s time
   interval. Determine the frequency and period of
   its motion.
2. A child swings back and forth on a swing 12 times
   in 30.0 s. Determine the frequency and period of
   the swinging.

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Practice Questions

• The speed of sound in air at room temperature is
  343 m/s. The sound wave produced by striking
  middle C on a piano has a frequency of 256 Hz.
• Calculate the wavelength of this sound.
• Calculate the wavelength for the sound produced
  by high C, one octave higher than middle C, with
  a frequency of 512 Hz.

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Practice Questions

1. Interstellar (a.k.a. between the stars)
   hydrogen gas emits radio waves with a wavelength
   of 21 cm. Given that radio waves travel at 3.0 x
   108 m/s, what is the frequency of this
   interstellar source of radiation?

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Reflection and Transmission

• Chapter 11 ( 11-11)

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Waves at Boundaries

• When a wave moves from one medium to another, its
  frequency remains the same but the speed changes
• As the speed is related to the properties of the
  medium, the behaviour will depend on the media
  involved
• The behaviour at the boundary will depend on
  whether the wave is travelling from a less dense
  medium to a more dense medium or vice versa

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Waves at Boundaries

• an incident wave reaches a boundary between 2
  media
• part of incident wave continues on in new medium
  with same frequency ? transmitted wave
• part of wave moves backward from boundary in old
  medium ? reflected wave
• if difference in media is small, amplitude of
  transmitted wave will be almost as big as
  incident wave amplitude of reflected wave will
  be relatively small (most of energy transmitted)
• if 2 media densities are very different, most of
  energy will be reflected

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Less Dense to More Dense Boundary

• Whenever wave passes from less dense to more
  dense medium, reflected wave is inverted

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More Dense to Less Dense Boundary

• Whenever wave passes from more dense to less
  dense medium, reflected wave is erect, not
  inverted
• Video 1
• Video 2

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Wave Interference

• Chapter 11 ( 11-11, 11-12)

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Wave Superposition

• Principle of Superposition states
• "the displacement of a medium caused by two or
  more waves is the algebraic sum of the
  displacements caused by individual waves"
• result of superposition is interference

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Wave Superposition

• Constructive interference occurs when amplitudes
  are in same direction
• result is wave with larger amplitude than any
  individual wave

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Wave Superposition

• Destructive interference occurs when amplitudes
  are in opposite direction
• as 2 pulses overlap, displacement is reduced

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Standing Waves

• waves are able to pass through one another
  unchanged
• 2 pulses with equal but opposite displacements
  meet (destructive interference) ? find one point
  that is undisturbed ? node
• 2 pulses with equal displacements in the same
  direction meet (constructive interference) ? find
  point of maximum amplitude ? antinode
• wave in which nodes and antinodes are stationary
  ? standing wave

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Fixed Both Ends

• Nodes at either end
• 1st harmonic is half a wavelength, with an
  anti-node (maxima) in the middle
• 2nd harmonic is one wavelength with a node in the
  middle and maxima between nodes

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Fixed One End ( 12-5)

• Generally seen in sound waves
• 1st harmonic is one quarter of a wavelength with
  a node and maxima
• 2nd harmonic is 3/4s of a wavelength with two
  nodes and two maxima

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Guitar String

• A guitar string has a given (open) length, given
  tension (and therefore mostly constant wave speed
  in a string) and therefore, when a string is
  plucked, a specific frequency is heard
• If the string is then shortened by a certain
  amount, a higher frequency can be played

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Superposition and Spectra

• Physics 11

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Multiple waves

• We now understand the very basics of waves but
  reality usually does not involve one just one
  wave.
• Multiple radio stations transmitting into the
  room
• Waves on the surface of a pool as people are
  jumping in
• White light (it is a composite of waves in the EM
  spectrum)
• So what doe these waves look like?

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Superposition

• Superimpose two waves together.
• Add them together
• For each value of x, add the value of each wave
  to get a resultant

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Real Waves are Superpositions

• This means that real waves have a number of waves
  adding together to make them up.
• Each part having a different wavelength
• The wavelengths that are used to construct a
  complex wave are referred to as a Spectrum
  (plural, Spectra)

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Spectrum Graphs

• Real waves are composed of many components
• To keep track of what wavelengths are used, a
  simple chart is often made.
• Consider the emission spectrum of Hydrogen
• It tells us what wavelengths are present,
  indicating the wavelength qualitatively with the
  color of light

Hydrogen
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How are spectra formed at the atomic level?
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Intensity Spectra

• Spectra plots can include information about
  amplitude at each wavelength
• Consider these plots made for common white
  light or WL sources

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Wave Behaviour

• Physics 11

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Diffraction ( 11-13, 24-6)

• When a wave impinges on a single opening, it will
  diffract
• That is, a plane wave will spread through space
  and the spreading angle is a function of
  wavelength and opening

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Single Slit Diffraction

• If light is impingent on a single slit, the light
  wave will spread
• The spreading angle is related to the size of the
  opening and the wavelength of light used

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Two Point Sources

• Two point sources will also interfere to create
  an interference pattern
• The interference pattern is based on wavelength
  and separation of point sources

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Youngs Double-Slit Experiment ( 24-3)

• If light is impingent on two slits, the light
  will spread from each slit like in the single
  slit case
• However, the waves will interfere with each other
  and an interference pattern will result

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Diffraction Gratings

• A diffraction grating combines the behaviour of a
  single slit and double slit and is created by
  creating many grooves or slits on a transparent
  or reflective material

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Diffraction Grating

• These examples of diffraction gratings have many
  grooves (or slits) and as a result, separates
  light into its constitute wavelengths (colours)

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Doppler Effect ( 12-8, 12-9)

• When an source is moving with respect to an
  observer (or vice versa) the frequency of the
  sound will shift due to the Doppler Effect
• As a result, it is possible to determine whether
  an object is moving toward or away from us if we
  know the reference frequency

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Doppler Effect
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Doppler Effect

• For sound
• As a sound source moves towards the observer or
  receiver, the frequency or pitch increases
• As the sound source moves away from the receiver,
  the frequency decreases

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Sonic Boom

• A sonic boom is the sound associated with the
  shock waves created by an object traveling
  through the air faster than the speed of sound.
• Sonic booms generate enormous amounts of sound
  energy, sounding much like an explosion.
• Ex supersonic jets, cracking of a whip, pop of
  a balloon

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For light

• We can see the same behaviour with light since
  light (in a vacuum) must always travel at the
  speed of light (3.0x108 m/s)
• However, since nothing can travel faster than the
  speed of light (in a vacuum) it is impossible to
  see behaviour akin to a sonic boom with light (in
  a vacuum)

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Red and Blue Shift

• When the wavelength or frequency of light is
  changed, so is its colour
• For visible light, this means that when an
  emitter is moving away from Earth, the wavelength
  observed is increased and light is said to be red
  shifted
• When light is emitter by a body moving toward
  Earth, wavelength is decreased and we say that it
  is blue shifted
• Ex rotation of galaxies Hubbles expansion of
  Universe

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Cerenkov Radiation

• Cerenkov radiation is EM radiation emitted when a
  charged particle (such as an electron) passes
  through a medium at a speed greater than the
  speed of light in that medium.
• Ex blue light from nuclear reactor

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Reflection ( 11-11, 23-2)

• According to ray optics, reflection can be
  modelled using a ray impingent on a mirror at
  some angle and reflected at the same angle

?i ?r
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Refraction ( 11-13, 23-4, 23-5, 23-6)

• Refraction is the change in direction or bending
  of light at boundary between 2 media
• Optically Dense - when speed of light in one
  medium is slower than that in another
• when angle of incidence 0o , angle of
  refraction 0o speed changes but passes straight
  through, along the normal
• when light travels into a medium where it travels
  faster, angle of refraction gt angle of incidence
  OR if light enters less optically dense medium,
  refracted rays bend away from the normal
• if light enters more optically dense medium,
  refracted rays bend toward the normal
•  
• Index of Refraction (n) - ratio of the speed of
  light in a vacuum to its speed into a material

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Refraction
Light bends inward when entering medium   of
higher index of refraction
Light bends outward when entering medium of lower
index of refraction
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Snells Law

• Light moving from smaller n to larger n is bent
  toward normal vice-versa
• ni is index of refraction for incident medium
• nr is index of refraction for second medium are
  angles of incidence refraction
• refractive index (n) can be found by measuring
  angles of incidence refraction

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Critical Angle

• Critical Angle (?c) occurs when the refracted ray
  lies along the boundary of the medium surface 

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Total Internal Reflection

• Total Internal Reflection occurs when light
  passes from a more optically dense medium to a
  less optically dense one at an angle so great
  that there is no refracted ray
• Ex fiber optic cable, internal body probe

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