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Waves

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Title: Waves


1
Waves Energy Transfer
  • Physics 11

2
Introduction to Waves
  • Chapter 11 (11-1, 11-7, 11-8)

3
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
4
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

5
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.

6
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)

7
Amplitude
  • The Amplitude, A, of a wave describes how much
    the wave deviates from its equilibrium/average
    position
  • (math class, the sinusoidal axis)

Time
8
Types of Waves
9
Sound Waves
-a longitudinal wave
Light (EM) Waves
10
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

11
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

12
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

13
Electromagnetic (EM) Waves
  • Frequencies of EM waves are displayed on the EM
    spectrum

14
Electromagnetic (EM) Waves
  • visible light of different wavelengths perceived
    as colors (R-O-Y-G-B-I-V)

15
Electromagnetic (EM) Waves
  • Individual wavelengths can be observed using a
    diffraction grating

16
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17
Matter Waves
  • Wave-like behavior of particles, such as
    electrons
  • Use quantum mechanics to describe it

Electron diffraction pattern
18
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
19
Do waves move?
  • There is nothing physical that moves from one
    point to another
  • The disturbance does travel
  • The Universal Wave Equation

?,
T
20
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.

21
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.

22
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?

23
Reflection and Transmission
  • Chapter 11 ( 11-11)

24
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

25
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

26
Less Dense to More Dense Boundary
  • Whenever wave passes from less dense to more
    dense medium, reflected wave is inverted

27
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

28
Wave Interference
  • Chapter 11 ( 11-11, 11-12)

29
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

30
Wave Superposition
  • Constructive interference occurs when amplitudes
    are in same direction
  • result is wave with larger amplitude than any
    individual wave

31
Wave Superposition
  • Destructive interference occurs when amplitudes
    are in opposite direction
  • as 2 pulses overlap, displacement is reduced

32
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

33
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

34
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

35
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

36
Superposition and Spectra
  • Physics 11

37
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?

38
Superposition
  • Superimpose two waves together.
  • Add them together
  • For each value of x, add the value of each wave
    to get a resultant

39
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)

40
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
41
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42
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43
How are spectra formed at the atomic level?
44
Intensity Spectra
  • Spectra plots can include information about
    amplitude at each wavelength
  • Consider these plots made for common white
    light or WL sources

45
Wave Behaviour
  • Physics 11

46
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

47
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

48
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

49
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

50
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

51
Diffraction Grating
  • These examples of diffraction gratings have many
    grooves (or slits) and as a result, separates
    light into its constitute wavelengths (colours)

52
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

53
Doppler Effect
54
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

55
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

56
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)

57
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

58
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

59
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
60
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

61
Refraction
Light bends inward when entering medium   of
higher index of refraction
Light bends outward when entering medium of lower
index of refraction
62
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

63
Critical Angle
  • Critical Angle (?c) occurs when the refracted ray
    lies along the boundary of the medium surface 

64
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

65
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