Title: Waves
1Waves Energy Transfer
2Introduction to Waves
- Chapter 11 (11-1, 11-7, 11-8)
3Waves 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
4Frequency
- 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
5Quick 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.
6Common 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)
7Amplitude
- The Amplitude, A, of a wave describes how much
the wave deviates from its equilibrium/average
position - (math class, the sinusoidal axis)
Time
8Types of Waves
9Sound Waves
-a longitudinal wave
Light (EM) Waves
10Mechanical 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
11You 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
12Electromagnetic (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
13Electromagnetic (EM) Waves
- Frequencies of EM waves are displayed on the EM
spectrum
14Electromagnetic (EM) Waves
- visible light of different wavelengths perceived
as colors (R-O-Y-G-B-I-V)
15Electromagnetic (EM) Waves
- Individual wavelengths can be observed using a
diffraction grating
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17Matter Waves
- Wave-like behavior of particles, such as
electrons - Use quantum mechanics to describe it
Electron diffraction pattern
18Properties 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
19Do waves move?
- There is nothing physical that moves from one
point to another - The disturbance does travel
- The Universal Wave Equation
?,
T
20Practice Questions
- A metronome beats 54 times over a 55 s time
interval. Determine the frequency and period of
its motion. - A child swings back and forth on a swing 12 times
in 30.0 s. Determine the frequency and period of
the swinging.
21Practice 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.
22Practice Questions
- 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?
23Reflection and Transmission
24Waves 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
25Waves 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
26Less Dense to More Dense Boundary
- Whenever wave passes from less dense to more
dense medium, reflected wave is inverted
27More 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
28Wave Interference
- Chapter 11 ( 11-11, 11-12)
29Wave 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
30Wave Superposition
- Constructive interference occurs when amplitudes
are in same direction - result is wave with larger amplitude than any
individual wave
31Wave Superposition
- Destructive interference occurs when amplitudes
are in opposite direction - as 2 pulses overlap, displacement is reduced
32Standing 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
33Fixed 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
34Fixed 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
35Guitar 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
36Superposition and Spectra
37Multiple 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?
38Superposition
- Superimpose two waves together.
- Add them together
- For each value of x, add the value of each wave
to get a resultant
39Real 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)
40Spectrum 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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43How are spectra formed at the atomic level?
44Intensity Spectra
- Spectra plots can include information about
amplitude at each wavelength - Consider these plots made for common white
light or WL sources
45Wave Behaviour
46Diffraction ( 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
47Single 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
48Two 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
49Youngs 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
50Diffraction 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
51Diffraction Grating
- These examples of diffraction gratings have many
grooves (or slits) and as a result, separates
light into its constitute wavelengths (colours)
52Doppler 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
53Doppler Effect
54Doppler 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
55Sonic 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
56For 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)
57Red 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
58Cerenkov 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
59Reflection ( 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
60Refraction ( 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
61Refraction
Light bends inward when entering medium of
higher index of refraction
Light bends outward when entering medium of lower
index of refraction
62Snells 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
63Critical Angle
- Critical Angle (?c) occurs when the refracted ray
lies along the boundary of the medium surface
64Total 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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