Waves & Energy Transfer Physics 11. Introduction to Waves Chapter 11 (§11-1, 11-7, 11-8)
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Transcript of Waves & Energy Transfer Physics 11. Introduction to Waves Chapter 11 (§11-1, 11-7, 11-8)
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.
Time
CrestTrough
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”
PeriodFrequency
1 T
f1
sHz 11515
Quick Example
A pendulum has a period of 0.25s, what is it’s 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.
HzssT
f 41
25.0
1
25.0
11
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)
Amplitude
The “Amplitude”, A, of a wave describes how much the wave deviates from it’s equilibrium/average position (math class, the sinusoidal axis)
Time
Mechanical Waves
So far we have only dealt with things that oscillate in time.
Waves can exist in substances tooDisturbances of this sort are referred to as
‘Mechanical Waves’ Water wavesSound wavesWaves in springs
You may be wondering about Light..
Light is a wave too, but it doesn’t 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
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-raysDo not require a medium for transmission
• visible light of different wavelengths perceived as colors (R-O-Y-G-B-I-V)
Electromagnetic (EM) Waves
Matter Waves
Wave-like behavior of particles, such as electrons
Use quantum mechanics to describe it
Electron diffraction pattern
Properties of Waves
Period T, still existsThe 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 wayWavelength, λ, a new quantity.
Distance from crest to crest (or trough to trough)
λ,
T
Do waves move?
There is nothing physical that moves from one point to another
The disturbance does travelThe Universal Wave Equation:
fv λ,
T
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.
Practice Questions
3. 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.
a. Calculate the wavelength of this sound.
b. Calculate the wavelength for the sound produced by high C, one octave higher than middle C, with a frequency of 512 Hz.
Practice Questions
4. 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?
Waves at BoundariesWhen 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
Waves at Boundariesan 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
Less Dense to More Dense Boundary
Whenever wave passes from less dense to more dense medium, reflected wave is inverted
More Dense to Less Dense Boundary
Whenever wave passes from more dense to less dense medium, reflected wave is erect, not inverted
Video 1Video 2
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
Wave Superposition
Constructive interference occurs when amplitudes are in same direction
result is wave with larger amplitude than any individual wave
Wave Superposition
Destructive interference occurs when amplitudes are in opposite direction
as 2 pulses overlap, displacement is reduced
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
Fixed Both Ends
Nodes at either end1st 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
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 3/4’s of a wavelength with two nodes and two maxima
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
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 roomWaves on the surface of a pool as people are
jumping inWhite light (it is a composite of waves in the EM
spectrum)
So what doe these waves look like?
Superposition
Superimpose two waves together.Add them together
For each value of x, add the value of each wave to get a resultant
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’)
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
Intensity Spectra
Spectra plots can include information about amplitude at each wavelength
Consider these plots made for common ‘white light’ or WL sources
Various WL sources
-500
0
500
1000
1500
2000
2500
3000
3500
4000
4500
350 400 450 500 550 600 650 700 750
Wavelength (nm)
Reli
tive i
nte
nsit
y (
arb
un
its)
solar 1
incandecent bulb
flouresent blub
lcd white
crt white
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
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
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
Young’s 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
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
Diffraction Grating
These examples of diffraction gratings have many grooves (or slits) and as a result, separates light into its constitute wavelengths (colours)
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
Doppler Effect
For sound…As a sound source moves towards the observer or receiver, the frequency or pitch increasesAs the sound source moves away from the receiver, the frequency decreases
Sonic BoomA 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
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)
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; Hubble’s expansion of Universe
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
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
θi = θr
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
> 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
ss v
cn
Refraction
Light bends inward when entering medium of higher index of refraction
Light bends outward when entering medium of lower index of refraction
Snell’s 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
Critical Angle
Critical Angle (θc) occurs when the refracted ray lies along the boundary of the medium surface
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