3. Waves Flashcards
1
Q
What is a wave?
A
A regular disturbance that carries energy from one place to another
2
Q
What does a wave transport?
A
Energy, not matter
3
Q
When a wave is present in a medium, what happens to the individual particles?
A
They are temporarily displaced from their rest position; there is always a force acting upon the particles that restores them to their original position
4
Q
What are the two ways of showing wave motion in a graph?
A
- displacement-time
* displacement-distance
5
Q
What is displacement?
A
Instantaneous distance from the equilibrium (undisturbed) level
6
Q
What is amplitude?
A
The maximum displacement from the equilibrium position
7
Q
What is wavelength?
A
The distance between any two points on adjacent cycles which are vibrating in phase
8
Q
What is the meaning of ‘in phase’?
A
At the same point in the cycle
9
Q
What is time period?
A
The time taken for one complete cycle (oscillation/wave)
10
Q
What is frequency?
A
The number of oscillations (or cycles) in one second
11
Q
Equation for time period?
A
T = 1/f
12
Q
What is the wave speed equation?
A
c =fλ
13
Q
Derivation of the wave equation?
A
- speed = distance / time = wavelength / period
- c = λ/T = λ/f⁻¹
- c = λf
14
Q
What is phase difference?
A
The difference between two waves having the same frequency and referenced to the same point in time
15
Q
What is phase difference expressed in?
A
Degrees, radians or fractions of a cycle
16
Q
Would two oscillators with the same frequency and different phases have a phase difference?
A
Yes - they would be out of phase with each other
17
Q
What is the range of values for phase difference?
A
- degrees - 0 to 360
* radians - 0 to 2π
18
Q
What is antiphase?
A
When the phase difference is 180 degrees (π radians)
19
Q
What is the equation for phase difference?
A
- x/λ x 360 (degrees)
* x/λ x 2π (radians)
20
Q
What are transverse waves?
A
When the displacement is at right angles to the direction of the wave
21
Q
What are longitudinal waves?
A
When the displacement is parallel to the direction of the wave
22
Q
What type of wave is light?
A
Transverse, electromagnetic
23
Q
What type of wave is sound?
A
Longitudinal, mechanical
24
Q
What are mechanical waves?
A
Waves that travel by vibrating particles in a medium
25
Can mechanical waves travel in a vacuum?
No
26
What are electromagnetic waves?
Waves that can travel through a vacuum
27
What is the speed of light in a vacuum?
3 x 10⁸ m/s
28
What happens when an electromagnetic wave hits a surface?
The wave can be reflected, transmitted or absorbed
29
What happens to an object when it absorbs an electromagnetic wave?
Its temperature increases
30
In what planes can the displacements of oscillations in transverse waves be?
In all planes
31
What are plane-polarised waves?
Have the oscillations in one plane only
32
How is light polarised?
* by absorbing all planes of oscillation except one
| * by reflection
33
What is Polaroid plastic formed from?
Many tiny crystals, all lined up
34
Which planes of oscillation does Polaroid plastic absorb?
All of them except the vertical one
35
When light is polarised by reflection, which way is the plane of polarisation?
Horizontal
36
What happens if you wear sunglasses made from Polaroid plastic and look at water?
Reflection off the water surface is absorbed, because its plane of polarisation is perpendicular to that of the Polaroid
37
Why do you not get dazzled by the reflected glare from water when wearing Polaroid sunglasses?
The plane of polarisation of the water is perpendicular to that of the Polaroid
38
What happens if two pieces of Polaroid are 'crossed' so that their transmission planes are at right angles?
No light will get through
39
How can transverse and longitudinal waves be distinguished?
Transverse waves can be polarised; longitudinal cannot
40
What are electromagnetic waves a combination of?
Electric and magnetic field waves produced by moving charges
41
What is polarisation used in?
* sunglasses
| * alignment of aerials for transmission and reception
42
When are waves superposed?
When two waves of the same type are in the same place at the same time
43
How is the resultant displacement at any point found when two waves are superposed?
By adding displacements of each separate wave
44
What is interference?
The adding together of waves
45
What is the principle of superposition?
At a point where two or more waves meet, the instantaneous displacement (amplitude) is the vector sum of the individual displacements due to each wave at that point
46
When will interference be constructive?
When waves are in phase and the same frequency
47
What must the path difference be for constructive interference?
nλ (where n is a whole number of wavelengths)
48
When will interference be destructive?
When waves are in antiphase and have the same frequency
49
What must the path difference be for destructive interference?
(1+n/2)λ i.e. an odd number of wavelengths
50
What does it mean when waves are phase linked?
The waves have a constant phase difference
51
When are superposed waves easier to 'see'?
* the waves are of similar amplitude (↑ contrast between maxima and minima)
* the waves have similar frequencies - otherwise the interference patterns create change so fast that they are difficult to detect
* the waves have a constant phase difference i.e. they are phase linked
52
Examples of coherent sources?
* light produced by a laser
* sound from two loudspeakers connected in parallel
* light emerging from two apertures illuminated by the same source
53
What are coherent sources?
Sources that have synchronised phase changes, as well as same frequency and λ
54
What are nodes?
On stationary waves, points that are always at equilibrium and 0 oscillation
55
What are antinodes?
On stationary waves, points of maximum oscillation
56
On a stationary wave, what it the distance from one node to the next?
1/2 λ
57
How are stationary waves formed on a string?
* vibrator moves up and down - sends travelling wave down cord
* wave reflected at end, so 2 travelling waves overlap and interfere
* has antinodes and nodes; distance between nodes = 1/2λ
58
What is the resonant frequency of a rubber band?
Where the band vibrates with large amplitude
59
Comparison of the frequencies of particles in stationary and travelling waves?
* stationary - all particles (except nodes) have the same frequency
* travelling - all particles have the same frequency
60
Comparison of the amplitudes of particles in stationary and travelling waves?
* stationary - varies from 0 (nodes) to maximum (antinodes)
| * travelling - same for all particles
61
When does resonance occur?
When the frequency driving the system matches the natural frequency of the system
62
Comparison of the phase difference between two particles in stationary and travelling waves?
* stationary - mπ (m = no. of nodes between the two particles)
* travelling - 2πx/λ (x = distance apart)
63
Comparison of the energy of particles in stationary and travelling waves?
* stationary - energy stored and not transferred
| * progressive - energy transferred
64
What is a stationary wave?
Where energy is stored rather than transmitted - formed when 2 coherent waves travelling in opposite directions interfere to produce nodes and antinodes
65
What can increase the pitch of a note on a guitar string?
* ↑ tightness/tension
* ↓ length of string
* ↓ thickness of string
66
What does the 1st harmonic depend on?
1st harmonic frequency f depends on tension T in wire, its length l and its mass per unit length
67
What is the equation to calculate the frequency of the 1st harmonic?
f = 1/2l x √T/μ
68
What happens when the air at one end of the a tube/pipe is caused to vibrate?
A longitudinal wave travels down the tube, and is reflected at the opposite end - forming a stationary wave
69
Where are the anti-nodes in an open pipe?
At both ends
70
Why are waves reflected at the ends of open pipes?
Air acts as a barrier outside
71
For the fundamental frequency in an open pipe, what is the pipe length?
λ/2
72
For an open pipe, which frequency is the first overtone?
2nd harmonic (2f₁)
73
What is the frequency for the second harmonic in an open pipe?
2f₁
74
For the second harmonic in an open pipe, what is the pipe length?
λ
75
For an open pipe, which frequency is the second overtone?
3rd harmonic (3f₁)
76
What is the frequency for the third harmonic in an open pipe?
3f₁
77
For the third harmonic in an open pipe, what is the pipe length?
3λ/2
78
Which harmonics can be obtained from an open pipe?
All of them
79
At resonant frequencies in a closed pipe, where are the nodes and anti-nodes?
Node at closed end, anti-node at open end
80
Describe the amplitude of the particles in a closed pipe.
Amplitude ↓ gradually from the maximum at the open to zero at the closed end
81
For the fundamental frequency in a closed pipe, what is the pipe length?
λ/4
82
For a closed pipe, which frequency is the first overtone?
3rd harmonic (3f₁)
83
What is the frequency for the third harmonic in a closed pipe?
3f₁
84
For the third harmonic in a closed pipe, what is the pipe length?
3λ/4
85
For a closed pipe, which frequency is the second overtone?
5th harmonic (5f₁)
86
What is the frequency for the fifth harmonic in a closed pipe?
5f₁
87
For the fifth harmonic in a closed pipe, what is the pipe length?
5λ/4
88
Which harmonics can be obtained in a closed pipe?
Odd harmonics
89
Why are standing waves only produced at certain frequencies?
There needs to be a whole number of stationary wave loops fitting into the length of the string
90
What does the double slit interference pattern consist of?
Equidistant parallel fringes alternating between:
* maxima (constructive interference)
* minima (destructive interference)
91
What happens when waves are travelling in the same direction and overlap?
They interfere
92
What does it mean if two sources are coherent?
They emit identical waves which start in phase
93
How can light that is in phase be produced for the double slit experiment?
* use 2 coherent sources
| * use single source with double slits
94
What does it mean if two sources are coherent?
They have the same frequency, wavelength and synchronised phase changes
95
What is the equation for the double slit interference pattern?
x = λD / a
96
What does x stand for in x = λD / a?
Distance between adjacent fringes
97
What does a stand for in x = λD / a?
Distance between slits (slit width)
98
What does D stand for in x = λD / a?
Distance from slits to screen
99
For small angles, what does sinθ equal?
tanθ
100
If all types of wave interfere, why can't we see interference patterns?
To obtain a clear interference pattern it requires two coherent waves of monochromatic light- light is usually emitted in bursts of waves, after which is a random phase change
101
How is light usually emitted?
In bursts of waves, each burst lasting 10⁻⁹s, after which there's a random phase change
102
What is a monochromatic source?
A source of a single wavelength
103
What is usually used as a monochromatic light source?
A sodium lamp
104
Is there interference when two separate light sources are used?
Never
105
What is fringe separation?
The distance between neighbouring bright fringes
106
What happens to the double slit interference pattern if green light is used instead of red?
Wavelength is decreased so distance between adjacent fringes decreases
107
What happens to the double slit interference pattern if white light is used?
The central fringe is white, with red edges. Other fringes will be spectra with the blue end towards the middle of the overlap area
108
What happens to the double slit interference pattern if the screen is moved further away?
D↑ so distance between adjacent fringes increases
109
What happens to the double slit interference pattern if the phase difference between 2 sources is changed to 180°?
The maxima will become minima and vice versa
110
What happens to the double slit interference pattern if both slits are made narrower?
Wider interference so there are more dots, but fainter as there is less light through (x ↑)
111
What happens to the double slit interference pattern if one slit is narrower than the other?
The waves don't fully cancel out
112
How can you increase x in the young's slits experiment?
* ↑ D - measurement easier and more accurate but fringe intensity decreased
* ↓ a - practical limit to this
* ↑ wavelength
113
Can mechanical waves interfere?
Yes
114
What is diffraction?
When a wave passes through a gap and spreads out
115
What happens to diffraction when the gap width ↓?
Diffraction ↑
116
When is diffraction strongest?
When the gap with is similar to the wavelength of the wave
117
Why do waves passing through a single gap interfere?
* only 1 slit but more than 1 wave
* single slit can be thought of as large no. of sources next to each other
* each 'source' produces coherent wave - overlap and interfere
118
What happens, when light is shone on a diffraction grating, when the wavelength is increased?
* short λ (e.g. blue light) - narrow diffraction pattern
| * long λ (e.g. red light) - broad diffraction pattern
119
What happens when white light is shone on the diffraction grating instead of monochromatic?
* white light yields less clear patterns (as position of dark bands depends on λ)
* colours appear; only central band is white
120
Difference between single and double slit pattern?
* single slit - central max. fringe that is twice the width of the other fringes
* double slit pattern has equally spaced fringes
121
How many slits are on a diffraction grating?
1000s
122
Which method produces a better diffraction pattern?
Diffraction grating - as not much light gets through the double slits so are dim and unclear
123
What is a diffraction grating?
A set of slits for light waves to pass through
124
How do you calculate the number of slits per meter on a diffraction grating?
m = 1/d
125
Diffraction grating equation?
dsinθ = nλ
126
What does d stand for in dsinθ = nλ?
Distance between slits
127
What does θ stand for in dsinθ = nλ?
Angle to maxima
128
What does n stand for in dsinθ = nλ?
Integer number to next bright fringe
129
What does λ stand for in dsinθ = nλ?
Wavelength of light
130
In the diffraction grating equation, what is the significance of sinθ never being greater than one?
There is a limit to the number of spectra that be obtained
131
What is the zero-order maximum?
The waves that produce the bright spot straight on - paths are all the same length, so phase difference is zero
132
What is the equation for the maximum number of orders?
n = d/λ
133
Why is sinθ not present in the equation for the maximum number of orders?
It will give a maximum when sinθ=1, so cancels out
134
When using the equation n=d/λ, which quantity must be a whole number?
n
135
Which is more accurate, the diffraction grating or the double slit method?
Diffraction grating
136
Why is the diffraction grating more accurate than the double slits?
* double slits - fringes formed are slightly blurred → large errors
* diffraction grating - images are clear and measurements accurate, also final result is an average of several calculations
137
What can diffraction gratings be used for?
Analysis of spectra
138
What is an optical fibre?
A long, thin, cylindrical core of glass, encased in a cladding of glass of lower refractive index
139
What is refraction?
A change in the direction of light as it passes across a boundary between two transparent substances
140
What happens, in terms of refraction, if light passes across a boundary at 90° to a surface?
It doesn't refract
141
What is a refractive index?
A measure of the optical density of a material relative to air
142
What is the approximate refractive index of air?
1
143
What is the equation for the refractive index of a material?
n = c/v
144
What does each letter stand for in the equation n=c/v?
n = refractive index
c = velocity of light in vacuum
v = velocity of light in the medium
145
What is the word definition of Snell's law?
The ratio of the sines of the angles of incidence and refraction are constant when it passes between two given media
146
What is Snell's law?
n₁sinθ₁ = n₂sinθ₂
| i.e. sin i / sin r = constant
147
What are the two conditions for total internal reflection?
* light passes from more to less dense medium
| * angle of incidence > critical angle
148
What is total internal reflection?
When light passes from a more to less dense medium, and the angle of incidence > critical angle, all light is reflected back to the less dense medium
149
What is the critical angle?
The limiting angle of incidence, as the angle of refraction cannot exceed 90°
150
What is the angle of refraction when the angle of incidence is equal to the critical angle?
90°
151
How is critical angle calculated in air?
sin c = 1 / n
152
How does light travel along an optical fibre?
By total internal reflection, only escaping when it reaches the other end
153
What is an endoscope?
A medical instrument that uses optical fibres to look inside the body
154
What do endoscopes consist of?
* a coherent bundle of fibres (lens system)
| * an incoherent bundle of fibres (light delivery system)
155
What happens if a fibre is bent too tightly?
Angle of incidence will be less than critical angle and light will escape
156
What can endoscopes be used to look at?
Digestive, respiratory and female reproductive systems
157
What are the positives of endoscopes?
Can diagnose patients without an incision, often without anesthetic
158
In an optical fibre, when will total internal reflection occur?
As long as θ is larger than the critical angle
i.e. sin θ > n of cladding ÷ n of core
159
In medicine, what are the uses of optical fibres?
* endoscopes
| * lasers - burn tissue to heal wound
160
What is a coherent bundle of fibres?
Where the fibres stay in the same relative position along their length
161
What are some of the problems for optical fibres?
* scratches can cause light to leak
* two fibres touching can cause light to pass from one to the other - 'cross talk'
* dispersion
162
How can scratches and cross talk be resolved when using optical fibres?
Using cladding
163
Does cladding have a lower or higher refractive index than the core?
Lower
164
How is light sent down an optical fibre?
In 'pulses' or 'bursts'
165
How can a pulse be distorted in an optical fibre?
* attenuation - some energy absorbed so pulse has smaller intensity
* dispersion - causes pulse broadening
166
What are the two types of dispersion?
* material (chromatic) dispersion
| * modal (multipath) dispersion
167
How does multipath dispersion occur?
A pulse can take a variety of different paths through a fibre, meaning a single pulse can spread out over time
168
How can multipath dispersion be decreased?
* use monomode fibres with a core diameter of only a few wavelengths, so light travels via one path
* cladding
169
How can cladding help to reduce multipath dispersion?
Refractive index of cladding is only slightly lower than the refractive index of the core, so the critical angle is larger than is would be at a glass-air boundary → only small range of angles that can be transmitted
170
What is the diameter of a typical mono-mode fibre?
10 micrometers (1-10 x 10⁻⁶ m)
171
How can material dispersion be reduced?
Using monochromatic light (red will travel faster than blue)
172
What colour of light should be used in an optical fibre?
Red - it travels faster
173
What is it called when in a prism, white light is split into a spectrum of colours?
Dispersion
174
In a prism, what colour light is refracted more: red or blue?
Blue
175
Why is blue refracted more than red in a prism?
Blue light travels more slowly in glass than red light
176
When is pulse distortion more of a problem?
When the pulses are very short and close together
177
When are single fibres used?
In communications
178
When are bundles of fibres used?
In endoscopes
