Waves 2 * Flashcards
1
Q
What is a wave?
A
The oscillation of particles or fields
2
Q
What is a progressive wave?
A
A wave that carries energy from place to place without transferring any material
3
Q
What is a wave cycle?
A
One complete vibration of a wave
4
Q
What is the displacement of a wave and what is the unit?
A
How far a point on the wave has moved from its equilibrium position (metres)
5
Q
What is the amplitude of a wave and what is the unit?
A
The maximum magnitude of displacement (metres)
6
Q
What is the period of a wave?
A
The time taken for a whole cycle to pass a given point (seconds)
7
Q
What is the wavelength of a wave and what is the unit?
A
The length of one whole wave cycle, from crest to crest or trough to tough (metres)
8
Q
What is the frequency of a wave and what is the unit?
A
The number of oscillations per second passing a given point (hertz)
9
Q
What is the phase of a wave?
A
A measurement of the position of a certain point along the wave cycle
10
Q
What is the phase difference of a wave?
A
The amount one wave lags behind another
11
Q
What are units for phase and phase difference?
A
Degrees or radians
12
Q
What are the symbols for displacement, amplitude, wavelength, period, and frequency?
A
Displacement = x, amplitude = A wavelength = λ, period = T, frequency = f
13
Q
What is reflection?
A
When a wave is bounced back when it hits a boundary
14
Q
What is refraction?
A
When a wave changes direction as it enters a different medium
15
Q
What equation relates frequency and time period?
A
f = 1/T
16
Q
What is the wave equation?
A
v = fλ
17
Q
What is c?
A
The speed of light in a vacuum - 3 x 10^8 m/s
18
Q
What type of waves of EM waves?
A
Transverse
19
Q
Give some examples of transverse waves.
A
EM waves, water waves
20
Q
What are the two types of graphs that can be drawn to show a transverse wave?
A
1 - displacement against distance along the path of a wave
2 - displacement against time for a point as the wave passes
21
Q
What does the distance between two crests/troughs represent on a displacement-distance graph?
A
Wavelength
22
Q
What does the distance between two crests/troughs represent on a displacement-time graph?
A
Time period
23
Q
Electromagnetic waves travel as vibrations through…
A
… magnetic and electric fields
24
Q
When looking at a graph representing a transverse wave, what must you look out for?
A
The label on the x axis. This may be distance or time, depending on what the graph is showing
25
Describe the vibrations on a transverse wave.
At right angles to the direction of energy transfer
26
Give some examples of a longitudinal wave.
Sound, pressure
27
What are the parts of a longitudinal wave?
Compressions, rarefactions
28
Do transverse and longitudinal waves require a medium?
Transverse - usually no
Longitudinal - usually yes
29
How are longitudinal waves represented on a graph?
Displacement against time.
30
Describe the vibrations in a longitudinal wave.
Parallel to the direction of energy transfer
31
What is a polarised wave?
A wave that only oscillates in one direction
32
Can transverse and longitudinal waves be polarised?
Transverse - yes
Longitudinal - no
33
What is polarisation?
Causing a transverse wave to only vibrate in one direction usually by passing it through a polarisation filter
34
What is some evidence for light being a transverse wave?
It can be polarised by reflection. A longitudinal wave could not do this, so light must be a transverse wave
35
Why can light waves be polarised?
They are a mixture of different directions of vibration. This means that they can be polarised by allowing only some of these directions to pass through a filter.
36
What is a polarising filter?
A panel that polarises waves by only allowing a specific direction of vibration to pass through
37
What happens in terms of polarisation when light is reflected off some surfaces?
It becomes partially polarised. This mean some of it vibrates in the same direction
38
What happens when two polarising filters are arranged at right angles to each other?
No light will get through
39
What happens if the two filters aren't quite at right angles? What is done to the filter to prove this?
It instead reduced the intensity of the light passing through it, but still allows some light through. By rotating the filter, we can see the change in intensity.
40
Is most light we see polarised?
No - most light we see is polarised
41
How does glare work?
Light reflected off some surfaces is partially polarised - some of it is made to vibrate in the same direction.
When light is reflected off surfaces like water, glass or tarmac enters the eye, it can cause glare.
42
How does glare reduction work?
The fact that reflected light is partially-polarised allows us to filter some of it out with polarising filters.
If you view partially-polarised reflected light through a polarising filter at the right angle, you can block out some of the reflected light, while still letting through light which vibrates at the angle of the filter. This reduces the intensity of light entering your eye.
43
What is the effect of reducing glare used for?
Reducing unwanted reflections in photography, and in polaroid sunglasses to reduce glare
44
What does the amount of polarisation depend on?
The angle of the incident light
45
How do polaroid sunglasses work?
Partially polarised light is reflected into a polarising filter at the correct angle. This blocks out the unwanted glare.
46
How do TV and radio signals make use of wave polarisation?
The broadcasting aerial has rods, which emit polarised waves. TV aerials on homes have horizontal rods. These rods must be lined up in order to get maximum signal strength. The same thing happens with radio aerials.
47
Give two examples of when wave polarisation is used.
Polaroid sunglasses, and TV and radio signals
48
What does the principle of superposition state?
When two or more waves cross, the resultant displacement equals the vector sum of the individual displacements
49
Graphically, how do you superimpose waves?
Add the individual displacements at each point along the x axis and then plot these.
50
What happens when a crest meets a crest (or a trough meets a trough) and what is this called?
Constructive interference. The amplitude of the wave is increased.
51
What happens when a crest meets a trough of the same size and what is this called?
Destructive interference. The displacements cancel themselves out.
52
How do you work out the displacement of a combined wave?
Add the displacements of the two waves
53
What does it mean when two points on a wave are in phase?
They are both at the same point in the wave cycle. They are the same wavelength and velocity.
54
Which quantities are the same about points on a wave which are in phase?
Same velocity and same displacement
55
How many degrees is one complete wave cycle said to be?
360
56
How many radians is one complete wave cycle?
2π
57
What is the SI unit for an angle?
Radians
58
What is the phase difference of a vibrating particle?
The fraction of a cycle it has completed since the start of a cycle
59
What is the phase difference between two particles?
The fraction of a cycle between the vibrations of the particles measured in either degrees or radians. Difference in their positions in a wave's cycle.
60
Waves with a phase difference of 0 degrees or a multiple of 360 degrees are said to be?
In phase
61
Waves with a phase difference of an odd number multiple of 180 degrees are said to be
exactly out of phase/in antiphase
62
When are two sources said to be coherent?
When they have the same wavelength and frequency, and they have a fixed phase difference between them
63
When are interference patterns most clear?
When the two sources are coherent
64
What is path difference and when is it relevant?
How much further a wave has travelled compared to another. This is used when looking at the type of interference between two waves that will occur at a certain point
65
Assuming that two sources are coherent and in phase, at what path difference will constructive interference occur?
At a whole number of wavelengths
Path difference = nλ
66
Assuming that two sources are coherent and in phase, at what path difference will destructive interference occur?
At a whole number of integer wavelengths and a half
Path difference = (n + 1/2)λ
67
When are superposed waves easier to 'see'?
- The waves are of similar amplitude
-The waves have similar frequencies
- The waves have a constant phase difference
68
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
69
What is a stationary wave?
The superposition of two progressive waves with the same frequency moving in opposite directions
70
What type of wave forms a stationary wave?
A progressive wave
71
Do stationary waves transmit energy?
No
72
Describe how stationary waves in a string can be demonstrated.
A vibration generator is attached to a piece of string at one end, while the string is fixed at the other end.
The frequency of the generator is varied until a resonant frequency is found.
73
Describe how the wave on a fixed piece of string (so it reflects at the end) changes with frequency.
At most frequencies, the pattern on the string is a jumble. If the vibration generator produces an exact number of waves in the time it takes a wave to get to the end and back, the original and reflected waves reinforce each other. This produces a stationary wave; the overall pattern doesn't move along, it just vibrates up and down.
74
When do stationary waves only occur?
A wave interferes with its reflection, which only happens at specific frequencies. The nodes must occur at the point of return.
75
What is a node on a stationary wave?
Where the amplitude of vibration is zero. Points of total destructive interference.
76
What is an antinode on a stationary wave?
Where the maximum amplitude of the wave is. Points of constructive interference.
77
What are the sections of stationary wave on a string called?
Oscillating loops
78
What is resonant frequency for a stationary wave?
When an exact number of half wavelengths fit onto the string.
79
What is it called when one, two and three loops of stationary wave are found on a string?
1 loop - 1/2 wavelength - first harmonic
2 loops - 1 wavelength - second harmonic
3 loops - 3/2 wavelengths - third harmonic
80
What is the first harmonic?
When the stationary wave is vibrating at the lowest possible resonant frequency. One loop is on the string, with a node at each end.
81
At the first harmonic, what is the length of the section of string?
1/2λ
82
At the second harmonic, what is the length of the section of string?
λ
83
How many wavelengths are in the first harmonic for a closed tube?
The first harmonic has 1/4 wavelength.
84
How many wavelengths are in the second harmonic for a closed tube?
The second harmonic has 3/4 wavelengths
85
In a closed tube, what sound does a long wavelength create?
Deep
86
What does an open tube look like?
Antinode and both the entrance and exit. Usual number of wavelengths in a harmonic (1/2 in the first harmonic)
87
How are stationary microwaves found?
Microwave beam is reflected off a metal plate - the superposition of the wave and its reflection produces a stationary wave.
The nodes and antinodes are found by moving the probe between the transmitter and reflecting plate.
The meter or loudspeaker receives no signal at the nodes and maximum signal at the antinodes.
88
Describe how sound can be used to demonstrate stationary waves.
How do you find the speed of sound from this?
A loudspeaker produces sound waves in a glass tube.
Lycopodium powder is laid along the bottom of the tube. The powder is shaken away from the antinodes and left undisturbed at the nodes.
The distance, d, between each pile of powder (node) is λ/2 so λ = 2d.
The speed of sound = v = fλ
so v=2df. The frequency of the generator is known.
89
Compare the frequency of the first, second and third harmonic.
First = f, second = 2f, third = 3f
90
Which equation can be used to find the frequency of the nth harmonic on a piece of string?
f = c/λ
where:
f = harmonic frequency, c = speed of wave on string, and λ = the wavelength of the wave given in terms of the length of the string
91
What is the equation for phase difference in radians?
Phase difference = 2πd/λ
where d = the distance apart of the particles in wavelengths
92
Describe an experiment used to show how mass, length and tension change the resonant frequencies of a string.
1: Measure the mass and length and length of the string using a mass balance and ruler. Work out the mass per unit length in kg/m.
2: Set up the equipment. This involves connecting a vibration generator (connected to a signal generator) to a piece of string attached to a pulley and some masses. Clamp the entire setup to the bench.
3: Measure the length of the string between the vibration generator and the pulley. Work out the tension using T = mg, where m is the mass of the masses on the end of the string.
4: Turn on the signal generator and adjust the frequency until the first harmonic is found.
Depending on the experiment, you can choose to either change the mass (per unit length), the length or the tension of the string. Choose one to change and keep the rest the same.
93
What are the first, second, third etc harmonics known as collectively?
The resonant frequencies
94
Which factors during the stationary wave experiment may affect the resonant frequencies?
Length of the vibrating string
Tension in the string
Type of string (different mass per unit length)
95
In the stationary wave experiment, what do the letters µ, M, L, T, m, and g represent?
µ = mass per unit length of the string, M = mass of the string, L = length of the vibrating string, T = tension in the string, m = mass of the masses in the end of the string, g = gravitational field strength
96
What is the unit for tension?
Newtons (N)
97
How can the tension in the string in the stationary waves experiment be varied?
Add or remove masses to vary the tension.
98
How can the string type in the stationary waves experiment be varied?
Use different string samples but keep it the same length.
99
How does string length affect the resonant frequency in the stationary wave experiment?
The longer the string, the lower the resonant frequency. The half wavelength at the resonant frequency is longer.
100
How does the type of string affect the resonant frequency in the stationary wave experiment?
The heavier the string, the lower the resonant frequency. Waves travel more slowly down the string. A lower wave speed makes a lower frequency.
101
How does tension affect the resonant frequency in the stationary wave experiment?
The higher the tension, the higher the resonant frequency. Waves travel more quickly on a taut string. A higher wave speed makes a higher frequency.
102
In the stationary wave experiment, what equation is used to give the first harmonic frequency of a string?
f = (1/2L) x √(T/µ)
103
What is diffraction?
The spreading out of waves when passing through a gap or going around an object.
104
What determines the amount of diffraction observed?
The wavelength of the wave compared to the size of the gap.
105
When is diffraction most noticeable?
When the gap is the same size as the wavelength.
106
How does a narrower gap affect diffraction?
It is increased
107
How does a smaller wavelength affect diffraction?
It is decreased
108
What happens in terms of diffraction when the gap is a lot bigger than the wavelength?
Diffraction is unnoticeable
109
What happens in terms of diffraction when the gap is a lot smaller than the wavelength?
The waves are mostly just reflected back
110
When both are not in direct line of sight, why can sound be heard around a doorway, but light cannot be seen?
The doorway is a gap of a similar size to the wavelength of sound, so it diffracts to the listener. However, the gap is much larger than the wavelength of light, so the diffraction is not noticeable.
111
In a single-slit white light diffraction pattern, what is the order of colours in each spectrum band and why?
Blue is on the inner side and red is on the outer side. This is because red light has a longer wavelength so it diffracts more.
112
What happens to each fringe in a single-slit diffraction pattern as you move from the central maximum?
The fringes become less bright.
113
What is intensity of light?
The power per unit area
114
In a single-slit diffraction pattern, how does the width of the central maximum compare to the outer fringes?
It is twice as wide. The outer fringes are all of the same width
115
Name two monochromatic light sources.
Laser, vapour lamps and discharge tubes.
116
Do two light sources have to be in phase to be coherent?
No, as long as they have a constant phase difference.
117
What is the single-slit equation?
W = 2Dλ / a
where:
W = width of the central maximum, D = distance between the slit and screen, λ = wavelength, a = slit width
118
What is needed to demonstrate two-source interference?
Two coherent sources
119
Why are two loudspeakers coherent sources of sound waves?
They have the same frequency/wavelength and constant phase difference. This is achieved by both speakers being connected to the same signal generator.
120
What is another name for the experiment to demonstrate two source interference?
Young's double slit experiment.
121
In Young's double slit experiment, what do the slits act as?
Two coherent sources of light
122
Can a white light source be a coherent source?
No, due to the various frequencies of light in it
123
What is fringe separation?
The distance from the centre of a a bright fringe to the centre of the next one
124
What is the danger of a powerful laser?
If you looked at the beam directly, your eye would focus it onto your retina, which would be permanently damaged.
125
What are some safety precautions that must be taken when working with a laser?
1. Never shine the laser towards a person
2. Wear laser safety goggles
3. Avoid shining the beam at a reflective surface
4. Have a warning sign on display
5. Turn the laser off when it is not needed
126
How can Young's double slit experiment be adapted for microwaves?
Replace the laser and slits with two microwave transmitter cones attached to the same signal generator.
Replace the screen with a receiver probe.
Move the probe along where the screen was and you'll get an alternating pattern of strong and weak signals.
127
What is the equation for Young's double slit experiment?
w = λD/s
where:
w = fringe spacing, λ = wavelength, D = distance from slits to screen, s = slit separation
128
In Young's double slit experiment, what is the easiest way to get an accurate reading for w?
Measure several fringes and divide by the number of fringe widths between them
129
In Young's double slit experiment, what must you be careful when measuring several fringes?
When dividing to find w, remember to divide by the number of fringe widths between them, not the number of fringes. (10 bright line have 9 fringe widths between them)
130
Compare single and double slit diffraction patterns in terms of fringe widths and intensities.
Single slit:
Widest central maximum and equal outer fringes.
Brightest central maximum and decreasing intensity of outer fringes.
Double slit:
All fringes of equal width.
Decreasing intensity of outer fringes
131
In a double slit interference pattern, why does the intensity of the fringes decrease as you get further away from the central maximum?
Because it's multiplied by the single slit diffraction pattern for either of the slits separately.
132
Compare the double slit interference pattern pattern for red and blue light.
The blue light creates a smaller fringe separation. This makes the pattern appear more compact.
133
Describe and explain what is observed with double slit interference of white light.
White central fringe - every colour contributes at the centre
Inner fringes are tinged with blue on the inside and red on the outside - red fringes are more spaced out than blue fringes.
After a few fringes, there is no clear fringe pattern - the different colours' patterns have all blended.
134
What was the importance of Young's double slit experiment?
It was evidence for light interference and diffraction. This was important in the debate between Newton's corpuscular theory of light and Huygens' wave theory of light, supporting Huygens' theory.
135
Explain what happens when Young's double slit experiment is repeated with more slits.
The same shaped pattern is observed, except the bright bands are brighter and the dark bands are darker, giving a sharper pattern.
136
What makes the pattern so sharp when monochromatic light is passed through a diffraction grating?
There are many beams reinforcing the pattern.
137
What is the advantage of observing sharper lines in interference patterns?
It allows for more accurate measurements.
138
In double slit interference, what conditions must be met in order for a pattern to be seen?
Each slit must be sufficiently narrow to diffract the light enough.
The two slits must be close enough for the diffracted waves to overlap.
139
Explain simply why single-slit diffraction patterns are observed.
The waves from different points across the slit interfere to reinforce or cancel each other out.
140
Explain why a diffraction grating produces several sharp line.
Diffracted light waves from adjacent slits reinforce each other in certain directions only and cancel out in all other directions.
It works just like double slit interference, except with many more slits. More slits result in more sharp lines, so there are several distinct, sharp lines produced by a diffraction grating.
141
What is the equation for distance between slits in a diffraction grating?
dsinθ = nλ
142
What must you be careful of when putting 'd' into the diffraction grating equation?
d is the slit spacing, not the number of slits per metre, which is how the data may be given.
143
When given a grating with 300 slits per mm, what value of d is used?
300 slits/mm = 300,000 slits/m
Therefore, d = 1/300,000
144
What effect does increasing slit separation have on the diffraction grating pattern?
It is more compact.
145
How can you calculate the maximum order for a given diffraction grating and wavelength? Explain why this works.
θ can never be greater than 90, so the greatest value of sinθ is 1. This leaves d = nλ. Then you can solve for n. Round n down to the nearest integer.
146
What is X-ray crystallography?
The wavelength of x-rays is similar to the spacing between atoms in crystalline solids. So x-rays directed at a thin crystal form a diffraction pattern. The crystal acts like a diffraction grating.
Looking at the diffraction pattern, the spacing of the atoms can be calculated.
147
What was x-ray crystallography used for?
To discover the structure of DNA.
148
What is the absolute refractive index of a material?
The ratio between the speed of light in a vacuum, c, and the speed of light in that material, cₛ.
149
When does light travel the fastest?
In a vacuum.
150
Why does light slow down in optically dense materials?
It interacts with the particles in the material.
151
The more optically dense a material is, the more that light...
slows down when entering it.
152
The optical density is measured by what?
Its refractive index
153
What does a high optical density mean for its refractive index?
Higher optical density = higher refractive index
154
What symbol is used for the speed of light in a vacuum?
c
155
What is the equation for absolute refractive index?
n = c/cₛ
156
What symbol is used for the speed of light in a material?
cₛ
157
What is the symbol for absolute refractive index?
n
158
The speed of light in air is only a bit smaller than the speed of light, c, so you can assume that nₐᵢᵣ = ?
nₐᵢᵣ = 1
159
What is relative refractive index?
The ratio of the speed of light in material one to the speed of light in material two.
160
What is the symbol for relative refractive index of a boundary?
₁n₂
relative refractive index of a boundary, going from material 1 to material 2.
161
What is the speed of light in a vacuum?
3 x 10⁸ ms⁻¹
162
What is the difference between absolute and relative refractive index?
Absolute refractive index is the ratio of the speed of light in a vacuum compared to the speed of light in the material.
Relative refractive index is the ratio of the speed of light in material 1 to the speed of light in material 2.
163
What are the equations for relative refractive index?
₁n₂ = c₁ / c₂ = n₂ / n₁
164
In refractive calculations, how are air and vacuum perceived?
They are essentially the same since the both have a refractive index of about 1.
165
What is the angle of incidence and what is the symbol?
The angle that incoming light makes to the normal, θ₁.
166
What is the angle of refraction and what is the symbol?
The angle that the refracted ray makes to the normal, θ₂.
167
What must you be careful of when dealing with the angle of incidence and the angle of refraction?
They are measured from the normal, not the boundary.
168
Which way does light bend when it enters a more optically dense material?
Towards the normal
169
Which way does light bend when it enters a less optically dense material?
Away from the normal
170
What is the critical angle?
The angle of incidence at which the angle of refraction is 90° so that the light is refracted along the boundary.
171
What is the equation for the critical angle?
sinθ꜀ = n₂ / n₁
172
What is total internal reflection?
When light going from a more optically dense to a less optically dense material hits the boundary at an angle greater than the critical angle and is completely reflected.
173
What are the conditions for total internal reflection?
The incident substance has a larger refractive index than the other substance.
The angle of incidence exceeds the critical angle.
174
What is an optical fibre?
A very thin flexible tube of glass or plastic fibre that can carry light signals over long distances using TIR.
175
Describe how an optical fibre works.
The fibre has a very high refractive index, but is surrounded by a cladding with a lower refractive index. This enables TIR and protects the fibre.
The fibre is narrow so the light always hits the boundary at an angle greater than the critical angle. Light that enters at one end is totally internally reflected to the other end.
176
Name some design features of an optical fibre.
Thin - ensures light hits at an angle above the critical angle and prevents modal dispersion.
Cladding of lower refractive index - protects the fibre from scratches and ensures TIR happens.
177
What are the two reasons for cladding on an optical fibre?
- Protects the fibre from scratches.
- Ensures TIR happens (by having a lower refractive index).
178
What are the two reasons for making an optical fibre thin?
- Ensure light hits at an angle above the critical angle.
- Prevents modal dispersion.
179
Name two uses of optical fibres.
Endoscopes, communications
180
What are the benefits of optical fibres being used to transmit phone and cable TV signals?
Light has high frequency which means that the signal can carry lots of information.
Light doesn't heat up the fibre so no energy is lost.
There is no electrical interference.
Fibre optics are cheap to produce.
The signal can travel very far, very quickly, with minimal signal loss.
181
What are the two ways in which a signal can be degraded?
Absorption, dispersion
182
What is signal degradation by absorption and how does it affect the signal?
Some of the signal's energy is lost through absorption by the material of the fibre. This reduces the amplitude.
183
What does dispersion cause?
Pulse broadening
184
What is pulse broadening?
The received signal is broader than the initial signal. Broadened pulses can overlap each other, leading to information loss.
185
What are the two types of signal dispersion?
Modal dispersion and material dispersion.
186
What is modal dispersion and how does it affect the signal?
Light rays enter the fibre at different angles and so take different paths. Some arrive later than others (rays taking a path straight down than middle of the fibre arrive faster than rays taking a longer path). This causes pulse broadening.
187
What is material dispersion and how does it affect the signal?
Different wavelengths experience different amounts of diffraction as they travel at different speeds in the fibre. This cause some parts of the signal to take a longer time to travel down the fibre than others, causing pulse broadening.
188
How can signal degradation by absorption be reduced?
Use a highly transparent fibre to stop absorption.
Use an optical fibre repeater.
189
How can modal dispersion be reduced?
Use a very narrow fibre - small path difference.
190
How can material dispersion be reduced?
Use monochromatic light.
191
What is an optical repeater and what does it prevent?
A device that boost and regenerates the signal every so often. This reduces signal degradation by absorption and dispersion.
192
When signal dispersion is large, what can happen?
Broadened pulses can overlap, causing confusion and information loss.
193
How does a medical endoscope work?
- Has two bundles of fibres.
- One is used to illuminate the area of the body.
- A lens forms an image on the end of the other bundle.
- The fibres then take this image back to the other end, where it can be viewed.
194
What is important about the bundle of fibre in an endoscope?
The bundle must be coherent, so that the image on the other end is not muddled up.
195
In what planes can the displacements of oscillations in transverse waves be?
In all planes
196
What is a coherent bundle of fibres in an endoscope?
When the fibre ends are in the same relative positions (the fibres arrange themselves in the same order to recreate the original image).
