Waves Flashcards
(87 cards)
1
Q
What is a wave?
A
A regular disturbance that carries energy from one place to another.
A wave transports energy and not matter.
2
Q
Waves in a medium?
A
When a wave is present in a medium (when there’s a disturbance moving through a medium), the individual particles of the medium are only temporarily displaced from their rest position. There is always a force acting upon the particles that restores them to their original position.
3
Q
Displacement?
A
Instantaneous distance from the equilibrium (undisturbed) position.
4
Q
Amplitude (a)?
A
The maximum displacement from the equilibrium position.
5
Q
Time period (T)?
A
The time taken for one complete cycle (oscillation/wave) and measured in seconds,s.
6
Q
Frequency (f)?
A
The number of oscillations/cycles in one second and measured in Hertz, Hz.
7
Q
Wavelength (λ)?
A
The distance between any two points on adjacent cycles which are vibrating in phase.
NB: In phase means at the same point in the cycle.
8
Q
Equation for T?
A
T=1/f
Period/time taken for a wave to move one wavelength.
9
Q
Displacement-time graph?
A
The motion of one particle as a function of time - ‘Movie’.
Peak-peak: Period, T
Contains amplitude.
10
Q
Displacement-distance graph?
A
‘Snapshot’ of all the particles. It shows the position of all the particles at one particular time.
Peak-peak: Wavelength, λ
Contains amplitude.
11
Q
The wave equation?
A
c=fλ Derivation: speed=distance/time=wavelength/period c=λ/T=λ/1/f=fλ (suvat, assuming a=0)
12
Q
What is phase difference?
A
The difference, expressed in degrees or radians, between two waves having the same frequency and referred to the same point in time.
Two oscillators that have the same frequency and no phase difference are in phase.
Two oscillators that have the same frequency and different phases have a phase difference and are out of phase with each other.
Two oscillators that have the same frequency and a phase difference of 180° as in antiphase.
13
Q
Converting between degrees and radians?
A
360° = 2π rad 180° = π rad 90° = π/2 rad
14
Q
ΔPhase?
A
For degrees:
θ=(x/λ) x 360°
For radians:
θ=(x/λ) x 2π
15
Q
Using both graphs?
A
To show the motion of a single particle from a displacement-distance graph at t=0, the particles move to the left.
16
Q
Example: vertical displacement of knot in the next complete cycle?
A
- Begin by moving down to max. displacement.
- The change direction and reach top max. displacement (through equilibrium level).
- Then back to original position.
17
Q
Transverse waves?
A
The oscillations are at right angles to the direction of the wave.
e.g. all electromagnetic waves, including light.
18
Q
Longitudinal waves?
A
The oscillations are parallel to the direction of the wave.
e.g. sound, ultrasound, p waves.
19
Q
Mechanical waves?
A
e. g. sound and water
- Travel by vibrating particles in a medium. They can’t travel through a vacuum.
- Electromagnetic waves (e.g. light and infrared) are the only waves which can travel through a vacuum.
20
Q
Electromagnetic waves?
A
- Waves that travel as transverse and transfer energy from one place.
- They all travel at the same speed in a vacuum (3x10^8ms^-1).
21
Q
MED?
A
- Magnetic field: Upwards.
- Electric field: To the right.
- Wave direction: SouthEast.
22
Q
The principle of superposition?
A
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.
The adding together of waves is called interference.
23
Q
Constructive interference?
A
Waves with the same frequency (and wavelength) and similar amplitude superpose.
The waves are in phase (0° phase difference) and the resultant wave has twice the amplitude as the originals.
24
Q
Destructive interference?
A
Waves with the same frequency (and wavelength) and similar amplitude superpose.
The waves are in antiphase (180° phase difference) and the resultant wave has an amplitude of 0.
25
Stationary/Standing waves?
Waves involve movement and changes, but sometimes waves can be trapped in space, e.g. the 'twang' of a guitar string.
The waves travel along the string and are reflected at the ends, so we have two identical waves travelling in opposite directions.
26
Nodes?
Points on the resultant wave that are always at equilibrium. At these points, the two waves cancel.
There is no oscillation at a node.
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Anti-nodes?
Points on the resultant wave that oscillate with larger amplitude. They are points of maximum oscillation.
28
Inter-nodal distance?
The distance from one node to the next node (and one anti-node to the next anti-node) is always half a wavelength.
29
Characteristics of stationary waves (FAPE)?
Frequency: All particles, except at the nodes, vibrate at the same frequency.
Amplitude: The amplitude varies from 0 at the nodes to a max. at the antinodes.
Phase Difference: mπ, where m is the number of nodes between the two particles.
Energy: Stored and not transferred.
Given point A lasts for 0.5λ.
30
Characteristics of progressive waves (FAPE)?
Frequency: All particles vibrate at the same frequency.
Amplitude: The amplitude is the same for all particles.
Phase Difference: 2πx/λ where x=distance apart
Energy: Transferred.
Given point A is just the point.
31
Transverse stationary waves?
- These can be created on a rubber cord.
- A vibration generator can be used to send waves along the cord. The waves reflect back from the far ends, and meet waves on their way from the vibration generator.
- At certain frequencies, the rubber cord vibrates with a larger amplitude. These are resonant frequencies.
32
How is a standing wave formed?
The vibrator moves up and down and sends a travelling wave along the cord.
The wave is reflected at the end, so two travelling waves (with same f and λ) in opposite directions.
When (if) they overlap, they interfere and form a standing wave.
A standing wave has points which vibrate with max amplitude (antinodes) and points that have min amplitude (nodes). The distance between neighboring nodes is λ/2.
33
Resonant frequencies of a stretched spring?
Standing waves are only produced at certain frequencies.
This is because you must have a whole number of stationary wave 'loops' fitting into the length of the string.
The length of each loop is exactly half of the wavelength of the waves sent from the vibration generator.
NB: The ends are fixed thus must be nodes.
34
Tuning of a guitar?
-The pitch of a note corresponds to frequency.
-The first harmonic frequency, f, depends on the tension, T, in the wire, its length, l, and mass per unit length, μ, according to the equation:
f = 1/2l(√T/μ)
35
Factors to increase pitch?
- Decreased length of string.
- Decreased thickness of string.
- Increased tightness of string.
36
The first 6 harmonics?
- The first pattern only has one loop. This is the fundamental frequency or first harmonic.
- The second pattern has two loops. This is the second harmonic. The wavelength has halved because the frequency has doubled.
- The third pattern has three loops. This is the third harmonic, etc.
37
Vibrations in air columns?
When the air at one end of a tube or pipe is caused to vibrate, a longitudinal wave travels down the tube, and if reflected at the opposite end.
The resultant of the two waves (incident and reflected) is a stationary, longitudinal wave.
38
Closed pipes?
A closed pipe is closed at one end and open at the other.
At resonant frequencies, a node is produced at the closed end and an antinode at the open end.
The amplitude of the particles decreases gradually from the max. at the open end to 0 at the closed end.
-At the fundamental frequency, f1, the length of the pipe is λ/4.
-The first overtone is the third harmonic, the frequency is 3f1 and the length of the pipe is 3/4λ.
-The second overtone is the fifth harmonic, the frequency is 5f1 and the length of the pipe is 5/4λ.
NB: With a closed pipe, only the old harmonics can be obtained.
39
Open pipes?
An open pipe is open at both ends.
When a longitudinal wave is produced at one end, it is reflected at the other end, because the air outside the tube acts as a barrier.
Antinodes are produced at both ends.
-At the fundamental frequency, f1, the length of the pipe is λ/2.
-The first overtone is the second harmonic, the frequency is 2f1 and the length of the pipe is λ.
-The second overtone is the third harmonic, the frequency is 3f1 and the length of the pipe is 3/2λ.
NB: With an open pipe, ALL harmonics can be obtained.
40
What is polarisation?
The oscillations in a transverse wave are at right angles to the direction of the wave.
The displacement of the oscillations can be in all planes.
Plane-polarised waves have the oscillations in one plane only, which contains the direction of propagation of the wave.
41
How can light be polarised?
Most sources of light give off unpolarised light.
The light can be polarised by absorbing all planes of oscillation except one using Polaroid filters.
If two filters are parallel, the light will pass through the first - where it is vertically polarised - and the the second.
If two filters are crossed, so that the transmission planes are at 90° to each other, the vertically polarised light gets blocked as it cannot pass through the horizontal transmission plane. No light passes through.
Crossed polaroids are found in liquid crystal displays on calculators and petrol pumps.
Light can also be polarised by reflection.
Some of the light reflected from water is polarised with the plane of polarisation horizontal.
42
Polaroid plastic?
Polaroid plastic is used in some sunglasses. It contains many tiny crystal all lined up together.
If you wear sunglasses made from Polaroid plastic, reflection off the water surface is absorbed because its plane of polarisation is perpendicular to the plane of polarisation of the Polaroid.
This avoids dazzle.
If two pieces of Polaroid are 'crossed' so that their transmission planes are at right angles, no light will get through.
43
The double slit interference pattern (Young's Slits)?
Consists of parallel equidistant fringes alternating between:
- maxima where the waves interfere constructively.
- minima where the waves interfere destructively.
44
The effect of path difference?
If two waves produced at the two slits are in phase:
a) The wavelengths have zero path difference, arrive in phase and constructively interfere - bright fringes.
b) The path difference is exactly one wavelength, so the two waves are in phase and constructively interfere - bright fringes.
c) The path difference is half a wavelength, so the waves are 180° out of phase. They interfere destructively - dark fringes.
45
Interference with light?
Waves of all type interfere. If we use two light sources, we never see an interference pattern.
Does this mean light is not a wave?
This is because light is emitted in bursts of waves, and each burst lasts 10^-9 seconds, after which there is a random phase change.
46
How is a clear interference pattern obtained?
To obtain a clear interference pattern, we require two coherent waves (same frequency, same wavelength and synchronized phase changes/constant phase difference) of monochromatic light.
This is achieved by using the same light source incident on two slits.
What would happen if the phase difference between the two sources kept changing?
47
Equation for fringe spacing?
```
sinθ=λ/a and tanθ=x/D
if θ<<10°, sinθ=tanθ
λ/a=x/D thus x=λD/a
x=distance between adjacent fringes (fringe width)
a=distance between slits (slit width)
D=distance from slits to screen
λ=wavelength
```
48
Increasing x?
- Increasing D, the distance from the slits. This makes measurement easier and more accurate but fringe intensity is decreased.
- Decreasing a, the slit width but there is a practical limit to this.
- Increasing λ, the wavelength.
49
Double slit interference?
The monochromatic source is a source of a single wavelength. A sodium lamp is usually used.
The single slit diffracts the light and so illuminates both of the double slits.
It and the first slit can be represented by a laser as it is a monochromatic, coherent source of light.
The interference pattern formed will only occur in the area of overlap.
50
The pattern?
The interference fringes appear as parallel bright and dark bands, parallel to slits S1 and S2.
The distance between neighboring bright fringes (from start of one bright fringe to start of next bright fringe) is called fringe separation, x.
51
Changing the pattern?
Red light is changed to green light: λ decreases thus x decreases. The maxima are less spread out and the overall pattern is narrower.
White light is used: Each dot is a different color. The central dot is white and the other dots are split into rainbow - red further out than blue.
The screen is moved further away: D increases thus x increases.
The phase difference between the two sources is changed to 180°: The maxima and minima switch thus red and black switch.
The slits are moved further apart: a increases thus x decreases.
Both slits are narrower: Wider interference thus more dots which are more spread out thus x increases. The dots are fainter as less light can get through.
One slit is narrower than the other one: Don't fully cancel out.
52
What is diffraction?
When a wave passes through a gap, it spreads out.
As the width of the gap decreases or λ increases, the diffraction becomes more pronounced.
Diffraction is strongest when the gap width is similar to the wavelength of the wave.
53
Diffraction of light using a single slit?
When a wave passes through a single gap, it produces a pattern with fringes.
-The pattern shows a central fringe with further fringes either side of it.
-The central fringe is twice as wide as each of the outer fringes which are all the same width.
-The intensity of the fringes is greatest at the center of the central fringe. The peak intensity of each fringe decreases with distance from the center.
The fringes are caused due to interference.
But if there's only one slit, isn't there only one wave?
54
Single slit?
A single slit can be thought of as a large number of sources next to each other. Each source produces a coherent wave. As the waves overlap, they interfere.
If every wave has a wave which is 180° out of phase, they will all cancel out. Destructive interference produces a minimum intensity fringe.
55
What causes a greater angle of diffraction (more spread out)?
- Greater wavelength.
- Greater distance.
- Narrower slits.
56
Diffraction grating?
Not much light gets through the two narrow slits used in Young's double slits. The fringes produced are not very sharp, and they are also quite dim.
A diffraction grating produces a much better distinction.
A diffraction grating is a set of slits, or lines, for light waves to pass through (instead of just two slits, there are thousands).
57
The single slit pattern?
Consists of a central maximum fringe which is twice the width of the other fringes.
58
The double slit pattern?
Consists of equally spread fringes.
| It is affected by the width of the two slits.
59
Diffraction grating equation?
dsinθ=nλ
d=distance between slits
θ=angle to maxima
n=integer number to next bright fringe
λ=wavelength
NB: sinθ can never be greater than 1, so there is a limit to the number of spectra that can be obtained.
NB: If questions ask to determine whether anymore orders could be observed, try with the n=2.
Max. number of orders: n=d/λ
Round down - absolute maximum.
Double for both sides and add 1 for central.
60
Diffraction grating v Young's double slit?
- The diffraction grating is much more accurate than the Young's double slit method.
- The fringes formed with Young's slits are slightly blurred and so measurements can involve quite large errors.
- The images with diffraction grating are very clear and the measurements are very accurate.
- Another advantage is that the final result is an average of several calculations.
61
What is an experiment that will demonstrate the wave nature of sound?
Measuring diffraction of sound through a doorway.
62
Why do we often assume that compared to the speed of sound, the speed of light is infinite?
In calculations, we assume that light reaches an observer at 0 seconds, implying it takes no time.
63
Why does the speed of sound not depend on frequency?
The sound produced from a gun consists of multiple frequencies yet all of the sound is heard by the observer at the same time.
64
What is a spectrometer?
A spectrometer uses a diffraction grating to split a beam of light into its constituent wavelengths and enables the angles of the diffracted beam to be measured.
An application of this is determining the composition of stars.
If white light is directed into a spectrometer, the normal ray emerging will be white light whereas the diffracted ray will be split into a spectrum.
65
What is refraction?
The bending of waves as they change speed after entering a medium of different optical density at an angle to the normal.
Light travels at different speeds in different media - light travels slower in optically dense media.
The changing of speed causes light to refract.
When light enters a more optically dense media, it refracts towards the normal - θi>θr.
When light exits a more optically dense media, it refracts away from the normal - θi
66
What is refractive index?
The extent to which a material will cause light to bend.
n = sin(i)/sin(r)
i = the angle between the light ray arriving at the boundary and the normal.
r = the angle between the light ray leaving the boundary and the normal.
NB: Only for when light travels from air into the substance.
OR
A measure of the optical density of a material relative to air i.e. the ratio of the speed of light in a vacuum to the speed of light in the medium.
n = speed of light in vacuum/speed of light in medium
n = c/v
The greater the difference in refractive index between two media, the more the light is refracted at the boundary.
67
Snell's Law?
-The refractive index can be used to determine the angle at which light bends using Snell's law.
-When light hits the boundary between two transparent media, it splits into two parts.
-One part reflects back into the first medium and the other refracts into the second media.
-The exception to this is total internal reflection.
-Snell’s law of refraction for a boundary:
n1sinθ1 = n2sinθ2
-For a ray travelling across a series of parallel boundaries:
n1sinθ1 = n2sinθ2 = n3sinθ3 = n4sinθ4
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Types of refractive index?
- Relative refractive index: n2/n1 for a ray travelling from medium 1 into medium 2.
- Absolute refractive index: The refractive index for a ray travelling from a vacuum into a medium. This is a property of the medium.
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Example of refraction?
When white light enters a prism, it is dispersed into all the colors of the spectrum.
Each color has a different wavelength and the shorter the wavelength, the slower the light travels through the prism.
Shorter wavelengths have a greater refractive index thus are refracted more.
70
Total internal reflection?
When a ray travels from a medium of higher refractive index to a medium of lower refractive index, the angle of refraction is larger than the angle of incidence.
The angle of refraction can't exceed 90°, therefore there is a limiting angle of incidence - the critical angle (θc), above which no refracted ray can be formed.
If the angle of incidence is greater than the critical angle, the rays reflect back into the first medium.
LOOK AT BINO AND PERISCOPE DIAGRAMS.
71
Why is total internal reflection only possible from high refractive index to low refractive index?
Light must bend away from the normal which only occurs when light enters a less dense media.
72
Critical angle?
The angle of incidence at which the refracted ray travels along the boundary between the two media.
- When θi>θc - total internal reflection.
- When θi
73
Diamonds?
- They have a very high refractive index thus a small critical angle.
- This increases the dispersion effect when white light enters.
- The small critical angle means light may be totally internally reflected several times before leaving the diamond.
- This increases the dispersion effect further, making it sparkle.
74
What would happen if a transparent stone was immersed in a liquid of the same refractive index?
It would appear to be invisible as light would travel straight through it.
75
What happens when light passes from air to a material of higher refractive index?
- It slows down and bends towards the normal.
- λ decreases.
- Frequency stays the same.
76
What is an optical fibre?
A flexible, transparent fibre made of glass or plastic, slightly thicker than a human hair which can transmit light with no reduction in intensity.
Light travels along the fibre by total internal reflection, only escaping when it reaches the other end.
If the fibre is bent too tightly, i
77
Endoscopes?
An endoscope uses optical fibres to look inside the body. It consists of:
- A rigid or flexible tube.
- A light delivery system to illuminate the organ or object under inspection. The light source is outside the body and goes down a bundle of optical fibres.
- A lens system transmitting the image from the object to the viewer, again through a bundle of optical fibres.
- An additional channel to allow entry of medical instruments.
78
Benefits of endoscopes?
- They can be used to look at digestive systems, respiratory systems and female reproductive systems without the need for an incision.
- Diagnosis can be made without the need for major surgery and often without anesthetic.
- The use of a small incision can also allow doctors to examine inside joints and the abdomen.
79
Incoherent/coherent?
1. Incoherent bundle of fibres.
2.Coherent bundle of fibres:
The fibres stay in the same relative position along their length.
-In the illuminating bundle, the fibres are arranged randomly.
-In the viewing bundle, the fibres are arranged so that they remain in the same relative position so that each part of the image is in the same position as it was on the object.
80
Lasers?
Used in medicine to burn tissue in order to heal a wound.
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Binoculars?
- Optical instruments that magnify distant objects.
- A pair of right angles prisms bend the path of light.
- Total internal reflection shortens the length of light
82
Communications?
'Pulses' of light are sent down the fibre to carry data.
(see diagram)
The fibres are highly transparent to reduce light absorption.
83
Pulse distortion?
Results in a more loss of light thus a weaker signal and light can't travel as far.
This is more of a problem when the pulses are short and close together (i.e. at higher bit-rates).
The pulse is distorted due to:
Attenuation: Some energy is absorbed so the pulse has a smaller intensity.
Dispersion: Causes pulse broadening.
1. Material (Chromatic) Dispersion
2. Modal (Material) Dispersion
84
Material dispersion?
A pulse of white light sent down a fibre will stretch because the red light will travel faster than the blue light along the fibre.
Infrared (monochromatic light) is used to reduce material dispersion.
85
Modal dispersion?
```
A pulse can take a variety of different paths through a fibre meaning a single pulse of light can spread out over some time.
Using a cladding of lower refractive index reduces the critical angle so rays with a low angle of incidence are refracted out of the fibre.
Monomode fibres (thin optical fibres) are used with a core diametre of only a few wavelengths (1-10x10^-6m), in which light can only travel via one path.
```
86
Purpose of cladding?
-Reduces modal dispersion.
The refractive index of cladding is only slightly lower than the refractive index of the core, thus the critical angle is larger than at a glass-air boundary.
Therefore there is only a small range of angles/fewer modes that can be transmitted.
-Stops "cross talk".
Light can't pass through cladding thus can't pass from one fibre to another.
Two fibres touching can cause light to pass from one to the other when the surface of the fibre is scratched - this isn't secure.
-Stops scratches.
Scratches can cause light to leak.
87
How is laser light different from the light from a filament lamp?
- Laser light is monochromatic. It is composed of waves of single frequency/wavelength, whereas the light from a lamp consists of a range of wavelengths.
- Laser light is collimated. An approximately parallel beam is produced. A lamp produces light that spreads out in all directions from the source.
- Laser light is coherent - waves produced are in constant phase with each other; whereas light from a filament lamp is incoherent.
- Laser light is polarised - the vibrations are in 1 plane only.
