1
Q
Amplitude
A
Amplitude (A) is the maximum distance a particle is displaced from its rest position.
- The greater the amplitude of a wave, the more energy it is carrying.
2
Q
Wavelength
A
Wavelength (λ) is the distance between two successive corresponding positions in a wave
3
Q
Frequency
A
Frequency (f) is the number of waves passing any point each second, measured in hertz (Hz)
4
Q
Period
A
Period (t) is the time taken for one wave to pass any point, measured in seconds (s)
5
Q
Energy transfer of waves
A
Energy can be transferred by the wave motion between two places. The direction of proapgation of the wave is in the same direction as the energy flow.
- Waves can not transfer matter (eg. particles and mass).
6
Q
Sound waves
A
Sound waves require vibrating air particles to propagate.
Eg. A speaker
- When a speaker produces music, it vibrates back and forth. As it moves forward, it pushes on the closest air particle, whch, in turn, pushes on the next air particle (and so on).
- As the speaker moves backward, it pulls the closest air particle with it, which, in turn, pulls on the next air particle (and so on).
- Vibrating air particles cause any neighbouring air particles to vibrate and so on
- Once the air particles closest to your ear begin to vibrate, they will then vibrate your eardrum. This will be interpreted by your brain as sound. Thus, the sound energy has been transferred from the speaker to your ear by vibrating air particles.
7
Q
Mechanical wave
A
A mechnical wave is a wave that requires a medium to travel, and therefore cannot travel through a vacuum.
- Mechanical waves are either transverse or longitudinal (eg. sound waves, water waves, waves made on ropes/string/springs and earthquakes).
8
Q
Pulse
A
The single movement of a particle
- The pulse of a sound will be transferred through the air by each individual partice of air undergoing on vibration (backwards and forwards movement).
9
Q
Transverse waves
A
In transverse waves, particles move perpendicular to the motion of the wave.
- The motion of the individual particles in the medium is a temporary displacement of mass, as the particles (and their mass) will return to their starting position after the wave motion has stopped. The crest and trough of a wave are the points of maximum displacement of the particles in the medium.
10
Q
Longitudinal waves
A
In longitudinal waves, particles move parallel to the motion of the wave.
- The areas of compression in the wave are where many particle come together and create regions of higher pressure. The areas of rarefaction in the wave are where many particles spread apart and create regions of lower pressure.
11
Q
Electromagnetic wave
A
An electromagnetic wave is a wave that does not require a medium to travel, and can therefore travel through a vacuum.
- Electromagnetic waves are produced when electrons are made to accelerate, or when electrons change energy levels in an atom.
- Radio waves, microwaves, infrared, ultraviolet, x-rays and gamma rays
- Maximum speed is 3 x 10^8 ms^-1
12
Q
How is energy transferred in a transverse wave?
A
In transverse waves, particles move perpendicular to the motion of the wave. Assuming the wave is moving from left to right, the particle closest to the wave source will be moved up and down, and pull any neighbouring particles with it. As the first particle pulls on its neighbouring particles, it will transfer some of its energy to the particle being pulled. This will cause the first particle to slow down and eventually stop, as the neighbouring particle is being pulled.
In turn, the neighbouring particle will pull on its neighbours and transfer its energy. Because of this, all of the particles will be moving up and down as the wave passes by, and the energy will be transferred between the particles to follow the wave motion.
13
Q
How is energy transferred in a longitudinal wave?
A
In longitudinal waves, particles move parallel to the motion of the wave. Assuming the wave is moving from left to right, the particle closest to the wave source will be pushed from left to right, as region of higher pressure has been created by the source. As the first particle is pushed, it then creates a region of higher pressure next to its neighbouring particles, which pushes those air particles. As the first particle pushes its neighbouring particles, it will transfer some of its energy to the particle being pushed.
In turn, the neighbouring particle will create regions of higher pressure, push on its neghbours and transfer its energy. Because of this, all of the particles will be moving from left to right as the wave passes by, and the energy will be transferred between the particles to follow the wave motion.
14
Q
Wavefronts
A
A wavefront represents the leading edge of one complete wave.
- A ray is the direction of travel of a wave front (drawn as an arrow)
- Wavefronts are at right angles to rays
- Wavefronts must remain parallel, therefore, a wave changes direction as it changes speed entering or leaving a medium.
15
Q
‘In phase’
A
Points along a wave are ‘in phase’ if they undergo similar motion at the same time.
- Points ‘in phase’ are a whole number of wavelengths apart.
- Phase is measured as an angle. ‘In phase’ means a phase difference of 0°.
16
Q
‘Out of phase’
A
Points along a wave are ‘out of phase’ if they move oppositely to each other.
- Points ‘out of phase’ are an odd number of half wavelengths apart.
- Phase is measured as an angle. Exactly ‘out of phase’ means a phase difference of 180°.
17
Q
Calculating phase difference
A
- Determine how far of a wavelength apart the points are as a fraction
(eg. 1/4 of a wavelength) - Multiply the fraction by 360°
(eg. 1/4 x 360° = 90°)
(Therefore, points A and B. have a phase difference of 90°).
18
Q
Reflection and transmission of a pulse
Heavy string to light string
A
Heavy string to light string
- Pulse moves slower along heavy string and faster along the light string.
- A small pulse reflected and the same way up as the original pulse moves back along the heavy string.
- The amplitude will be smaller when reflected due to a decrease in energy (as not all the energy is reflected).
19
Q
Reflection and transmission of a pulse
Light string to heavy string
A
Light string to heavy string
- Pulse moves slower along heavy string and faster along the light string.
- A small pulse reflected and upside down to the original pulse moves back along the light string.
- The amplitude will be smaller when reflected due to a decrease in energy (as not all the energy is reflected).
- As the pulses in the light string are travelling faster, they are further from the boundary when reflected.
20
Q
Light waves
A
The wave model of light describes light as consisting of waves with a very small wavelength and travelling in straight lines from a source with a very large speed.
- When light passes from one medium to another (eg. from air to glass), some light is reflected and some is refracted into the second medium.
- When light passes from one medium to an optically denser one (eg. from air to glass), the speed of the light decreases.
21
Q
Refraction of plane waves at a straight boundary between deep and shallow water
A
- The waves angle of incidence (measured with respect to the normal) θ1 equals the angle that the incident wavefronts make with the boundary.
- The waves angle of refraction θ2 equals the angle that the refracted wavefronts make with the boundary.
- Water waves will change direction at a boundary between deep and shallow water. The waves will slow down as they enter the shallow water which will cause the wavelengths to shorten.
22
Q
Equation for wave refraction
A
1n2 = sin θ1 / sin θ2 = v1 / v2 = λ1 / λ2
Where,
- 1n2 is the relative refractive index (constant)
- v1 / v2 is the ratio of the wave speeds
- λ1 / λ2 is the ratio of the wavelengths
(Note - the frequency of a wave does not change when it is refracted)
23
Q
Wave equation
- For wave velocity
(with time)
A
v = λ/t
Where,
- v is the wave velocity
- λ is the wavelength
- t is the period
24
Q
Diffraction of waves
A
- Diffraction is the process of waves spreading as they pass through a gap
- Maximum diffraction occurs when the wavelength (λ) is approximately equal to the size of the gap.
- The wavelength of a wave does not change when it is diffracted.
eg. Sound waves have a longer wavelength compared to light waves. Because of this longer wavelength, the soundwaves can diffract around barriers through openings (as they are the same order of size as the wavelength of the sound waves). Comparatively, lightwaves cannot diffract as much as sound around barriers. Therefore, often people can hear objects, but not see them.
When waves pass through a gap, the waves are striking the ends of two barriers. The waves which pass through the gap bend behind both barriers.
25
Sound waves
When sound waves reach the ear, they cause the eardrum to vibrate rapidly. The sensation of loudness experienced depends on the intensity of the sound waves that reach the listener's ear.
- The itensity of sound is related to the rate of flow of energy. A louder sound wave has a greater amplitude.
- The pitch of the sound is related to the frequency of the wave.
26
Speed of sound
In air at 0°C, the speed of sound is 331 ms^-1
In water at 20°C, the speed of sound is 1,480ms^-1
- Sound travels slower than light.
27
Superposition
Superposition is the ability of waves to superimpose (add their displacements and their energy) as they move through each other.
(Eg. two rectangular pulses moving in opposite directions can pass through each other so that each pulse remains the same afterwards. The principle of superposition allows the two waves to be 'added' together by adding their displacements together at each instant in time.)
28
Constructive superposition
Constructive superposition is the case where two pulses are the same way up and their displacements add.
29
Deconstructive superposition
Deconstructive superposition is the case where two pulses are inverted with respect to each other and their displacements subtract to give 0.
30
Constructive interference
Areas of constructive inference are darkened areas where trough meets tough, and lightened areas where crest meets crest.
31
Deconstructive interference
Areas of deconstructive inference are areas between lightened and darkened areas of constructive inference where crest meets trough.
- Areas of deconstructive inference are where undisturbed water exists.
32
Interference
Wave interference occurs when two waves meet while travelling along the same medium.
33
Nodal lines
- Nodal lines are undisturbed lines of water.
- Nodes are a half number of wavelengths apart. This means that the waves arrive out of phase and therefore there is destructive interference, creating a node.
34
Antinodal lines
- Antinodal lines are lines of maximum disturbance and wave energy (moving double crests and moving double troughs).
- Antinodes are a whole number of wavelengths apart. This means that the waves arrive in phase and therefore there is constructive interference, creating an antinode.
35
Equation for path difference
| with nodal lines
PS1 - PS2 = (n - 1/2) λ
Where,
- PS1 is the number of lines between source 1 and the point
- PS2 is the number of lines between source 2 and the point
- n is the nodal line number
- λ is the wavelength
Note - Nodal line number is taken from the central dotted line
36
Equation for path difference
| with anti-nodal lines
PS1 - PS2 = nλ
Where,
- PS1 is the number of lines between source 1 and the point
- PS2 is the number of lines between source 2 and the point
- n is the antinodal line number
- λ is the wavelength
Note - Antinodal line number is taken after the central dotted line (middle line = 0)
37
Coherent sources
For interference to occur, light from the same wave must pass each time through both slits, meaning that the two sources must maintain a constant phase relationship. Two sources are coherent if they have the same frequency and have a constant phase relationship.
38
Light
Light is a type of electromagnetic radiation, which is made up of oscillaing electric and magnetic fields which travel together near a speed of 3 x 10^8 ms^-1. This is called the speed of light (c).
- Light is a form of energy. For each colour of light, the brighter the light, the more energy it has.
39
Electromagnetic spectrum
The electromagnetic spectrum includes visible light, as well as other different forms of electromagnetic radiation including radio waves, microwaves, infrared, ultraviolet, x-rays and gamma rays.
40
Straight-line propagation of light
Light travels in straight lines
- When two screens each with a small hole are placed in front of a bulb, the bulb can only be seen if the two holes are in a straight line with the bulb
- If an object is placed between a small source of light and a screen, a sharp shadow is seen on the screen
(eg. pinhole camera - an inverted image of the picture on the tissue paper would be seen. If light didn't travel in a straight line, the image would not be inverted)
41
Illumination of light
Light travels out in all directions from a light source, the further from the light source, the less the illumination.
Illumination is inversely proportional to the distance squared.
E ∝ 1/d^2
Where,
- E is the illumination
- d is the distance from the light source
42
Example of illumination of light
1. Light spreads out in all directions from point P
2. The large square is 2x the distance from the light source than the small square, and the same amount of light falls on both squares.
3. Because each side of the large square is 2x the size of the small square, the large square has 4x the area of the small square.
4. Therefore, the same amount of light illuminates 4x the area, so the light on the large square is only 1/4 as intense as on the small square.
43
Reflection of light
When light reaches a mirror or polished surfce it is reflected. The ray reaching the surface is the incident ray and the ray reflected from the surface is the reflected ray. The normal is the line perpendicular to the surface at the point where the incident and reflected ray meet.
- The angle of incidence (θ1) and the angle of reflection (θ2) are measured from the normal.
44
The laws of reflection
1. The incident ray, reflected ray and normal all lie in the same plane
2. The angle of incidence is equal to the angle of reflection (θ1 = θ2)
45
Irregular reflection and colours
Irregular (diffuse) reflection occurs when light is reflected from a surface in many different directions. Often the reflected light has a different colour from the incident light.
(eg. a red reflecting surface reflects only the red light and absorbs the other colours)
- At each point on a rought surface, light is reflected in such a way that the laws of reflection are followed.
46
Image formed by a plane mirror
- One virtual, upright image is formed.
1. The image appears to be behind the mirror.
This occurs because the position of the image that is seen depends on the direction from which light enters the eye. The light entering the eye is reflected from the mirror and appears to come from behind the mirror. The human eye accepts rays that appear straight entering it, and so the illusion of the image in the mirror is created.
2. The image is the same size as the object and is the same distance directly behind the mirror as it is in front.
This occurs because there is no light at the position of the virtual image. Behind the mirror, at the position of the virtual image it would not be able to be seen. Virtual rays from a virtual image are drawn as dotted lines and do not have arrows on them, as they are not actual rays of light. The virtual image appears to be at the intersection of the two reflected rays.
47
Images fromed by two plane mirrors at 90°
- Three virtual images are formed.
- Two virtual images of the object are each formed by reflections from one mirror only. The third virtual image is formed by reflections from both mirrors.
- If the angle between the mirrors is made less than 90°, more virtual images result.
48
Curved mirrors
- Shading on a mirror symbol indicates the non reflecting side of the mirror.
f = r/2
Where,
f is the focal length (distance between the pole of the mirror and the principal focus)
r is the radius of curvatue (distance between the pole of the mirror and the centre of curvature)
49
Parabolic mirrors
- Due to the parabolic shape (rather than spherical), they can bring a much wider beam which is parallel to the princpal axis into sharper focus than spherical mirrors.
50
Real and virtual images
An image is real if is formed from actual light rays and can be shown on a screen.
- Concave mirrors can produce either real or virtual images, depending on the position of the object.
- Convex mirrors can produce only virtual images, which are always upright and smaller than the object. Virtual images are formed behind the mirror between the principal focus and the mirror.
51
How to draw ray diagrams
1. Draw the principle axis, mirror line, mirror symbol and prinicpal focus.
2. Draw the object as an arrow.
3. Draw the incident ray from the top of the obect to the mirror, parallel to the principal axis. Then draw the reflected ray from the mirror through the principle focus (F).
5. Draw another incident ray from the top of the object through the principle focus (F). Then draw the relflected ray from the mirror, parallel to the principal axis.
6. The top of the image is where the two reflected rays from the top of the object meet. Draw the image as a vertical arrow.
52
Ray diagrams
Ray diagrams can be used to determine the nature of the image, as to wether it is inverted/upright, virtual/real, or englarged/diminished.
- Make sure each of the rays have an arrow to indicate the direction of the ray's travel.
- Make sure the reflections occur at the mirror line, to ensure a true representation of the image.
53
Curved mirror rules
| concave and convex
1. Equal angle rule
A ray that is incident on the pole is reflected at an angle that is equal to the angle of incidence.
2. Centre of curvature rule
A ray that passes through the centre of curvature (C) is reflected back along itself (centre of curvature = 2 x focal length, c = 2f)
54
Wave behaviour
```
- Reflection / Total internal reflection
(bouncing off)
- Refraction
(changing direction)
- Diffraction
(bending around)
- Interference
(add up / cancelling out)
```
55
Images formed in concave mirrors
1. The object is beyond C
An inverted, real and diminished image will be formed.
2. The object is at C
An inverted, real image will be formed, that is the same size as the object.
3. The object is between C & F
An inverted, real and enlarged image will be formed.
4. The object is at F
No image will be formed.
5. The object is in front of F
An upright, virtual and enlarged image will be formed, that is behind the mirror (eg. dentist mirror).
56
Negative signs for curves mirrors
- If di is behind the mirror, it is negative
- hi for a virtual image is negative
- f for a convex (diverging) mirror is negative
57
Refraction
- Rays of light from (the bottom of the pool) are refracted (bent) before reaching a persons eye
- Refraction is the change in speed of a light wave as it travels from one medium into another, causing it to change direction.
- When light travels into a medium of greater density, it refracts towards the normal as the medium of higher density has a higher refractive index.
- When light travels into a medium of less density, it defracts away from the normal as the medium of less density has a lower refractive index.
- Our brain makes us think that the rays are coming straight back from where they are, extended backwards, and this makes the object appear nearer to the surface of the water than it really is.
58
When refraction occurs..
The frequency (f) of the wave does not change when crossing the boundary, as the frequency of the wave is determined by whatever produces the wave. With this knowledge, by applying the wave equation v = fλ we can see that a change in speed (v), will be proportional to a change in wavelength (λ). Therefore, as the frequency remains constant, as the speed (v) increases, the wavelength (λ) will increase also.
59
Refractive index
If two different mediums (water/air/glass) have different refractive indices, light will refract differently at the boundary between them.
60
Special case of refraction through a block of material with parallel faces
When a light ray passes through a block of material with parallel faces, the light ray emerging from the block is parallel to the incident ray, but is displaced sideways by a distance (d).
61
Critical angle
- When light travels from one medium to another which is optically less dense, the angle of incidence (θ1) is less than the angle of refraction (θ2) and therefore light bends away from the normal. When this occurs, it is possible to have an angle of refraction (θ2) of 90°. The critical angle is the angle of incidence (θ1), when the angle of refraction is 90°.
62
Total internal reflection
- When rays of light at a very large angle of incidence hit the cold/hot air interface, the angle of incidence in greater than the critical angle, which causes all the light rays to reflected, undergoing total internal reflection to occur.
For total internal reflection to occur...
- The angle of incidence has to be greater than the
critical angle.
- Light ray must be travelling from a medium of a higher refractive index (optical density) to one of
lower refractive index.
63
Equation for critical angle
sinθc = n2 sin90°/n1
Where,
- θc is the critical angle
- n2 is the absolute refractive indices for medium 2
- n1 is the absolute refractive indices for medium 1
64
Dispersion
(Refraction by prisms)
- The beam of light that emerges from a prism diverges and spreads out more than the incident beam. If white light is used, the light that emerges can be seen as a spectrum of colours. Red deviates the least, and violent deviates the most (violet light has a short wavelength, meaning that it travels more slowly through a medium then light that has a long wavelength, meaning that it travels more quickly).
- The spectrum of colours forms because a material such as glass has a slightly different refractive indices for each of the different colours.
- The spreading out of light into a spectrum is called dispersion. Dispersion occurs at the first boundary (from air to glass) and at the second boundary (from glass to air)
65
Total internal reflection in prisms
Prisms can be used as high-quality mirrors to reflect light in optical instruments. Little dispersion occurs, because the rays enter and leave each prism at right angles. The light reflects inside the prism by total internal reflection. The incident angle on the surface inside the prism is 45°, which is greater than the critical angle for total internal reflection.
66
Converging lenses
(convex lenses)
The principal axis of a lens is the line joining the centres of curvature of its surfaces.
Converging lenses cause parallel light rays passing through them to converge. A ray of light, parallel to the principal axis, will converge to the principal focus (F), on the axis behind the lense.
67
Diverging lenses
(concave lenses)
The principal axis of a lens is the line joining the centres of curvature of its surfaces.
Diverging lenses causes parallel light rays passing through them to diverge. A ray of light, parallel to the principal axis will spread out as if it is diverging from the principal focus (F), on the axis in front of the lense.
68
Lenses
- Rays passing through the centre of a lense (optical centre (O)), are not deviated and go straight through the centre of a lens in a straight line.
- A lense has two principal foci on each side, that are at equal distances from the centre of the lens.
- The focal length (f) of a lens is the distance between the optical centre and a principal focus.
69
Images formed in convex mirrors
Regardless of the position of the object, the image will always be virtual, upright and diminished. The image is located behind the mirror by tracing the rays back to where they appear to come from.
70
Images formed by convex lenses
(Same as images formed in concave mirrors)
1. The object is beyond C
An inverted, real and diminished image will be formed.
2. The object is at C
An inverted, real image will be formed, that is the same size as the object.
3. The object is between C & F
An inverted, real and enlarged image will be formed.
4. The object is at F
No image will be formed.
5. The object is in front of F
An upright, virtual and enlarged image will be formed, that is located on the object's side of the lens.
71
Images formed by concave lenses
Regardless of the position of the object, the image will always be virtual, upright and diminished. The image is located on the object's side of the lens by tracing the rays back to where they appear to come from.
72
Wavefronts eg.
Wavefronts travel outwards from a point source (s) and form concentric circles.
- As time passes, each wave travels further out, while new wavefronts are generated and move out from the point source. At points far away from the source, wavefronts become nearly straight.
- Straight wave fronts can be made to converge to a focus or diverge from a focus using appropriately shaped regions of shallow water.
73
Why will an object within the focal length of a convex lense not show an image on film?
- When an object is inside the focal point, the image produce is virtual and therefore cannot be projected on the film. This is because the rays diverge when passing through the lense and do not meet/focus on the film so no picture will be formed.
74
Find if point x is a node or antinode
1. Calculate the frequency (f = 1/T)
2. Calculate the wavelength (v = fλ)
3. Calculate the path difference (distance to point x from 1 opening - distance to point x from other opening)
4. Divide the path difference by the wavelength
5. If the result is half a wavelength, point x must be a node. If the result is a whole wavelength, point x must be an antinode.
75
Sound heard walking past two speakers
The person walking in a straight line closer to the speakers will hear the loud and soft sounds at shorter distances as compared to the person walking in a straight line further away. This is because the anitnodal lines fan out from the speakers, and therefore the further away one is from the speakers, the further apart the loud and soft wounds will be.
- Louder sound is heard where waves from two sources constructively interfere, because the path difference between the two sound waves is nλ, so the total amplitude of the resultant wave increases, creating a louder sound.
- Quieter sound is heard where waves from two sources deconstructively interfere, because the path difference between the two sound waves is 1/2λ, so the total amplitude of the resultant wave decreases, creating a quieter sound.
76
Light shining through two slits and producing a pattern of multiple slits.
- Bright bands are due to constructive interference, which are regions where the crest of one wave
combines with the crest of another. The path
difference is either zero (central band) or a whole
number of wavelengths.
- Dark bands are due to destructive interference,
which are regions where the crest of one wave combines with the
trough of another wave. The path difference is
either half a wavelength or an odd mulitiple of half
wavelengths.
77
Distinguishing between real and virtual images
- A real image occurs where rays converge, whereas a virtual image occurs where rays only appear to converge.
- A virtual image is upright, and cannot be projected onto a screen.
- A real image is inverted, and can be projected onto a screen.
78
Difference between images produced in concave/convex mirrors (between f and c)
- The image formed by the convex mirror is upright, diminished and virtual.
- Convex mirrors are diverging mirrors, which means that no real light rays intersect on the same side of the mirror as the light source. This means all images in a convex mirror are virtual. All virtual images are upright and diminished.
- The image formed by the convex mirror is diminished because virtual light rays travel less before they appear to meet.
- The image formed by the concave mirror is inverted, enlarged and real.
- Concave mirrors are converging mirrors, which means that real light rays will intersect (if the object is beyond the focal point), creating a real image which is inverted and enlarged.
- The image formed by the concave mirror is enlarged because real reflected light rays travel longer before they meet. The largest image will be produced when the distance of the object is as close to f as possible. As this position, the reflected rays are nearly parallel, causing a large di and hi.
79
Distance of an object away from a concave mirror
- Distance will be negative, as image formed is virtual
- The image has been magnified 3x, so the image distance is 3x the object distance from the mirror
- Therefore, di = -3do
- Substitute values into 1/f = 1/do + 1/di
80
What changes could be made to a convex lense to produce an enlarged and upright image?
1. Move the lens closer to the object so that it lies within the focal length of the lens to produce a virtual, enlarged and upright image.
2. Use a thinner/less curved lens with a larger radius of curvature, so that the object lies within the focal length.
3. Decrease the refractive index of the glass so its focal length increases, so that the object lies within the focal length.
Science
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Mechanics66
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Electricity and Electromagnetism43
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Waves80
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Combined decks59
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3.4 Mechanics75
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Waves - Level 332
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Modern Physics Internal - Explanations - Level 348
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Electrical Systems - Formula - Level 376
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Modern Physics - Formula - Level 345
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Modern Physics - Definitions - Level 333
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Electrical Systems - Explanations - Level 363
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Electrical Systems - Definitions - Level 375
