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Superposition Flashcards

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1
Q

What is superposition?

A

When two or more waves of the same type meet, the resultant displacement at a point is the vector sum of the displacements due to each individual waves at that point

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2
Q

What is a requirement for superposition of transverse waves?

A

the two waves share the same axis of polarisation

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3
Q

What is interference?

A

It is the superposing of two or more waves of the same kind, forming new wave whose resultant amplitude is the sum of displacement of each wave

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4
Q

What does it mean by two waves are in anti-phase?

A
  • phase difference is in odd integer multiples of π radians
  • eg. π, 3π, 5π
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5
Q

What happens when two waves are in anti-phase?

A
  • perfect cancellation of signal takes place
  • troughs of one wave meet crest of the other wave
  • zero net displacement (eg. horizontal line for resultant displacement)
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6
Q

When does destructive interference occur?

A
  • occurs at a point when resultant displacement is smaller than the largest individual displacement at that point
  • two waves not necessarily in anti-phase
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7
Q

What is the difference between destructive interference and anti-phase?

A
  • extent is different
  • anti-phase is like complete destructive interference
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8
Q

What does it mean when two waves are in phase?

A
  • no phase difference between them
  • phase difference = 0 or integer multiple of 2π
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9
Q

What happens when two waves are in phase?

A
  • perfect addition of signal takes place
  • crest of one wave meets crest of another wave
  • maximum net displacement
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10
Q

When does constructive interference occur?

A
  • occurs at a point when resultant displacement is larger than individual displacement at that point
  • two waves not necessarily in phase
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11
Q

What is the difference between constructive interference and in phase?

A
  • extent is different
  • in phase is like complete constructive interference
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12
Q

What is diffraction?

A

Diffraction is the spreading of waves into its geometric shadow after passing through a slit/gap/aperture or obstacle

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13
Q

When does diffraction effect become prominent?

A

When size/width of the slit/edge is comparable to the incident wavelength

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14
Q

What are coherent sources?

A
  • Coherent sources are signal sources that could maintain constant phase difference between them and does not vary with time
  • implies that waves are of same frequency, wavelength and speed
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15
Q

Does same frequency between two sources imply coherence?

A

If speed of a wave changes (when medium changes), wavelength changes and phase difference will be non-constant when waves meet at a point

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16
Q

Can two different light sources make coherent sources?

A
  • No
  • two different light sources of same frequency/colour are incoherent because they have random emission of light pulses with random phase angles
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17
Q

What happens when there are two incoherent waves?

A
  • does not meet constructively or destructively at a point (meaning that at one instant and can constructive at another instant can be destructive)
  • does not give rise to permanent maximum or minimum
  • no interference pattern is observable
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18
Q

When is interference pattern observable?

A
  • waves must meet
  • wave must be of same type
  • amplitude of waves are similar
  • sources are coherent to maintain constant phase difference
  • waves must be of same frequency/wavelength and speed
  • for transverse wave, waves must have same plane of polarisation or both waves are unpolarised
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19
Q

If two sources are in phase with path difference of nλ what is the result at a point?

A
  • waves in phase
  • constructive interference

(think of path diff like a function, when you input what phase with nλ, the output is the same)

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20
Q

If two sources are in anti-phase with path difference of nλ what is the result at a point?

A
  • waves in antiphase
  • destructive interference

(think of path diff like a function, when you input what phase with nλ, the output is the same)

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21
Q

If two sources are in phase with path difference of (n+0.5)λ what is the result at a point?

A
  • in antiphase
  • destructive interference

(think of path diff like an inverse function, when you input what phase with (n+0.5)λ, the output is the opposite)

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22
Q

If two sources are in antiphase with path difference of (n+0.5)λ what is the result at a point?

A
  • in phase
  • constructive interference

(think of path diff like an inverse function, when you input what phase with (n+0.5)λ, the output is the opposite)

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23
Q

What are anti-nodal lines?

A

maximum amplitude due to constructive interference

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24
Q

What are nodal lines?

A

minimum amplitude lines due to destructive interference

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25
Q

What does water waves with interference look like?

A
  • straight line for zeroth order
  • higher order maxima and minima gets curvy
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26
Q

What does intensity look like for water waves with interference?

A
  • central maxima (0th order) has highest intensity
  • intensity decreases with increasing order of maxima/minima
  • intensity is inversely proportional to distance square
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27
Q

What does two source interference of sound look like?

A
  • if two source are in phase the central maxima is loud, then alternate between no sound and loud
  • if two source in anti-phase then central maxima is no sound, then alternate between loud and no sound (opposite)
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28
Q

In reality does two source interference of sound occur?

A

No as amplitude of sound waves decreases with distance so imperfect constructive and destructive interference occur

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29
Q

When is maxima obtained?

A

When waves meet in phase

30
Q

When is minima obtained?

A

When waves meet in anti-phase

31
Q

What are stationary waves?

A

Result of interference between two progressive waves of equal frequency and similar amplitude, travelling along the same line with same speed but in opposite directions

32
Q

What are the characteristics of stationary wave?

A
  • wave profile does not propagate
  • each particle oscillates with the same frequency but different amplitudes
  • within two consecutive nodes, every particle oscillates in phase
33
Q

What is antinode?

A
  • Point where amplitude is maximum
  • amplitude is double than that of component waves
34
Q

What is node?

A

amplitude is zero

35
Q

What is the difference between stationary wave and progressive wave in their amplitude?

A
  • Stationary wave: amplitude varies from maximum at antinodes to zero at nodes, all points between adjacent nodes and antinodes have different amplitude
  • Progressive wave: all points have same amplitude
36
Q

What is the wavelength of stationary wave?

A

twice distance between successive nodes or successive antinodes

37
Q

What is the difference in wavelengths between stationary and progressive waves?

A
  • Stationary wave: twice the distance between successive nodes or antinodes
  • Progressive wave: distance between two adjacent points which are in same phase
38
Q

What is the difference in frequency for stationary waves and progressive waves?

A
  • Stationary waves: all points oscillate in SHM at the same frequency of the wave except points at the nodes which do not oscillate
  • Progressive wave: all points oscillate in SHM at same frequency of the wave
38
Q

What is the difference for phase for stationary wave and progressive wave?

A
  • Stationary wave: all points within 2 adjacent nodes oscillate in phase
  • Progressive wave: all points within one wavelength has different phase
39
Q

What is the difference in waveform for stationary wave and progressive wave?

A
  • Stationary wave: waveform does not move
  • Progressive wave: waveform moves in the direction of wave propagation
39
Q

What is the difference in energy between stationary and progressive wave?

A
  • Stationary wave does not transport energy
  • Progressive wave transports energy
40
Q

How do stationary waves form?

A
  • two progressive waves of similar amplitude, same frequency and speed, travelling in opposite directions meet
  • resultant displacement is the sum of displacements of each waves, producing alternating nodes and antinodes
40
Q

What are the conditions necessary for the formation of stationary wave?

A
  • two progressive waves of similar amplitude, same frequency/wavelength and speed of or coherent, same type, moving in opposite directions meet at a point
  • for transverse waves, the waves are either both unpolarised or both share the same axis of polarisation
41
Q

What is the difference between nodes and antinodes of a stationary wave?

A
  • nodes are points on a stationary wave where the amplitude of vibration is zero or a minimum
  • antinodes are points on a stationary wave where the amplitude of vibration is maximum
42
Q

What is the difference between stationary wave and progressive wave?

A
  • energy is stored and not transported in stationary waves while progressive waves transport energy from one point to another
  • for stationary waves, amplitude of vibration varies from maximum at antinodes to minimum/zero at nodes whereas in progressive waves, all points have same amplitude
  • adjacent particles are in phase for stationary waves but are out of phase for progressive waves
  • waveform advances in progressive waves but not in stationary wave
43
Q

What is the speed of a stationary wave?

A

Speed of individual progessive waves that form the stationary wave

44
Q

How to make stationary waves from stretched strings?

A
  • string is made to oscillate with a vibrator connected to signal generator
  • waves is adjusted by changing the tension in the string using varying weights, alter the length from vibrator to pulley or alter frequency of generator
  • when frequency of signal generator matches natural frequency of string, a stationary wave is formed
45
Q

What does stationary wave pattern of stretched string look like?

A
  • 1st harmonic fundamental: L = λ/2
  • nth harmonic: L = n(λ/2)
46
Q

How do stationary wave form in Kundt’s tube?

A
  • incident waves are reflected at closed ends and phase inversion of π rad occurs
  • Length of tube, L = odd multiples of a quarter wavelength
  • since incident and reflected waves are of similar amplitude, same frequency/wavelength and speed and travels in opposite directions, a regular spaced displacment nodes and antinodes will be formed
  • heaps of powder gather at nodes due to destructive interference
47
Q

What is pressure antinode and when does it occur?

A
  • during rarefaction when there is minimum pressure
  • occur at displacement node
48
Q

What is pressure node and when does it occur?

A
  • during compression where there is maximum pressure
  • displacement antinode
49
Q

What is the effect of decreasing wavelength on interference pattern (what you can see on the screen)?

A
  • X decreases
  • see more number of bright and dark fringes on the screen
50
Q

What is the effect of decreasing slit opening on interference pattern (what you see on screen)?

A
  • increase X
  • less number of bright or dark fringes
51
Q

What is the effect of decreasing D on interference pattern (what you see on screen)?

A
  • X decrease
  • greater contast: bright fringe gets brighter
  • I = P/4πr², when r (D) decreases, I increases
52
Q

What is the effect on interference pattern when double slit is brought closer to the source?

A

I increases, greater contrast of bright and dark fringes

53
Q

What is the effect on interference pattern for increasing the slit width for the source (single slit)?

A

I increases, greater constrast of bright and dark fringes

54
Q

What is the effect of a slanted screen on interference pattern?

A
  • fringe separation increases as the screen is increasingly further away
  • intensity and constrast decreases as the screen gets further away

(diff depend on how it slant)

55
Q

What is the effect on interference pattern when one object is used to block one slit in double slit experiment?

A

change to single slit interference pattern

56
Q

What is the effect of blocking slit opening with glass on interference pattern?

A

interference pattern shift upwards

(if glass blocks the top slit)

56
Q

What is the effect on interference pattern when white light is used instead of monochromatic light?

A
  • splitting of different colours
  • central is white then violet then blue then green, all the way until the two sides are red
57
Q

What is resolving power?

A

Ability of the instrument to differentiate clearly between the images of two closed object

58
Q

What is Rayleigh’s criterion?

A

two images are just resolvable when the central maxima of one diffraction pattern is directly over the first minima of another diffraction pattern

θₘᵢₙ = λ/a

(angle between two

58
Q

What is α for resolving power?

A
  • angle between two sources
  • α = X/D = s/r
  • s: distance between sources

(think of math formula θ = s/r but not to be confused about with θₘᵢₙ)

59
Q

What is the relationship between α and θₘᵢₙ when the pattern is well resolved?

A

α > θₘᵢₙ

60
Q

What is the relationship between α and θₘᵢₙ when the pattern is just resolved?

A

α = θₘᵢₙ

61
Q

What is the relationship between α and θₘᵢₙ when the pattern is no resolved?

A

α < θₘᵢₙ

62
Q

What are the conditions for observable two-source interference fringes?

A
  1. waves meet at a point
  2. coherent sources
  3. equal or approximately equal amplitudes
  4. polarised in the same plane
63
Q

Why must two waves meet at a point for observable two-source interference fringes?

A

waves must meet first in order to have interference

64
Q

Why must there be coherent sources for observable two-source interference fringes?

A

so that observable interference pattern can be obtained

65
Q

Why must two waves have equal or approximately same amplitudes for observable two-source interference fringes?

A

so that complete or almost complete cancellation is achieved at points of destructive interference

66
Q

Why must two waves be polarised in the same plane or unpolarised for observable two-source interference fringes?

A

if the waves are not polarised in the same plane, then complete cancellation is not possible even at points where the two waves are completely out of phase

Physics (19 decks)

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