Superposition Flashcards
What is superposition?
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
What is a requirement for superposition of transverse waves?
the two waves share the same axis of polarisation
What is interference?
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
What does it mean by two waves are in anti-phase?
- phase difference is in odd integer multiples of π radians
- eg. π, 3π, 5π
What happens when two waves are in anti-phase?
- 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)
When does destructive interference occur?
- occurs at a point when resultant displacement is smaller than the largest individual displacement at that point
- two waves not necessarily in anti-phase
What is the difference between destructive interference and anti-phase?
- extent is different
- anti-phase is like complete destructive interference
What does it mean when two waves are in phase?
- no phase difference between them
- phase difference = 0 or integer multiple of 2π
What happens when two waves are in phase?
- perfect addition of signal takes place
- crest of one wave meets crest of another wave
- maximum net displacement
When does constructive interference occur?
- occurs at a point when resultant displacement is larger than individual displacement at that point
- two waves not necessarily in phase
What is the difference between constructive interference and in phase?
- extent is different
- in phase is like complete constructive interference
What is diffraction?
Diffraction is the spreading of waves into its geometric shadow after passing through a slit/gap/aperture or obstacle
When does diffraction effect become prominent?
When size/width of the slit/edge is comparable to the incident wavelength
What are coherent sources?
- 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
Does same frequency between two sources imply coherence?
If speed of a wave changes (when medium changes), wavelength changes and phase difference will be non-constant when waves meet at a point
Can two different light sources make coherent sources?
- No
- two different light sources of same frequency/colour are incoherent because they have random emission of light pulses with random phase angles
What happens when there are two incoherent waves?
- 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
When is interference pattern observable?
- 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
If two sources are in phase with path difference of nλ what is the result at a point?
- waves in phase
- constructive interference
(think of path diff like a function, when you input what phase with nλ, the output is the same)
If two sources are in anti-phase with path difference of nλ what is the result at a point?
- waves in antiphase
- destructive interference
(think of path diff like a function, when you input what phase with nλ, the output is the same)
If two sources are in phase with path difference of (n+0.5)λ what is the result at a point?
- 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)
If two sources are in antiphase with path difference of (n+0.5)λ what is the result at a point?
- 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)
What are anti-nodal lines?
maximum amplitude due to constructive interference
What are nodal lines?
minimum amplitude lines due to destructive interference
What does water waves with interference look like?
- straight line for zeroth order
- higher order maxima and minima gets curvy
What does intensity look like for water waves with interference?
- central maxima (0th order) has highest intensity
- intensity decreases with increasing order of maxima/minima
- intensity is inversely proportional to distance square
What does two source interference of sound look like?
- 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)
In reality does two source interference of sound occur?
No as amplitude of sound waves decreases with distance so imperfect constructive and destructive interference occur
When is maxima obtained?
When waves meet in phase
When is minima obtained?
When waves meet in anti-phase
What are stationary waves?
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
What are the characteristics of stationary wave?
- wave profile does not propagate
- each particle oscillates with the same frequency but different amplitudes
- within two consecutive nodes, every particle oscillates in phase
What is antinode?
- Point where amplitude is maximum
- amplitude is double than that of component waves
What is node?
amplitude is zero
What is the difference between stationary wave and progressive wave in their amplitude?
- 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
What is the wavelength of stationary wave?
twice distance between successive nodes or successive antinodes
What is the difference in wavelengths between stationary and progressive waves?
- Stationary wave: twice the distance between successive nodes or antinodes
- Progressive wave: distance between two adjacent points which are in same phase
What is the difference in frequency for stationary waves and progressive waves?
- 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
What is the difference for phase for stationary wave and progressive wave?
- Stationary wave: all points within 2 adjacent nodes oscillate in phase
- Progressive wave: all points within one wavelength has different phase
What is the difference in waveform for stationary wave and progressive wave?
- Stationary wave: waveform does not move
- Progressive wave: waveform moves in the direction of wave propagation
What is the difference in energy between stationary and progressive wave?
- Stationary wave does not transport energy
- Progressive wave transports energy
How do stationary waves form?
- 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
What are the conditions necessary for the formation of stationary wave?
- 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
What is the difference between nodes and antinodes of a stationary wave?
- 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
What is the difference between stationary wave and progressive wave?
- 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
What is the speed of a stationary wave?
Speed of individual progessive waves that form the stationary wave
How to make stationary waves from stretched strings?
- 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
What does stationary wave pattern of stretched string look like?
- 1st harmonic fundamental: L = λ/2
- nth harmonic: L = n(λ/2)
How do stationary wave form in Kundt’s tube?
- 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
What is pressure antinode and when does it occur?
- during rarefaction when there is minimum pressure
- occur at displacement node
What is pressure node and when does it occur?
- during compression where there is maximum pressure
- displacement antinode
What is the effect of decreasing wavelength on interference pattern (what you can see on the screen)?
- X decreases
- see more number of bright and dark fringes on the screen
What is the effect of decreasing slit opening on interference pattern (what you see on screen)?
- increase X
- less number of bright or dark fringes
What is the effect of decreasing D on interference pattern (what you see on screen)?
- X decrease
- greater contast: bright fringe gets brighter
- I = P/4πr², when r (D) decreases, I increases
What is the effect on interference pattern when double slit is brought closer to the source?
I increases, greater contrast of bright and dark fringes
What is the effect on interference pattern for increasing the slit width for the source (single slit)?
I increases, greater constrast of bright and dark fringes
What is the effect of a slanted screen on interference pattern?
- 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)
What is the effect on interference pattern when one object is used to block one slit in double slit experiment?
change to single slit interference pattern
What is the effect of blocking slit opening with glass on interference pattern?
interference pattern shift upwards
(if glass blocks the top slit)
What is the effect on interference pattern when white light is used instead of monochromatic light?
- splitting of different colours
- central is white then violet then blue then green, all the way until the two sides are red
What is resolving power?
Ability of the instrument to differentiate clearly between the images of two closed object
What is Rayleigh’s criterion?
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
What is α for resolving power?
- 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)
What is the relationship between α and θₘᵢₙ when the pattern is well resolved?
α > θₘᵢₙ
What is the relationship between α and θₘᵢₙ when the pattern is just resolved?
α = θₘᵢₙ
What is the relationship between α and θₘᵢₙ when the pattern is no resolved?
α < θₘᵢₙ
What are the conditions for observable two-source interference fringes?
- waves meet at a point
- coherent sources
- equal or approximately equal amplitudes
- polarised in the same plane
Why must two waves meet at a point for observable two-source interference fringes?
waves must meet first in order to have interference
Why must there be coherent sources for observable two-source interference fringes?
so that observable interference pattern can be obtained
Why must two waves have equal or approximately same amplitudes for observable two-source interference fringes?
so that complete or almost complete cancellation is achieved at points of destructive interference
Why must two waves be polarised in the same plane or unpolarised for observable two-source interference fringes?
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
