Superposition

Question 1

State 2 conditions which are necessary for waves T1 and T2 to interfere

Answer 1

1. The waves must be of the same kind

2. The waves must overlap be at the same place at the same time

Question 2

conditions for 2 waves to produce an observable / well defined interference pattern ?

Answer 2

SEE CONTEXT

1. coherent (constant phase difference and same frequency wrt to each other)
   - DOES NOT IMPLY THAT THEY ARE IN PHASE JS CONSTANT DIFF
2. waves emitted roughly same amplitude
3. transverse waves (light ONLY not water) must be unpolarized / be polarised in the same direction
4. same type of wave
5. The two waves must overlap

Question 3

show how the principle of super position can be used to explain the formation of 2 source interference fringes

Answer 3

Waves from two sources can overlap and interfere. The resultant displacement at any point at any instant is the vector sum of the individual displacements caused by
each wave.

At positions where the two waves arrive in phase, constructive interference occurs, resulting in high-intensity fringes.

At positions where the two waves arrive out of phase, destructive interference occurs, resulting in zero-intensity fringes.

Question 4

why in practice, interference fringes can only be seen if light from a single source is split into two ?

Answer 4

Light waves from two independent light sources are not coherent, and the phase difference between them changes rapidly and randomly. Thus, the resultant fringe pattern would also change rapidly – too fast for the human eye to follow. By using light from a narrow region of a single source and splitting the light into two, we have effectively two coherent sources, which will produce stable interference fringes that can be seen.

Question 5

what is the principle of superposition

Answer 5

When two or more waves of the same type meet/superpose {NOT: superimpose} at a point, the resultant displacement {NOT: amplitude} of the waves is equal to the vector sum of their individual displacements at that point.

Question 6

what does interference mean ?

Answer 6

Interference refers to the superposition of coherent waves which results in a change in the overall intensity.

Question 7

Diffraction of (light)

Answer 7

refers to the spreading [bending] of (light) waves when they pass through an opening [gap], or round an obstacle into the “geometrical shadow” region.
(For significant diffraction to occur, the size of the gap approx wavelength of wave)

Question 8

grating vs young double slit

Answer 8

fringes sharper and positions more precisely determined, less uncertainty in computing wavelength

angular displacement larger so percentage uncertainty decreases

Question 9

using higher orders to determine wavelength (ad and dis)

Answer 9

ad : angular displacement theta larger so less percentage uncertainty in measuring angle
dis :
1. dimmer (less bright) than 1st order fringe
2. higher order spectra tend to overlap causing difficulty in measurements

Question 10

Phase difference between the 2 waves (from the double slit) at any point X (on the screen), lying between the central maximum & the 1st maximum, is (approximately) proportional to the distance between X and the central maximum

Path difference - dependent on phase difference of source while phase diff is independent of phase diff at source

Answer 10

Using 2 waves of equal amplitude xo, the resultant amplitude of the central bright fringe is doubled {2xo}.
Also the resultant intensity increases by 4 times {not 2}

Question 11

assumptions for young double slit formula , fringe separation and positions for dark and bright fringes

Answer 11

see notes

Question 12

what does it mean when images are just resolved

Answer 12

Two images are said to be just resolved snd can be distinguished when the central maximum of one image falls on the first minimum of the second image.

Question 13

what are nodes and antinodes ?

Answer 13

Node: a region of destructive superposition where the waves always meet out of phase by pi radians. Hence displacement here is permanently zero {or minimum}

Antinode: a region of constructive superposition where the waves always meet in phase. Hence a particle here vibrates with maximum amplitude. {but it is NOT a point with a permanent large displacement! J08P2Q5b, 1m}

Question 14

what are stationary waves and how are they formed ?

what are progressive waves ?

Answer 14

Stationary (standing) wave is one
 whose waveform/wave profile does not advance /move,
 where there is no net transport of energy,
 where the positions of antinodes and nodes do not change, or where there are certain points which are permanently at rest

A stationary wave is formed when two progressive waves of the same frequency, amplitude and speed, travelling in opposite directions are superposed. (NOT SUPERIMPOSED)

speed calculated is the speed of the incident and reflected progressive waves

A progressive wave is a propagation of vibrations or oscillations, transferring energy or momentum in the
direction of wave propagation.

Question 15

a car with its 2 headlights switched on is approaching an observer, why at long distance from observer the images of headlights blur / not resolved

Answer 15

The light diffracts after passing through the pupil of the eye

Each headlight produces a diffraction pattern in the eye

As the distance from the observer increases, the angular separation between the two headlights decreases, and the two diffraction patterns begin to overlap

If the distance is far enough, the diffraction patterns overlaps almost completely and cannot be distinguished or resolved.

Question 16

changes to diffraction pattern when longer wavelengths are used

Answer 16

When visible light of a longer wavelength is used, the central maximum of the observed diffraction pattern will become broader as the light will spread more (i.e. more diffraction) when pass through the single slit. As sin θ = λ / b, where θ is the angle subtended from the central maximum to the first minimum of the diffraction pattern, λ is wavelength of light and b is the slit width, when the wavelength of light increases, θ will increase.

Question 17

when white light is incident on a single slit, the centra fringe is coloured at the edges and have a white central region. Explain

Answer 17

The amount of spreading (or diffraction) of light is dependent on the wavelength.

When white light, consists of different wavelengths, is incident on a single slit, the different wavelengths of light overlap at the central region giving white light. At the
edges, the different wavelengths of light (which gives white light when overlap) spread by different amount and land on different parts of the screen, not overlapping.
Thus the edges is coloured.

Question 18

pressure changes in nodes and antinodes

Answer 18

maximum pressure change occurs at the nodes {NOT at the antinodes} because every node changes from a point of compression to become a point of rarefaction half a period later and is a pressure antinode
At antinodes, there is no variation in pressure and is a pressure node

Question 19

why a stationary wave is observed on the string only at particular frequencies of vibration of the plate

Answer 19

The stationary wave is observed only when the driver frequency of the oscillating plate f matches the natural frequencies of the string (resonance). Given that both ends of the strings must be nodes, and the wave speed v is fixed, the length of the string L must be integral multiples of half a wavelength: v = f λ and L = n (0.5λ), n = 1, 2, 3… (HALF BECAUSE BOTH ENDS NODES AND HALF A WAVELENGTH CORRESPONDS TO NAN