12 Superposition

Question 1

Principle of Superposition

Answer 1

When two or more waves of the same type, meet at a point in space, the resultant displacement of the waves at any point is the vector sum of the displacements due to each wave acting independently at that point

Question 2

Stationary waves

Answer 2

Waves whose waveform does not advance and there is no translation of energy. The amplitude of the waves varies according to position from zero at the nodes to a maximum at the antinodes

Question 3

Requirements for a stationary wave to form

Answer 3

• Two progressive waves of same frequency and same speed
• Travelling in opposite directions towards one another
• Having similar or identical amplitudes
• Unpolarised OR polarised along the same axis

Question 4

Soft boundary

Answer 4

Reflected wave will not be inverted

Question 5

Hard boundary

Answer 5

Reflected wave will be inverted

Question 6

Characteristics of a stationary wave

Answer 6

• Waveform does not move/no net energy
• Certain points do not oscillate
• Distance between adjacent nodes = Distance between adjacent antinodes = λ/2

Question 7

Node

Answer 7

Points that do not oscillate in a stationary wave

Question 8

Antinodes

Answer 8

Points that have the largest amplitude

Question 9

Relationship between pressure and displacement nodes in longitudinal stationary waves

Answer 9

Pressure nodes coincide with displacement antinodes
Pressure antinodes coincide with displacement nodes

Question 10

Fundamental frequency of a stationary wave in a string

Answer 10

f = v/2L
Where L is the length of the string

Question 11

Closed end of a pipe is the displacement [ ]

Answer 11

node

Question 12

Open end of a pipe is the displacement [ ]

Answer 12

antinode

Question 13

Fundamental frequency of a stationary wave in an open pipe

Answer 13

f = v/2L

Question 14

Fundamental frequency of a stationary wave in a closed pipe

Answer 14

f = v/4L

Question 15

End Correction

Answer 15

The pressure node in an open end is slightly outside the tube

Question 16

Diffraction

Answer 16

The bending or spreading out of waves when they travel through a small opening or when they pass round a small obstacle.

Question 17

Position of minima for single slit diffraction

Answer 17

sinθ = m (λ / b)

Question 18

Rayleigh criterion

Answer 18

When the centre of the diffraction pattern of an image is directly over the first minimum of the diffraction pattern of the other image
θ ≈ λ / b

Question 19

Coherence

Answer 19

Sources are coherent if they have a constant phase difference with respect to time

Question 20

Conditions for observable two-source interference pattern

Answer 20

1. Waves must overlap to produce regions of maxima and minima
2. Sources must be coherent
3. Waves must have the same/approximately the same amplitude
4. Waves must be unpolarised or have the same plane of polarisation

Question 21

Fringe separation for double slit interference

Answer 21

λ = ax / D
(where x is the fringe separation)

Question 22

Positions for constructive interference for diffraction grating

Answer 22

d sinθ = nλ
d =1/N (where d is distance between slits and N is number of slits per metre)

Question 23

Progressive wave

Answer 23

A wave which carries energy from one point to another by means of vibrations or oscillations within the wave

Question 24

Interference

Answer 24

Superposing of two or more coherent waves to produce regions of maxima and minima in space, according to the principle of superposition

Question 25

Constructive interference

Answer 25

The interference that occurs when two or more waves meet at a point such that the resultant displacement is greater than the largest individual displacement

Question 26

Destructive interference

Answer 26

The interference that occurs when two or more waves meet at a point such that the resultant displacement is less than the largest individual displacement