Superposition

Question 1

State the principle of superposition

Answer 1

when two or more waves of the same kind meet, the resultant displacement at any point is the vector sum of the displacements of the individual waves at that point

Question 2

resultant displacement of a wave is

Answer 2

the vector sum of the displacements due to each individual wave

Question 3

Explain how a stationary wave is formed (different from the conditions required for stationary waves)

Answer 3

Incident waves from the source get reflected at the fixed ends

a stationary wave is formed by the superposition of the incident and reflected waves of the same frequency, wavelength and speed, travelling in opposite directions

Question 4

What is a transverse wave

Answer 4

A wave in which the vibration of the particles are perpendicular to the direction of travel of wave energy

Question 5

What is polarisation?

Answer 5

Polarisation is to cause the vibrations of the particles in the wave to occur in a single plane only, with the direction of vibrations perpendicular to the direction of propagation of energy.

Question 6

State 3 conditions that must be satisfied in order that two waves may interfere.

Answer 6

1. Wave sources must be coherent with constant phase difference
2. Amplitude of both waves must be similar.
3. Waves cannot be polarised in mutually perpendicular planes

Question 7

What is coherence

Answer 7

sources that have a constant phase difference

Question 8

What is interference?

Answer 8

Interference is from the superposition of two or more waves from coherent sources.

Question 9

What is the diffraction of a wave?

Answer 9

the spreading of waves when they pass through an opening or around an obstacle

Question 10

state two conditions required to form stationary waves

Answer 10

the two waves must be of the same type having the same frequency, wavelength, and speed, travelling in opposite directions

Question 11

features of a stationary wave that distinguish it from progressive waves (energy transfer)

Answer 11

stationary -> no energy transfer along direction of propagation of wave as energy is stored locally

progressive -> energy is transferred in the direction of propagation of the wave

Question 12

features of a stationary wave that distinguish it from other waves (amplitude)

Answer 12

stationary -> amplitude varies according to position of particle from 0 at nodes to Max at antinodes
progressive -> amplitude is the same for all particles

Question 13

features of a stationary wave that distinguish it from progressive waves (phase)

Answer 13

stationary -> particles between two adjacent waves are in phase, particles in adjacent segments are in antiphase

progressive -> phase of particles are all different

Question 14

features of a stationary wave that distinguish it from progressive waves (frequency)

Answer 14

stationary -> all particles vibrate in SHM with same frequency as component wave except the nodes

progressive -> all particles vibrate in SHM with same frequency as the wave

Question 15

features of a stationary wave that distinguish it from other waves (wavelength)

Answer 15

Stationary -> 2x distance between a pair of adjacent nodes or antinodes

Progressive -> distance between 2 successive points which are in phase

Question 16

features of a stationary wave that distinguish it from other waves (waveform)

Answer 16

stationary -> does not advance

progressive -> advances with the velocity of the wave

Question 17

define node

Answer 17

point of no oscillaition

Question 18

define antinode

Answer 18

point with maximum oscillation

Question 19

resonant frequency of a swing and open pipe

Answer 19

f = (nv)/2L

Question 20

resonant frequency of a closed pipe

Answer 20

f = (nv)/4L

Question 21

path diff and total phase difference of constructive interference

Answer 21

path diff = nλ
total phase difference = n(2π)

Question 22

path diff and total phase difference of destructive interference

Answer 22

path diff = (n+1/2)λ
total phase difference = (n+1/2)(2π)

Question 23

formula for fringe separation

Answer 23

x = (λD)/a

x = fringe separation
λ = wavelength
D = distance between screen and double slit
a = slit separation

Question 24

formula indicating position of first minima in single slit diffraction

Answer 24

sinθmin = λ/b

θmin = angle that the first minima makes with the central maxima
λ = wavelength
b = slit width

Question 25

Rayleigh’s criterion

Answer 25

two sources are just distinguishable if the central maximum of one diffraction pattern falls on the first minimum of the diffraction pattern of the other

Question 26

limit of the angular separation such that the sources are just resolved:

Answer 26

θres = λ/b

Question 27

for diffraction grating, formula for the nth order maxima is

Answer 27

dsinθ = nλ

d = slit separation
λ = wavelength
n = order of maxima
θ = angle that the nth order makes with the central maxima

Question 28

Conditions for interference

Answer 28

• waves must be coherent
• similar amplitudes
• cannot be polarized in mutually perpendicular planes