superposition

Question 1

explain what it is meant by superposition

Answer 1

the principle of superposition states that when two or more waves of the same kind meet at a point in space, the resultant displacement at that point is equal to the vector sum of the displacements of the individual waves at that point

Question 2

what is meant by an antinode

Answer 2

It is the point on the stationary wave where the amplitude is the maximum

Question 3

what is meant by a node

Answer 3

it is the point on the stationary wave where the amplitude is 0

Question 4

what is a stationary wave

Answer 4

it is the result of the superposition of two progressive waves of the same type, frequency, amplitude and speed, travelling along the same line but in opposite directions

Question 5

what happens when two waves of the same type, frequency, speed and amplitude,, but are antiphase with each other meet at a point in space

Answer 5

The resultant amplitude of the stationary wave is 0, i.e it is a straight line

Question 6

what happens when two waves of the same type, frequency, amplitude and speed, but are in phase with each other meet at a point in space

Answer 6

the 2 waves reinforce each other and the resultant amplitude of the wave would be twice that of the amplitude of individual waves.

Question 7

What are the key properties of a stationary wave

Answer 7

1. The particles of the wave oscillate about their respective equilibrium positions with the same frequency. but different amplitudes. (note: follows frequency of component waves)
2. All particles oscillate in phase between two adjacent nodes.

Question 8

formula for stationary wave on string

Answer 8

wavelength = 2L/n , where n represents the harmonic

frequency = v/wavelength

Question 9

what is a notable feature of stationary waves in a closed piper

Answer 9

there are no even harmonics for the stationary wave

1st harmonic 3rd harmonic 5th harmonic

Question 10

for a stationary wave on a string, the harmonic number represents…

Answer 10

the number of half wavelengths present, i.e. n= lumdah/2

Question 11

for a stationary wave in a closed pipe, the harmonic number represents

Answer 11

the number of quarter wavelengths present, i.e. n= lumdah/4

Question 12

formula for closed pipe stationary waves

Answer 12

(2n-1)th Lumdah = 4L/2n-1

where 2n-1 represents the number of quarter wavelenths present and is equal to that of the harmonic number

Question 13

for a stationary wave in an open pipe, the harmonic number represents

Answer 13

the number of half wavelengths present, i.e. n= lumdah/2

Question 14

formula for open pipe stationary waves

Answer 14

nth Lumdah= 2L/n

Question 15

what are the two types of wave interferences and their definitions

Answer 15

constructive interference:
occurs when two coherent waves arrive at the same point with a phase difference of zero to produce a maximum

destructive interference, occurs when two coherent waves arrive at the same point with a difference of pie rad to produce a minimum

Question 16

state what it means by coherent

Answer 16

waves are coherent when they have a constant phase difference

Question 17

what does it mean by interference

Answer 17

it is the superposition of 2 or more waves to give a resultant wave whos amplitude is given by the principle of superposition

Question 18

what are the properties of waves in a 2 source interference

Answer 18

the waves of the sources must be coherent

the waves must have a similar amplitude

for em waves, the waves must be unpolarised or polarised in the same plane

Question 19

formula for path difference when waves undergo constructive interference

Answer 19

path diff = n lumdah, where n represents the number of wave lengths and is the nth order maximum, where bright fringes or sounds occur

Question 20

formula for path difference when waves undergo destructive interference

Answer 20

path diff = (n+1/2) lumdah,

Question 21

what is the formula for the spacing between successive fringes in a double slit experiment, and what are the conditions for this formula to be used

Answer 21

x= (n * lumdah * D ) / a

where x = spacing between bright fringes
D= distance between slit and screen
a= slit separation

condition:
angle theta from the normal is small
the rays are almost parallel

Question 22

what is the formula for path difference in a constructive wave in diffraction grating

Answer 22

asin nththeta = n lumdah

sin nth theta= (n lumdah)/a

e.g. asin 1st theta= 1 lumdah
a sin 2nd theta = 2 lumdah

where:
n represents the maxima number
nth theta represents the angle for the respective maxima number
a represents the slit separation , where a=1/N with N being the number of grating lines per meter

Question 23

what is the formula to determine the maximum order of the bright fringes

Answer 23

for maximum fringes

nth theta <90 degrees
sin nth theta < 1
n lumdah/d < 1
n<a/lumdah

Question 24

what is the formula for the single slit minima

Answer 24

b/2 sin nth theta= n lumdah/2
therefore:
sin nth theta = n lumdah/b

where n represent the order of the minima
b represents the width of the slit

Question 25

what is the formula for the separation of 2 minimas on the screen for a single slit diffraction, and what are the conditions for the formula to be used

Answer 25

y= D(2 theta) = 2Dlumdah / b

1. theta must be less than 6
2. distance D must be larger than slit width B

Question 26

what is the rayleigh criterion

Answer 26

two images are just resolved by an aperture when the central maximum of the diffraction pattern of one image falls on the first minimum of the diffraction pattern of the other image

Question 27

formula for reyleigh criteria for normal and circular aperture

Answer 27

theta min= lumdah/b

where lumdah = wavelength of the radiating wave and b is the slit width

for circular aperture:
thetamin = 1.22 * (lumdah/D)

where D is the diameter of the aperture.