1.5 Interference of Waves

1.5 Interference of waves

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Learning Outcomes
state the principle of superposition,
explain the interference of waves,
draw interference patterns,
interpret interference patterns, and
solve problems involving


Water waves move towards the side of the boat
and are reflected back
The incident waves and the reflected waves are
superposed.
Ripples can be seen clearly in areas where the
water is calm
principle of superposition.

Wave interference
Phenomenon when two or more
waves meet while traveling along
the same medium at the same
time


Principle of superposition of waves

Two mechanical waves superposed (1) produce a
wave with a higher amplitude (2).

Principle of Superposition of waves

When two waves superpose,
the resulting displacement
of the medium at any location is the
algebraic sum of the
displacements
of individual waves.

5cekap here 22feb2011



How does interference occur???

A crest superposes a A through superposes a
crest, the displacement trough, the displacement
of the resultant wave is of the resultant wave is
the sum of the the sum of the
displacement of displacement
individual waves at
every point. the displacement is
negative.

2 type of Interference
1. Constructive interference
occurs when a crest meets a crest and
when a trough meets a trough.

2. Destructive interference
occurs crests meets/superposes with
troughs.


Constructive interference
Interference that occurs at any location along
the medium where the two interfering waves
have a displacement in the same direction

occurs when a crest meets a crest
//when a trough meets a trough.

Destructive interference
Interference that occurs at any location
along the medium where the two interfering
waves have a displacement in the opposite
direction


Destructive interference
A crest that superposes a trough wave arrives
exactly out of phase,
the crest of a wave meets the trough of the other.
They cancel each other and the water is calm,


Destructive interference of two waves
with different amplitude


Interference by 2 coherent sources


Coherent sources
The waves from coherent sources have
the same frequency (f), same wavelength
(λ) and constant phase difference.

The difference in the distances of a point
from the two sources is called path
difference.
Two waves with a path difference of 2λ.

Node Nodal lines

Antinodal lines Antinode

Path difference of Z from S1 and S2 =|
x1-x2|


1. For constructive interference (point Z),
path difference=nλ
2. For destructive interference (point W),
Path difference= (n+1/2) λ


Factors affecting the
interference

Young’s Formula

Young’s formula
Wavelength
of the waves,

a = the distance between two coherent
sources of wave,
x = the separation between two adjacent nodal
or antinodal lines
D = the perpendicular distance between waves
source to the position where x is measured.

1.When a & D constant, λ increase, x?
x increase
2.When D & λ constant, a increase, x?
x decrease
3. When a & λ constant, D increase, x?
x increase


Example 1.2

In a ripple tank experiment, two water superpose and form
Interference patterns.
The distance between the two vibrating sources is 3.0 cm.
The separation between two adjacent nodal line is 5.4 cm,
at a distance of 10.5 cm from the two sources.
Calculate the wavelength of the water waves produced

5.4 cm
10.5 cm

? 3.0 cm

Young’s Formula

In a ripple tank experiment, two water waves
superpose and form interference patterns. The
distance between the two vibrating sources is 3.0
cm. The separation between two adjacent nodal line
is 5.4 cm, at a distance of 10.5 cm from the two
sources.
Calculate the wavelength
of the water waves produced.


Young’s Double-slit experiment


A laser beam after passing through
a double slit

Forming an interference pattern consisting alternate
dark & bright fringes


Young’s Double-slit experiment (pg 27)

Bright fringe
bri
gh
Dark fringe
t
Bright fringe

Dark fringe
Bright fringe
Dark fringe

Bright fringe
Dark fringe

Monochromatic source, propagate perpendicularly
towards a double-slit form interference fringes.

Bright fringe Dark fringe

Exp on Interference of sound wave


What do the blue & red lines
represent?


Homework:
1. QR 1.5 page 28 (#1-3)
2. Page 46, Section B.


1. QR 1.5 page 28

1.What is the meaning of two
coherent waves?
Two sets of waves that have same
wavelength, frequency and constant
phase different.


2. Figure shows A and B are two sources of wave
from the motor engine of two boats. The
frequencies of these two sources of wave are 5
Hz and 10 Hz.
(a) What happens to the amplitude of wave at
the point of superposition when
(i) the crests of the waves from A and B meet,
(ii) the crests of the wave from source A meet
the troughs of the wave from source B?
(b) Are the waves A and B coherent? Explain.

Figure
Two boats approaches each other.


2.
(a) (i) The amplitude will be twice
(ii) The amplitude will be zero
(b) No, different frequency


3.Figure shows S1 and S2 which are two
spherical sources attached to the vibration
bar of a ripple tank. The two sources are
separated at a distance of 5.0 cm.
(a) Are the waves produced by S1 and S2
coherent? Explain.
(b) State the phenomena produced at the
position P, R and T.

3
(a) Yes, they come from the same source
(Same f, λ and phase difference)
(a) R and P : Constructive Interference
T : destructive Interference


Homework
Page 46, Section B.
*Both semicircular waves must have same
size of λ.
(c) From the diagram, measure D and x.
(d) Calculate λ.


The destructive
interference of two waves
with different amplitude.
A crest with amplitude of a
unit meet a trough with
amplitude of -2a units
the resulting displacement
amplitude is
-a unit


Destructive
interference
a crest of one wave
propagates from the left
superposed on another
trough coming from the
right.
The resulting wave will
cancel each other.
There is no resulting
disturbance in the
medium.

interference of 2 sources of lines.
The dotted red lines join places where the waves
arrive there in phase
Red lines called antinodal lines
join places of constructive interference.

blue lines where calm water is formed
waves arrive there exactly out of phase.
Blue lines are called nodal lines.
join the places of destructive interference


The distance of Z from the S1 is x1,
the distance of Z from the S2 is x2.
The path difference of Z from S and is x2-x1.
consructive interference (S), the path difference = nλ.
destructive interference (W), the path difference = (n +1/2) λ
n is an integer. www.myfunphysicsworld.blogspot.com

Draw two adjacent antinodal lines on both the
photographs.
a. How does the separation of the antinodal lines
differs?
b. If the separations of the two sources of
vibrations are a1, and a2, what is the reIationship
between a1 and a2 to that of the separations of
the antinodal lines?
c. How do you measure the wavelengths of the
two sources of wave?
d. Are the waves produced by the two sources of
vibration coherent? Explain.

when the sources are closer to each other, the nodal
and antinodal lines of the interference pattern
decrease in number and are more widely spaced.
when the separation of the two dippers decrease, the
nodal (and antinodal) lines increase in number and
also become closely spaced.
If the separation is further increased, the nodal lines
become so close together until they are hardly
noticeable.
As the wavelength of the waves increases, the
separations of the nodal and the antinodal lines will
increase.
The number of the antinodal or nodal lines will
decrease.

1.5 Interference of Waves

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