1.5 interference

CHAPTER 1: WAVES
1.5 Analysing Interference of Waves

PRINCIPLE OF
SUPERPOSITION
• 1
The Principle of superposition
states that at any instant, the
wave
displacement
of
the
combined motion of any number
of interacting waves at a point is
the sum of the displacements of
all the component waves at that
point.
• The principle of superposition states that the when
two /more waves meet at a certain point, the
resultant displacement at that point is the
vector sum of the individual waves

PRINCIPLE OF
SUPERPOSITION
• 2
Figures 1.46 (a), (b) and (c) show the
combined amplitude produced when two waves,
both of amplitude a, from opposite directions
meet.

PRINCIPLE OF
SUPERPOSITION
• 3
Interference pattern is a result
of the superpositions of waves.

INTEFERENCE OF WAVES
When two or more waves meet, they
superpose or combine at a particular point.
The waves are said to interfere.

INTERFERENCE OF WAVES
• 1
Interference is the superposition of two waves
originating from two coherent sources. Sources
which are coherent produce waves of the same
frequency (f), amplitude (a) and in phase.
Wave A
Wave B

• 2
The superposition of two waves emitted from
coherent sources gives either constructive or
destructive interference.

• 3
Constructive interference occurs when the
crests or troughs of both waves coincide to
produce a wave with crests and troughs of
maximum amplitude.

• 4
Destructive interference occurs when the crest of
one wave coincides with the trough of the other wave,
thus canceling each other with the result that the
resultant amplitude is zero

• 5
Figure 1.47 shows the occurrence of constructive
interference and destructive interference.

• 6
An antinode is a point where constructive
interference occurs, whereas a node is a point
where destructive interference occurs. From Figure
1.48, it can be seen that the antinodes line joins all
antinodes while the node lie joins all nodes.

• Experiment 1.8 : To investigate the interference of water
waves
(I)

Different wavelengths (

λ)

• Problem statement
What is the relationship between the wavelength, λ, and
the distance between two adjacent node lines (or
antinode lines), x, in the interference pattern?

• Experiment 1.8 : To investigate the interference of water
waves
(I)

λ


)

• Hypothesis
The distance between two adjacent node lines (or
antinode lines), x, increases as the wavelength
increases.

• Experiment 1.8 : To investigate the interference of
water waves
(I)
)

λ

• Variables:
• (a) Manipulated:Frequency of the dippers or
wavelength
• (b) Responding:
Distance between two
consecutive node lines, or, antinode lines (x)

λ

(I)
(c)Fixed Variables:

)

(i) Distance between two sources (a)
(ii) Distance from sources to the point where the
distance between two adjacent node lines or
antinode lines (x) is measured (D)

• (I) Different wavelengths ( )
λ
• Apparatus/Materials
• Ripple tank, spherical dippers and mechanical
stroboscope.

λ

• Procedure
• 1
A ripple tank is set up with two spherical dippers
in contact with the surface of the water.
• 2
The distance between the two spherical dippers
is fixed at 4 cm.

λ

• Procedure
• 3
The motor and the rheostat are adjusted to
operate the motor at low frequency.
• 4
The pattern of the interference of the waves is
observed with a stroboscope and the pattern is
drawn.
• 5
Steps 3 and 4 are repeated with the vibrator
operating at a higher frequency. The waves
produced have a shorter wavelength.

Low f

High f

• (I) Different wavelengths (
• Observation

λ

)

• (I)


• Discussion

λ

)

• 1
Table 1.2 shows that when the two waves combined to
produce waves of larger amplitude as shown by the regions
which are bright (where the crests of the two waves coincide)
and the darker regions (where the troughs coincide). This part
of the pattern of waves shows the crests and troughs which are
reinforced as a result of constructive interference.

• Discussion
• 2
In some regions where the water is still,
without any ripples, the crests and troughs of the
two waves coincide and eliminate each other
(destructive interference). Since the amplitude is
zero, there is no wave motion.


λ

)
• 3
The results in Table 1.7 shows that when the
frequency is higher, i.e., the wavelength is shorter,
the distance between two adjacent node lines or
antinode lines, x, is smaller.

• Conclusion
• The distance between two consecutive node lines or
node lines (x) increases when the wavelength of the
water waves ( ) from the source increases.

λ

⇒ xαλ


λ

• Conclusion

The hypothesis is valid.

)

• (II) Different distances between the two sources of
waves (a)
• How is the distance between the two sources of
waves, a, related to the distance between two
adjacent node lines or antinode lines, x, in the
interference pattern?

waves (a)
• Hypothesis
• If the distance between two sources of waves, a, is
decreased, the distance between two
consecutive node lines or antinode lines, x,
increases.

(II) Different distances between the two sources of waves (a)
Variables
(a) Manipulated : Distance between the two sources (a)
(b) Responding: Distance between the two consecutive
node, or antinode lines (x)
• (c) Fixed:
• (i)
Frequency of dippers (f) or wavelength (λ)
• (ii)
Distance from sources to the point where the distance
between two adjacent node, or antinode lines (x) is
measured (D)
•
•
•
•

waves (a)
• Apparatus/Materials
• Ripple tank, Spherical dippers, metre rule and
mechanical stroboscope

• (II) Different distances
between the two sources of
waves (a)
• Procedure
• 1
The ripple tank is set up
as shown in Figure 1.49.
• 2
The distance between
two spherical dippers, a, is
fixed at 4 cm.
• 3
The motor is switched on
and the rheostat is adjusted
to obtain waves with medium
wavelength.

• (II) Different distances
between the two sources of
waves (a)
• Procedure
• 4
The interference
pattern is observed with
stroboscope and the
pattern is drawn.
• 5
Steps 3 and 4 are
repeated with the distance
between the two spherical
dippers reduced to 2 cm

waves (a)
• Observations

• Conclusion
• The distance between two consecutive node (or
antinode) lines, x, is inversely proportional to the
distance between the two sources.

1
⇒ xα
a
• The hypothesis is valid.

RELATIONSHIP BETWEEN ,
A, X AND D

• Keys:
• a = distance between two coherent sources
•
= wavelength
•λ x = distance between two consecutive node (or
antinode)lines
• D = distance from the two sources to the point of
measurement of x

A, X AND D
• From the interference pattern (Figure 1.52) and
factors that influence the interference pattern in
Experiment 1.8, we found that

xαλ

and

xα

1
a

λ
⇒ xα
a
λ
x=D
a
ax

∴λ =

D

A, X AND D
• Example 10
• In the interference of two coherent sources of
a
waves, the separation between two spherical
dippers is 3 cm and the distance between two x
D
consecutive node lines is 4 cm measured at a
distance of 15 cm from the two coherent sources of
λ
waves. Calculate the wavelength of the water
waves originating from the sources.

ax
λ=
D

A, X AND D
• Example 10
• Solution
• Substituting a = 3 cm, x = 4 cm, D = 15 cm into the
formula
• λ = ax
D

3x4

• λ=
15
• = 0.8 cm

INTERFERENCE OF LIGHT
WAVES
• 1
Interference of light waves, like that of water
waves and sound waves, also requires two coherent
sources.

WAVES
• 2
Waves emitted from two coherent sources have
the same frequency (or wavelength) and in phase.

WAVES
• 3
Light emitted by a single source consists of
waves which extend over a wide range of
wavelengths and are not in phase. Because of this,
it is difficult to have two sources of light which are
coherent.

WAVES
• 4
In 1801, Thomas Young produced two coherent
light sources in his experiment now referred to as
Young's double-slit experiment.

WAVES
• 5
Principle of Young's double-slit experiment:
• (a) Yellow light emitted by a sodium-vapour lamp
has a very narrow frequency band. For all
practical purposes, it can be considered as
monochromatic light which is light of only one
frequency or wavelength.

WAVES
• 5
• Figure 1.53 Young's double-slit experiment
•

WAVES
• 5


• (b) Slits S1, and S2 give rise to two coherent light sources
since the light passing through them are from the same
monochromatic light, the sodium-vapour lamp.

WAVES
• 5
• (c) Interference occurs as a result of the superposition
of the two light waves originating from S1 and S2. A
pattern consisting of a series of parallel and alternating
bright and dark fringes is formed.
•

WAVES
• (d) The bright fringes are
regions where
constructive interference
occurs, whereas the dark
fringes are regions of
destructive interference.

WAVES
• 5
• (e) Figure 1.54 shows the interference pattern obtained
in Young's double-slit experiment.

• Figure 1.54

WAVES
• 5
• (f) The widths of the bright and dark fringes are the
same.

QUIZ:
1. When coherent sound waves propagate
from two loudspeakers of 2 m apart, an
observer can hear the loudest sound. The
loudspeakers are connected to a source
waves with a frequency of 500 Hz and
observer walks a distance of 10 m in front of
the loudspeakers. If the speed of sound is
300 ms-1, what is the distance between two
consecutive loudest sounds heard by the
observer?

QUIZ: Interference and refraction
Diagram below shows the interference pattern of water waves.
Rajah dibawah menunjukkan corak interferen gelombang air.

What happens to the separation between two consecutive nodal lines, x, if the
depth of water in the ripple tank is increased?
Apakah yang akan berlaku kepada jarak pemisahan 2 garisan nodal berturutan, x,
jika kedalaman air dalam tangki riak meningkat?
A. Unchanged / Tidak berubah
B. Increase / Bertambah
C. Decrease / Berkurang

Factors affecting interference pattern
53

1. D x
Dαx
2. λ x
λαx
3. a ↓ x
aα 1
x

x = Dλ
a

1.5 interference

1.5 interference

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1.5 interference