1.5 Interference of Waves

1.5 Interference of waves1.5 Interference of waves

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Learning OutcomesLearning Outcomes

state the principle of superposition,state the principle of superposition,

explain the interference of waves,explain the interference of waves,

draw interference patterns,draw interference patterns,

interpret interference patterns, andinterpret interference patterns, and

solve problems involvingsolve problems involving


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


Wave interferenceWave interference

Phenomenon Phenomenon when two or more when two or more waves meetwaves meet while traveling along while traveling along the the same mediumsame medium at the at the same same timetime


Principle of superposition of wavesPrinciple of superposition of waves

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


Principle of Superposition of wavesPrinciple of Superposition of waves

When two waves superpose, When two waves superpose, the the resulting displacementresulting displacement

of the medium at any location is theof the medium at any location is the algebraic sum of the algebraic sum of the

displacementsdisplacements of individual waves.of individual waves.


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How does interference occur???How does interference occur???

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

A through superposes a A through superposes a trough, the displacement trough, the displacement of the resultant waveof the resultant wave is is the sum of the the sum of the displacement displacement the displacement is the displacement is negative.negative.


2 type of Interference2 type of Interference

1. Constructive interference 1. Constructive interference

occurs when a crest meets a crest and occurs when a crest meets a crest and when a trough meets a trough.when a trough meets a trough.

2. Destructive interference2. Destructive interference

occurs crests meets/superposes with occurs crests meets/superposes with troughs. troughs.


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

occurs when a crest meets a crest occurs when a crest meets a crest

//when a trough meets a trough.//when a trough meets a trough.www.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

Destructive interferenceDestructive interferenceInterference that occurs at any location Interference that occurs at any location along the medium where the two interfering along the medium where the two interfering waves have a waves have a displacement in the opposite displacement in the opposite directiondirection


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


Destructive interference of two waves with different amplitude


Interference by 2 Interference by 2 coherentcoherent sources sources


Coherent sourcesCoherent sourcesThe waves from coherent sources have The waves from coherent sources have the same the same frequency (f),frequency (f), same same wavelengthwavelength ((λλ) and constant ) and constant phase differencephase difference. .

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


Antinodal lines

Nodal lines

Node

Antinodewww.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

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


1. For constructive interference (point Z), path difference=nλλ2. For destructive interference (point W), Path difference= (n+1/2) λλ


Factors affecting the Factors affecting the interferenceinterference

Young’s Formulawww.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

Young’s formulaYoung’s formula

Wavelength Wavelength of the waves,of the waves,

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


1.When a & D constant, 1.When a & D constant, λλ increase, increase, x?x?

2.When D & 2.When D & λλ constant, a constant, a increase, x? increase, x?

3. When a & 3. When a & λλ constant, D constant, D increase, x? increase, x?

x increasex increase

x increasex increase

x decreasex decrease


Example 1.2Example 1.2

Young’s Formula

In a ripple tank experiment, two water superpose and formInterference 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

3.0 cm

5.4 cm10.5 cm

?


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


Young’s Double-slit experimentYoung’s Double-slit experiment


A laser beam after passing through A laser beam after passing through a double slita double slit

Forming an interference pattern consisting alternate dark & bright fringes


Young’s Double-slit experiment (pg 27)Young’s Double-slit experiment (pg 27)

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

bright

Bright fringeBright fringe

Dark fringeDark fringe








Bright fringeBright fringe Dark fringeDark fringe


Exp on Interference of sound waveExp on Interference of sound wave


What do the blue & red lines What do the blue & red lines represent?represent?


Homework: Homework: 1. QR 1.5 page 28 (#1-3)1. QR 1.5 page 28 (#1-3)

2. Page 46, Section B.2. Page 46, Section B.


1. QR 1.5 page 281. QR 1.5 page 28

1.What is the meaning of two 1.What is the meaning of two coherent waves?coherent waves?

Two sets of waves that have same Two sets of waves that have same wavelength, frequency and constant wavelength, frequency and constant phase different.phase different.


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

FigureTwo boats approaches each other.


2.2.

(a) (i) The amplitude will be twice(a) (i) The amplitude will be twice

(ii) The amplitude will be zero(ii) The amplitude will be zero

(b) No, different frequency(b) No, different frequency


3.Figure shows S3.Figure shows S11 and S and S22 which are two which are two spherical sources attached to the vibration spherical sources attached to the vibration bar of a ripple tank. The two sources are bar of a ripple tank. The two sources are separated at a distance of 5.0 cm.separated at a distance of 5.0 cm.

(a) Are the waves produced by S(a) Are the waves produced by S11 and S and S22 coherent? Explain.coherent? Explain.(b) State the phenomena produced at the (b) State the phenomena produced at the position P, R and T.position P, R and T.


33

(a)(a) Yes, they come from the same sourceYes, they come from the same source

(Same f, (Same f, λλ and phase difference) and phase difference)

(a)(a) R and P R and P : Constructive Interference: Constructive Interference

T T : destructive Interference: destructive Interference


HomeworkHomework

Page 46, Section B. Page 46, Section B.

*Both semicircular waves must have same *Both semicircular waves must have same size of size of λλ..

(c) From the diagram, measure D and x.(c) From the diagram, measure D and x.

(d) Calculate (d) Calculate λλ..


The destructive The destructive interference of two waves interference of two waves with different amplitude.with different amplitude.

A crest with amplitude of a A crest with amplitude of a unit meet a trough with unit meet a trough with amplitude of -2a unitsamplitude of -2a units

the resulting displacement the resulting displacement amplitude isamplitude is

-a unit -a unit


Destructive Destructive interferenceinterference

a crest of one wave a crest of one wave propagates from the left propagates from the left superposed on another superposed on another trough coming from the trough coming from the right.right.

The resulting wave will The resulting wave will cancel each other.cancel each other.

There is no resulting There is no resulting disturbance in the disturbance in the medium.medium.


interference of 2 sources of lines. interference of 2 sources of lines.

The dotted red lines join places where the waves The dotted red lines join places where the waves arrive there in phase arrive there in phase

Red lines called antinodal lines Red lines called antinodal lines

join places of constructive interference.join places of constructive interference.www.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

blue lines where calm water is formedblue lines where calm water is formed

waves arrive there exactly out of phase. waves arrive there exactly out of phase.

Blue lines are called nodal lines.Blue lines are called nodal lines.

join the places of destructive interferencejoin the places of destructive interference


The distance of Z from the SThe distance of Z from the S11 is x is x11, ,

the distance of Z from the Sthe distance of Z from the S22 is x is x22. .

The path difference of Z from S and is xThe path difference of Z from S and is x22-x-x11..

consructive interference (S), the path difference = nconsructive interference (S), the path difference = nλλ. .

destructive interference (W), the path difference = (n +1/2)destructive interference (W), the path difference = (n +1/2)λλ n is an integer.n is an integer. www.myfunphysicsworld.blogspot.comwww.myfunphysicsworld.blogspot.com

Draw two adjacent antinodal lines on both the Draw two adjacent antinodal lines on both the photographs. photographs.

a.a. How does the separation of the antinodal lines How does the separation of the antinodal lines differs? differs?

b.b. If the separations of the two sources of If the separations of the two sources of vibrations are avibrations are a11, and a, and a22, what is the , what is the

reIationship between areIationship between a11 and a and a22 to that of the to that of the

separations of the antinodal lines?separations of the antinodal lines?

c.c. How do you measure the wavelengths of the How do you measure the wavelengths of the two sources of wave?two sources of wave?

d.d. Are the waves produced by the two sources of Are the waves produced by the two sources of vibration coherent? Explain.vibration coherent? Explain.


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


1.5 Interference of Waves

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