Waves

Knowledge :

1. Any motion that repeats itself in equal intervals of time is called a periodic motion.

2. If a particle in a periodic motion moves back and forth over the same path, we call the

motion oscillatory or vibratory.

3. Some examples of periodic motion are the oscillation of the balance wheel of watch, a

violin string, a mass attached to a spring, a simple pendulum , a vibrating saw blade and

air molecules as a sound wave passes by.

4. Wave motion is due the vibration of particles from their rest position.

5. Several terms to describe a wave:

a. Wavelength ( ) , the distance between two adjacent points of the same phase

on a wave.

b. Amplitude ( a ) , is the maximum displacement of a crest or a trough from the

equilibrium position

c. Frequency ( f ) , is the number of waves produced by a source in one unit time.

d. Wave speed ( v ) , is the measurement of how fast a crest is moving from a

fixed point

e. Period ( T ) , is the time taken for an oscillation to complete one cycle

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a a

Crests

troughs

Equilibrium position

Wavelength ,

a

a

A blade

6. Waves are carries of energy. They transfer energy from one location to another. The

energy is represent by the amplitude of the wave.

Example :

When we throw a stone into a pond, a ripple spreads out in an

expanding circle from the source of disturbance. The energy of the

stone is converted to waves. A cork floating a distance away will move

up and down when the ripples passes it. Thus the ripple transfer

energy from the stone to the cork

7. There are many examples of waves such as microwaves, radio waves, sound waves.

These waves are divided into transverse and longitudinal waves.

a. Transverse wave

The direction of propagation of the wave formed is perpendicular to

the vibration of the medium

Example :

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Direction of propagation of wave

Direction of vibration

T

a

Energy is transferred from the stone to the cork which does not involve the transfer of water.

The movement of the hand to the left and right is perpendicular to the direction of propagation of wave

b. Longitudinal waves

Waves where the vibration of the medium is parallel to the direction

of propagation of the wave

8. Examples of transverse waves are water waves, radio waves, microwaves and etc. While

sound waves is a longitudinal waves.

9. The relationship between f and T is or

T is inversely proportional to f

If T increase, f will decrease and vice versa .

The unit of T is second while f is Hz @ s -1

10. The swing of a simple pendulum is always used to illustrate some of terms waves.

The maximum displacement is called amplitude ( a )

The time to swing from position A to B and back to A is called a period ( T ).

T simple pendulum where l = length of the pendulum and g = 10ms-1

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Direction of propagation of the wave

Direction of the vibration

T compression

rarefaction

a

A B

Frequency is defined as the number of complete swings of the pendulum bob

from A to B and back from B to A per unit time ,

When the bob is displaced to one side, the bob will gain potential energy, Ep

where :

o Ep = gravitational potential energy

o m = mass of the bob

o g = gravitational field strength ( 10 ms -2 ) ( round off to tens )

o h = maximum displacement from its equilibrium position

and when the bob is released to let it oscillates , the potential energy will transform to

kinetic energy , Ek , where

o m = mass of the bob

o v = the speed of oscillation .

11. Many of oscillating bodies do not move back and forth between precisely fixed limit. The

bob will stop after a long period of time. We call this phenomenon as damping. Damping

is caused by frictional force dissipate the energy of the motion.

12. Waves has speed. For example, the speed of sound waves is about 330 ms-1 and the

speed of light is 3.0 x 108 ms-1. The speed of wave can be determine by

o v = the speed of a wave

o f = the frequency of wave

o = the wavelength of a wave ( lamda )

13. We can see a wave in lab using a ripple tank.

14. A ripple tank consists of a square transparent plastic tray with a lamp on the top. The tray

has sloping sides so that any wave propagate will not be reflected back from the side

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15. Two patterns of wavefronts are :

16. Water waves have crests and troughs. A crest is the highest position of the wave, whereas

a trough is the lowest position. The crest act as a convex lens while the trough act as a

concave lens.

17. In a ripple tank, light rays from the lamp on top will focus onto the white screen below.

The bright lines correspnd to the crest, and the dark line correspond to the troughs.

Figure to show how wavefronts are formed

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Direction of propagation of wave

wavefronts

Straight waves produced by a bar

A bar( source)

Straight waves

Direction of propagation of wave.

.A round dipper as the source of the wave.

or

Circular waves

18. Displacement – distance graph

19. Displacement – time graph

Example 1 :

Figures below shows the displacement-distance graph and displacement-time graph of a

wave travelling from left to right.

Determine :

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distance

displacement

a

time

displacement

T

Time/s

20_

-20_

0_

Displacement / cm

1.2 s

20_

-20_

0_

Displacement / cm

3 m

Distance ( m )

a. The amplitude, a

20 .0 cm

b. The wavelength ,

2.0 m

c. The period , T

0.48 s

d. The frequency , f

= 2.08 Hz

e. The speed , v , of the wave

= 4.16 ms-1

Example 2

Figure shows a long spring along which a longitudinal wave is moving

a. What is meant by longitudinal wave?

Longitudinal wave is a wave in which the wave particles are oscillating in a

direction parallel to the direction of motion of the wave.

b. Mark on the diagram

i. With a letter C which represent a point of compression

ii. With a letter R which represent a point of rarefaction

iii. Mark on the diagram a distance equal to the wavelength of the wave and

label this distance as

c. Give an example of a longitudinal wave

Sound waves

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Example 3

Figure below shows water waves being generated by a linear dipper oscillating in a ripple

tank with a deep area and a shallow area.

a. State two changes when the wave enters the shallow are

1. wavelength becomes smaller

2. amplitude becomes bigger

b. If the frequency of the oscillating linear dipper is 5 Hz, the wavelength

of the waves in the deep area is 4.0 cm and the wavelength of the waves in the

shallow area is 3.0 cm, calculate :

i. the speed of the waves in the deep area

= 20 cms-1

ii. the speed of the waves in the shallow area

v = = 15 cms-1

Example 4

Each line in the diagram below is a crest line

The wave travels from X to Y in 2 s. What is the frequency of the wave?

Answer : 3 Hz

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Shallow areadipper

Deep area

X Y

Example 5

The diagram shows a wavefront pattern produced by a dipper vibrating at a frequency of

12 Hz in a ripple tank

What is the speed of the waves

Answer : 18 cms-1

20. If a periodic force is applied to a swing as its natural frequency, the amplitude of the

swing increases as the energy of the swing increases. The swing is said to be in

resonance.

21. At resonance the swing oscillates with a maximum amplitude.

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6 cm

dipper

Reflection of waves

Example 1

The diagram shows a light ray reflected on a plane mirror

What is the angle of incidence of the light ray?

Answer : 600

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ir

normal

Incident wavefronts

Reflected wavefronts

i is called the angle of incidence

r is called the angle of reflection

i 0 = r 0

Wavelength of the incident waves and the reflected waves are equal

The incident waves and the reflected waves will have the same speed in water of

equal depth

v, f and are remains constant in reflection

300

Refraction of waves

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Incident ray

Refracted ray

normal

i

r

air

water

The angle between the incident ray and the normal is called the angle of incidence, i

The angle between the refracted ray and normal is called the angle of refraction , r

When a wave passes through two medium with two different speed , the wave will

bent ( if i 00 )

This phenomenon is called as refraction.

Refraction is due to the change in the speed of wave when traveling from one

medium to another medium

The wave will refracted away the normal if it passes through a low speed medium

to high speed medium and vice versa

i. Less dense – high speed ; dense – low speed ( for light waves )

ii. Deep water – high speed ; Shallow water – low speed ( for water waves )

iii. Dense – high speed ; less dense – low speed ( sound waves )

The frequency , f does not change in refraction

Example 1

Complete the diagram below to show refraction when a plane water wave is passing through a

shallow area

Example 2

The diagram shows a plane water wave in a ripple tank moving across a convex transparent

block. Complete the diagram to show refraction when the plane water wave is passing through

the convex shallow area

Example 3

Complete the diagram below to show refraction when a plane water wave is passing through a

concave shallow area

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Shallow areaDeep area

Diffraction of waves

1. Diffraction of waves is a phenomenon when a wave is pass through an opening or around

an obstacles

2. v, f dan are remains constant in diffraction

3. The amount of diffraction ( the sharpness of the bending ) increases with increasing

wavelength

4. In fact, when the wavelength of the waves is smaller than the width of the obstacles, there

is less noticeable diffraction

Example 1

Example 2

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Diagram to show diffraction when a wave pass through an opening

Diagram to show diffraction when a wave pass through an obstacles

Interference of waves

1. Interference is a phenomenon when two waves meet while travelling along the same medium

2. Ripples riding higher on the surface of the sea near a boat. Water waves move towards the

side of the boat and are reflected back. The incident waves and the reflected waves are

superposed. This phenomenon is called interference . It can be explained by the principle of

superposition.

Principle of superposition of waves

1. The principle state that : When two waves interfered , the resulting of displacement of the

medium at any location is the algebraic sum of the displacements of the individual waves.

2. At the moment when two crests or two troughs are completely superposed, the resulting

shape of medium will be a crest or a trough with amplitude 2a.

3. This type of interference is called constructive interference .

4. On the other hand, if a crest of one wave propagates superposed on a trough of the second

wave, , the resulting wave will cancel each other. There is no resulting disturbance in the

medium .

5. This type of interference is called destructive interference

6. Either constructive or destructive interference to occur, the waves must be coherent.

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A crest superposed a trough

= Calm water.+

A crest superposed a crest A trough superposed a trough

==

2a2a

+

+a a a a

Diagram to show the transform of interference of waves

7. The result for interference :

a. water waves

b. light waves

c. sound waves

8. Lines join places of constructive interference are called antinodal lines.

9. Lines join places of destructive interference are called nodal lines.

10. Interference of light can be produced by passing light through a double slit. An

interference pattern consisting of alternate bright and dark fringes can be seen on a

distance screen. These alternate bright bands is called as interference fringes.

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Constructive interference - waves

Destructive interference – calm water

Constructive interference – bright fringe

Destructive interference – dark fringe

Constructive interference – loud sound

Destructive interference – weak sound

11. Formula used in interference is where

a is the distance between two sources of waves

x is the separation between two adjacent nodes or antinodes

D is the perpendicular distance between waves source to the position where

x is measured.

is the wavelength of the used wave.

Diagram to show Young’s double slit experiment

Example 1

The diagram shows an arrangement in Young’s double slide experiment to show the

interference of light.

The wavelength of laser light used is 600 nm and the separation of the two slits is 0.48

mm. what is the separation of the fringes of the interference pattern?

Answer :

1.5 mm

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screen

D= 1.2 m

Double slit

Laser light

Example 2

The diagram shows the fringes obtained from a double slit experiment using a

monochromatic light of wavelength 550 nm.

If the distance between the double slit and the screen is 1.5 m, what is the separation of

the double slit ?

Answer :

0.17 mm

Example 3

The diagram shows two circular water waves from two sources s1 and s2 overlapping as

they travel to the right. The circular lines indicate the crest lines of the water waves

What type of interference occurs at P, Q and R ?

P Q R

A. constructive constructive destructive

B. constructive destructive destructive

C. destructive constructive constructive

D. destructive destructive constructive

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24 mm

.

.

S1

S2

...

P

Q R

Example 4

Diagram below show two identical speakers that are connected to an audio generator. The

two speakers are a pair of coherent sources

A student walks along the line PQ which is 15 m away from the two loudspeakers. He hears a

loud sound and a weak sound alternately

a) What is meant by coherent sources?

Coherent sources are two oscillating sources which have a constant phase

difference.

b) Calculate the wavelength of the sound wave

= 0.227 m

c) The loud sound is caused by constructive interference of the sound waves. State

the condition for constructive interference to occur?

Constructive interference occurs when two waves meet in phase/ when the crest

of one wave meets the crest of the other wave.

d) The weak sound is caused by destructive interference of the sound waves. State

the condition for a destructive interference to occur?

Destructive interference occurs when the two waves meet in anti-phase

e) What is the effect of

i. Increasing the frequency of the sound wave

Separation of the loud sounds decrease

ii. Decreasing the distance between the two loudspeakers

Separation of the loud sounds increases

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Loud sound

Weak sound

Loud sound

Weak sound

Loud sound

Weak sound

Loud sound

Weak sound

Loud sound

6.8 m

Q

P

2.0 m

15.0 m

Loud speaker

Audio generator

Sound waves

Sound propagate in a medium as longitudinal waves

Loudness and pitch

A high pitch sound corresponds to a high frequency and a low pitch sound corresponds to

a low frequency of vibration

A loud sound corresponds to the amplitude of a sound. If we increase the amplitude of a

sound, the sound will be louder.

Applications of sound waves

a) Ultrasonic spectacles

Is ultrasonic spectacles to transmit ultrasonic waves. A blind men use it to see.

A receiver in the person’s ear will receive the sound reflected from an object.

b) Sonar

A shorter wavelength used to detect fishes and the depth of sea bed.

c) Ultrasound scanner

Ultrasonic echoes used in medicine to see the internal organ of inside the body

Electromagnetic waves

Gamma ray, X-ray , ultraviolet, visible light, infrared, ,microwave and radio

waves are parts of the electromagnetic spectrum

Electromagnetic waves travel at a speed of 3.0 x 108 ms-1

Applications of electromagnetic waves

1. Radio waves

There are various type of waves such as microwaves, VHF and UHF radio waves.

Microwaves have the shortest wavelength, being a few centimeters. They are used in

telecommunication as a transmitter. Radar systems are also use microwaves to find the

direction and the distance of an object

2. Infrared

The remote control that use to switch on our electrical appliances such as the television,

uses infrared. Infrared is also used in transmitting data between computers

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3. X-rays

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4. Gamma ray

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5. Ultraviolet light

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Question 1

Figure below shows the electromagnetic spectrum

a) What names are given to the waves in sections labeled W and Q?

W is X-ray, Q is visible light

b) From gamma ray to radio wave along the spectrum which property of the radiations has

a decreasing value and which property has an increasing value

Frequency is decreasing

Wavelength is increasing

c) State three common properties of all the electromagnetic waves

i. All electromagnetic waves are transverse waves

ii. All electromagnetic waves can pass through vacuum

iii. All electromagnetic waves have the same speed in vacuum

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Gamma rays W ultraviolet Q Infrared rays microwaves Radio waves

MODULE 2

Form 5

2007

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NAME

.........................................................................

FORM FIVE

.........................................................................

NAME OF TEACHER

...........................................................................

Created by : Hjh Gayah Madu

SM Teknik Kluang 2007

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