Everyday Examples• Sea waves• Radio waves• X rays• Light• Sound• Seismic waves• Kallang Wave• Traffic Conditions (approx)

Waves

• Waves spreads disturbance from one place to another

• The source of any wave is a vibration or oscillation

• Waves transfer energy from one place to another without the physical transfer of the medium between the two points. (eg. People doing Kallang wave)

Types of waves

• Transverse

• Longitudinal

• Mechanical --

How does particles vibrate?

Is a medium necessary?

Waves in a string

Direction of wavequarter wave

half wave

three quarter wave

full wave

(one complete wave)

vibrating source

one complete vibration

No vibration

half vibration

Waves in a stringvibrating source

two complete vibration two waves

Particle Vibration

Period of vibration

It is a time taken for one complete vibration or oscillation.

Transverse Waves

wave direction

vibration of particle

Transverse waves are waves in which the particles of the medium move at right angle to the direction of wave motion.

Water waves are produced by the water particles’ vibration.

Cross-section of a water wave

crest crest crest

trough trough trough

Crest is referred to the top of the wave.

Trough is referred to the bottom of the wave.

Motion of particles in Transverse waveswave direction

main positionor rest position

Particles are moving perpendicular to the wave motion.

No forward motion of particles in the wave.

Motion of particles in a wavestarting upwards

particle first waveparticle in second wave

Motion of particles in a wave

starting downwards

particle first wave

particle in second wave

Wave direction

2nd wave

1st wave

Wave moves forwardsand particles either move up or down perpendicular to the wave direction.

Show the directions of the particles labelled with letters.

A

BC

D

E

FG

motion of wave

Show the directions of the particles labelled with letters.

motion of wave

A B

C

D

E

F

G

Amplitude and wavelength1 Amplitude :

Amplitude of a wave is the maximum displacement made by the particle from its rest position.

wave motion

amplitude

amplitude

rest positionamplitude

amplitude

Wavelength is the distance between two successive particles which are at exactly the same point in their paths and are moving in the same direction.

wavelength

wavelengthwavelength

2 Wavelength (λ ):

Q1 A transverse wave is travelling to the right along a rope. The diagram below represents a photograph of the wave pulse at a particular instant.

P Q

direction of wave motion

The movement of the particles P and Q at the instant will be

P QA downward downwardB upward downwardC downward upwardD upward upward

Q2 The diagram below shows the profile of a transverse wave. Which distance represents one wavelength?

A

B

C

D G

F HE

A BD B EF C EH D GH

Q3 The diagram shows a ball floating in a tank of water

direction of wave ball

Which diagram shows the movement of the ball when the wave passes?

A B C D

Wavelength is the length of one complete wave.

1 wave

wavelength

3 Period(T)

Period is the time taken for one complete vibration or oscillation.

Period of an oscillation is 1.5 s.

It means that 1.5 s is needed to complete one oscillation.

4 Frequency(ƒ):Frequency is the number of complete vibrations or oscillations per unit time.

or

Frequency is the number of complete waves leaving the wave source per unit time.

Unit for frequency:

The hertz (Hz)

1 Hz is one complete vibration or oscillation in second.

E.g. If a source produces 5 complete waves in second, the wave frequency is 5 Hz.

If a pendulum made 50 complete oscillations in 40 s what is its frequency?

frequency, ƒ =50

40 = 1.25 Hz

Relationship between frequency and period

Let T = period in s

ƒ = frequency in Hz

ƒ = 1T or

e.g. The period of a pendulum is 0.25 s what is its frequency?

T =1ƒ

5 Wave speed:Wave speed is the speed at which the waves move through the medium.

The frequency depends on the source;

The wave speed depends only on the medium the waves are travelling through.

Wave equation:If a source produces waves at a frequency of 5 Hz.

That is, it produces 5 complete waves per second.

If the wavelength of the wave is 2 m, the waves will move forward by 5 x 2 m in one second. Its speed is 10 m/s.

1 2 3 4 5

Wave speed = frequency x wavelength

Let v = wave speed in m/sƒ = frequency of the wave in Hz

λ = wavelength of the wave in m

v = ƒλ

The wave moves on 10 m in 1 s, its speed is 10 m/s

P

the particle in the wave which makes 5 oscillations in 1 sP :

wave motion

2 m 2 m 2 m 2 m 2 m

P

P :

P

wave motion

P

wave motion

the particle in the wave which makes oscillations in 1 s f

wavelengthsf

ƒ λ = distance moved by wave in 1 s

wave speed, v =distance moved by wave

time taken to move

v = f λ ( m/s )

=

f λ metre

1 s

Q4 A vibrator dipped into water in a ripple tank has a frequency of 6 Hz. The resulting wave has a wavelength of 0.02 m. What is the speed of the wave?

Q5 A surf-board moves at 5 m/s on the crest of a wave. The distance between wave crests is 10 m.What is the frequency of the wave motion?

Displacement - position graphdisplacement

position along

wave direction

(at a single moment in time, like a photograph)

wavelength

wavelength

wavelength

a

displacement

amean rest or

position position along

wave direction

a = amplitude

Wavelength and amplitude can be read from the graph.

Displacement - time graphdisplacement

time

a

a

period T

period T

period T

mean rest or

position

displacement

time

Period and amplitude can be read from the graph.

Frequency of the wave can be calculated from period read from the graph.

f = 1/T

Q6 The diagram shows the outline of a water wave.

5

+ 0.6

-0.6

15 250

displacement/cm

displacement/cm

What are the values of the amplitude and the wavelength?

Amplitude

Q7 The diagram shows how displacement varies with time as a wave passes a fixed point.

time/s

displacement/cm

01 32 4

0.05

0.1

-0.05

-0.1

What is the frequency of this wave?

period

Q8 The displacement-time graph of a wave travelling across water at a particular place with a velocity of 2 cm/s is shown in the diagram.

0.1 0.30.2 time/s

2

-2

displacement/mm

00.4 0.60.5

-1

1

What is the wavelength of the wave?

Q9 A VHF radio station broadcasts at a frequency of 90 MHz (9.0 x 107 Hz). The speed of radio waves is 3.0 x 108 m/s

What is the wavelength of the waves broadcast by the station?

Wavefront Pattern of Water waves

Particles along the lines are moving in the same direction and at the same position in the wave.

These lines are called wavefronts of the wave.

Wavefronts of water wave

wave directionWavefront is always perpendicular to the wave direction.

The Ripple TankRipple tank can be used to demonstrate reflection and refraction of wave.

to battery and rheostat

straight wave dipper

Eccentric motor

rubber band

lamphouse

water

white screen

How is a wave pattern formed on screen?

screen

bright line

light

The distance between the two bright lines is the wavelength of the wave.

incident wavefronts

reflected wavefronts

reflector

After reflection, there areno change of wavelength frequency and speed.

There is a change of direction of waves.

Wave energy decreases after reflection.

incident wavefronts

reflected wavefronts

reflector

incident ray reflected ray

reflector

Normal

i r

Construction of wavefront diagram

reflected wavefront

Ssource

ICentre of reflection

reflecting surface

Reflection of circular waves

reflected wavefront

Ssource

ICentre of reflection

reflecting surface

Construction of reflection of circular waves

S I

Centre of reflectionsource

reflecting surface

P

SP = IP

Reflection of circular waves

i = r

Q

R

Construction of reflection of circular waves

1 Draw a line from S perpendicular to the reflecting surface and extent the line.

2 Mark I on the line such that SP=PI.

3 Use I as a centre and IQ as a radius, draw an arc QR which is the reflected wavefront.

4 Repeat step 3 by increasing radius which is equal to (IQ + wavelength).

S I

Centre of reflectionsource

reflecting surface

reflected wavefronti r normal

P

r

Reflection of circular wavesreflected ray

reflected ray

λ1

Refraction of Waves in Ripple Tank

denser medium less dense

deep water

glass plate

2λ

glass plateshallow water

slowfast

From less dense medium to denser medium :

wavelength and speed decreasesFrom denser medium to less dense medium :

wavelength and speed increases

2nd medium

i r

normal

i

1st medium

λ1λ

2

Shallow water deep water

refracted wave direction

glass plate

When a wave travels from one medium to another medium with different densities.

no change in frequency

change in wave length and velocity.

Q10 A dipper moving up and down makes waves in a ripple tank. What will happen if the dipper frequency is increased?

A The wave peaks will be higher and the troughs lower.

B The waves will move more slowly across the tank.

C The waves will move more quickly across the tank.

D The waves will be closer together.

Refractive indexRefractive index of a medium =

=λλ

1

2

= cc

1

2

c1= speed in 1st medium;

c2= speed in 2nd medium

sin i sin r

λ 1= c1/f1 λ 2= c2/f2 f1= f2

λλ

1

2Refractive index of a medium =

From less dense medium to denser medium :

wavelength and speed decreasesFrom denser medium to less dense medium :

wavelength and speed increases

2nd medium

i r

normal

i

1st medium

λ1λ

2

Shallow water

i r

normal

i

deep water

refracted wave direction

Construction of refracted wavefronts

Angle of refraction is given.

1 Construct angle of refraction, r.

2 From the point of intersection of wavefront and the boundary, draw a line perpendicular to the reflected wave direction.

3 Repeat step 2 by using different points of intersection.

i

r

i

Q11 Which diagram below shows correctly how the water waves are refracted when they travel from the deep end to the shallow end?

A B C D

Q12 The diagram shows a ripple tank with two different depths of water separated by a boundary XY.A wave generator is producing straight waves as indicated.

The separation of the wave fronts is not drawn to scale, but the angles between the wave fronts and the barrier XY are as shown above. What is the ratio of the speed of the waves in deep water to their speed in shallow water?

35°52°

wave generatorX

Y

Facts about light1 Light waves are transverse.

2 Light waves carry energy.

3 Light waves are emitted and absorbed by matter.

4 Light waves can travel through both vacuum and some matter.

5 Light waves travel at 3 x 108 m/s.

6 Light waves can be reflected and refracted.

7 Light waves are part of electromagnetic spectrum.

8 Light also shows particle-like properties.

9 Light waves travel faster in less dens medium than that in denser medium.

H/wk 2

TYS, Topic 3.1

• P1: Q32,33,35,40,44.

• P2, Sect A: Q14,15;

Sect B: Q6,12.