how waves behave

7/28/2019 How waves behave

1/20

6

How wavesbehave

96

Energy is conservedNow that we have a general idea of what a wave is and its basic

characteristics, we need to look at wave behaviour in more detail and

define different ways of representing wave behaviour using various

graphical methods.

We start with the fundamental principle of energy conservation.

This supports the entire discipline of physics (and was discussed

earlier in Section 4.4). The amount of energy in the universe is fixed,

so energy can be neither created nor destroyed. However, energy

may change from one form into another (energy transformation).

Waves are carriers of energy, and so they must be taken

into account when applying the principle of energy

conservation to systems in which waves are present.

6.1 Energy and wavesLet us consider a sound wave produced by a speaker in a science laboratory.

The speaker cone vibrates, pushing the air particles around it. The sound waves

propagate outwards in three dimensions from the speaker. They travel through

the air and eventually strike the walls, floor, windows and ceiling of the laboratory.

Let us look at this process from the point of view of energy. The energy used

to power the speaker is electrical energy, which is transformed into kinetic energy

as the speaker diaphragm wobbles back and forth. The kinetic energy is

transferred into the air particles in the room as the sound wave travels away from

the speaker. The energy spreads out into an increasing volume of space as the

wave propagates outwards from the speaker. Some energy is converted into heatin the speaker and the air. When the sound wave reaches aboundary, such as

the surface of a wall, some of the wave energy bounces back (is reflected), part of

it passes through (is transmitted) into the new medium and some of the energy is

lost as heat in the new medium (absorbed).

energy transformation, boundary,

intensity, inverse square law,

superposition, interference, phase,

constructive interference,

destructive interference, fixedboundary, free boundary, wave front,

ray, reflection, refraction, absorption,

law of reflection, incidence, normal


2/20

THE WORLDCOMMUNICATE

loudmusic

Figure 6.1.1 Your parents can also enjoy the music you play in your bedroom. Some sound energyis reflected and some is absorbed; however, unfortunately for your parents, some

sound energy is transmitted through the walls and door.

If you stand next to the speaker, the sound is loud; as you move away, the

volume decreases. Outside the room, you can still hear the sound but it is much

softer and probably muffled (Figure 6.1.1). This is because the energy that

reaches your ears decreases as you move away from the source of the sound wave.

There are three main reasons for this decrease in energy with distance.

The first reason is that some of the original kinetic energy from the speaker

diaphragm is converted into other forms of energy by the media it travels

through. Some is dissipated (absorbed) as heat by the air molecules and the

materials that make up the floor, walls and ceiling. The second reason is that not

all of the sound wave makes it out of the room as some of it is reflected back

inside. The third reason is the inverse square law, which is discussed below.

So as a wave travels from its oscillating source, the energy carried by the wavedecreases; however, as the energy of the system must be conserved, we can account

for the apparently missing energy by considering the absorption and reflection of

energy at boundaries. Mathematically this can be represented as follows:

Ewave=Etransmitted+Ereflected+ Eabsorbed

The energy of a wave is proportional to the waves amplitude squared.

In sound waves, the amplitude is related to the volume (loudness) of the sound;

in light waves, it is related to the brightness of the light.

Ewave amplitude2

But even if the wave were to travel through a perfect medium, which doesnt

absorb and dissipate the wave energy as heat, the sound volume (or even lightbrightness) decreases as you move away from the source. The rate of energy

transfer by a source of waves through a given area is called the waves intensity.

Intensity is measured in watts per square metre (W m2). The rate of energy

transfer is called power, so wave intensity can be described using the following

equation:

Intensity=energy

time areaor Intensity=

power

areaor I=

P

A

Explain that the relationship

between the intensity of EM

radiation and distance from a

source is an example of the

inverse square law:

I1

2d.


3/20

How wavesbehave6 H wavessbb hav

98

The energy density, and so the intensity, of a wave will decrease as you

move away from the source. Exactly how the intensity varies can be complicated

by many factors. The source, like a speaker, may mainly transmit the wave in one

direction and obstacles in the waves path may cause reflections and absorptions

of the wave energy. However, in the simplest case in which we assume that the

wave is transmitted uniformly in all directions with the mechanical energy

conserved as it spreads and we can ignore reflections and absorption, we can usethe inverse square lawto describe the variation of intensity with distance.

In this ideal case, all of the energy emitted by the source must pass through

the surface of a sphere with radius dmetres (Figure 6.1.2). The area of this

sphere will be 4d2, and the intensity of the wave at a point dmetres from the

source is given by the equation:

I=P

d4 2

d1 d

2

Figure 6.1.2 Energy produced by the speaker passes first through the surface of a sphere of radius d1,and then that same energy passes through the surface of the larger sphere of radius d2.

The equation below tells us that the intensity of a uniformly transmitted

wave with no mechanical energy loss decreases with the square of the distance d

from the source.

I12

d

In most cases, mechanical waves such as sound waves and water waves cannot

be accurately modelled using the inverse square law because energy is dissipated

as heat by the particles in the medium that the wave travels through. However,

electromagnetic (EM) waves do not require a medium to propagate and in airthere are practically no energy losses, so the inverse square law will predict

intensity levels for EM waves with high accuracy. For this reason, astrophysicists

use the inverse square law to compare and identify stars as there is little or no

energy loss in the vacuum of space.

Activity 6.1

PRACTICALEXPERIENCES

ActivityManual,Page48


4/20


Worked example

QUESTION

The Sun produces EM waves that propagate through space to the Earth. The Sun has a

power output of 3.86 1026 W.

a Calculate the intensity of the Sun as seen from Earth. (d= 149 597 900 km)

b How does this compare with the intensity of the Sun seen from Jupiter,approximately 5 times the distance away?

SOLUTION

a Calculate the intensity, given that P= 3.86 1026 W and d= 149 597 900 km.

Convert all units into SI units: d= 149 597 900 1000 m.

I=3 86 10

26.

W

4 (149 5 97 900 1000) m2 2

=

P

4d2= 1372.5 W m2

The intensity at the Earth is 1370 W m2 (to 3 significant figures).

b Assume the distance from the Sun to the Earth is dmetres. Then the distance from

the Sun to Jupiter is 5dmetres. Therefore IEarth

1

2dandI

Jupiter

1

(5d)2 25d2

1,

sothe intensity at Jupiter will be1

25or 4% the intensity at Earth.

Figure 6.1.3 Sunset on Mars. Mars is3

2times further from the Sun than the Earth, so the setting

Sun appears2

3of the size on Earth and its intensity is

4

9that received on Earth.

CHECKPOINT 6.11 Outline five different energy transformations that can occur as light waves propagate from a source in a

science laboratory.

2 If the distance from a light source is tripled, what happens to the intensity of light as viewed from each point?


5/20


100

6.2 SuperpositionThe concept of a wave was introduced in Chapter 5 as a vibration that transfers

energy from one place to another. The simplest mathematical representation of

waves are sine waves (y= sinx), and more complicated waves can be thought of

as combinations of different sine waves.This mathematical representation is very convenient and useful for physicists

in modelling and predicting wave behaviour. The ability to add different sine

waves together to model any complex wave situation arises because of a

fundamental property of wavessuperposition. Superposition is one important

property that distinguishes wave behaviour from particle behaviour.

Superposition is the amazing ability of two or more waves to combine

at the same point in space at the same time. Or to put it another way, the net

disturbance at any point in a medium is simply the sum of the separate waves

present. The superposition principle, which is a fundamental characteristic of

waves, was proposed by English physicist Thomas Young (17731829) in the

early nineteenth century (Figure 6.2.1).

This is simple to say and may notseem earth shattering, but consider what

would happen if we were to attempt

superposition with particles instead of

waves. Consider two tennis ballsit is

not physically possible for both tennis

balls to exist in exactly the same place at

exactly the same time (Figure 6.2.3). Try

it for yourself.

Now take two wavessay, crossed

beams of light from two torches (Figure

6.2.4). These waves can exist in exactly

the same place at exactly the same time

and when they do, they combine (or

superimpose) to make a more complex

wave. When the waves move past this

meeting point, they emerge as the

original uncombined light beams.

The powerful significance of this

property of waves may escape you as it is

difficult to conceptualise waves when we

are so accustomed to a particle world. Just imagine for a moment that the tennis balls

in our previous example could superimpose like waves, what would this look like?

The incoming tennis balls would meet and combine into a larger, probablyoddly shaped tennis ball. Then after the meeting place they would emerge as

single tennis balls again, indistinguishable from the original incoming balls

(Figure 6.2.5). There is also a more mathematical interpretation of the principle

of superposition, which is discussed in Section 6.4.

The term interference is used to describe the change in waves that occurs as

a result of superposition. The size and shape of the superimposed waves depend

on the amplitude, wavelength and frequency of the original waves. It also

depends on an additional wave propertyphase.

Describe the principle

of superposition.

THOMAS YOUNG

Thomas Young is considered to

be the father of physical optics

for his championing of the wave

theory of light and his explanation

of superposition. He was also a

talented linguist, learning Persian,

Arabic and Turkish. He used these

skills to translate some Egyptian

hieroglyphics using the Rosetta

Stone (Figure 6.2.2).

Figure6.2.1ThomasYoung

Figure 6.2.2TheRosettaStone

Figure 6.2.3 Two tennis balls unsuccessfullytry to occupy the same point in

space at the same time.

Figure 6.2.4 Light from two torches combinewhen they occupy the same

point in space at the same time.

Figure 6.2.5 Imaginary superposition oftwo tennis balls


6/20


1

6.3 PhasePhase is the key to understanding how waves superimpose and interact with

media and boundaries. Waves displace the particles of the media they travel

through. Let us consider one particle in the medium. Sometimes the particle is

displaced a maximum positive amount (crest) from its original position, sometimes

it is displaced a maximum negative amount (trough) and sometimes it is in its

original position (equilibrium). This means a particle is displaced by the wave in

a regular cycle: crest equilibrium trough equilibrium crest and so

on. The phase of a wave can be thought of as a label for the part of the

cycle that the particle is undergoing at a given time.Since we are using a sine function such asy= sin (x) to represent our wave,

the simplest way to label which part of the cycle the oscillating particle is in is to

state the value in brackets (x) (mathematically speaking, the argument). Since

the sine function comes traditionally from trigonometry, this value (the phase) is

normally given in angle units, such as radians or degrees; however, the phase is

not really an angle, just a mathematical label (Figure 6.3.1).

The idea of phase is easier to grasp when we think of the phase of two waves

relative to each other. If two waves cause a particle to be displaced the same

direction at the same time, they have a phase difference of 0 and are said to be

in phase. If the phase difference is 180 or radians, the waves are said to be

exactly out of phase (Figure 6.3.2).

Waves in phase Waves exactly 180

out of phase

Waves out of phase by

approximately 90

Figure 6.3.2 Waves in and out of phase

CHECKPOINT 6.31 Draw a diagram of two waves that have equal amplitude and frequency but are out of phase by 270 or

3

2

radians.

PHASE AND THEWAVE EQUATION

We have been using a very

simple equation, y= sin (x),

to describe wave behaviour. A more

powerful and useful description

requires a function that relates

horizontal displacement (x),

vertical displacement (y) and time

(t), and contains all the important

properties of that wave:

y A x ft= sin( )2

2

where A is the wave amplitude,

is the wavelength and fis

the frequency.

When using this equation to

describe a wave, the phase ()

of an individual wave is the

argument of the sine function:

= 2 2

x ft

CHECKPOINT 6.21 Define the concept of superposition.

2 Identify two properties common to both particles and waves.

Amplitudeoftheparticle

0 45 90 135 180 225 270 315 360

0 2 P32

2P

Deg

Rad

Phase (in degrees and radians)

P

Figure 6.3.1 The particle at point Phas a

phase of 45 or

4radians.


7/20


102

6.4 The superposition of wavesHere is a more mathematical interpretation of the superposition principle. It says

that when two waves cross the same part of space at the same time, the resulting

wave is simply the mathematical sum of the two original waves.

We can use a graphical method for superimposing two waves in sine form.We plot the waves on the same axes, accurately recording the amplitude, frequency

and phase. Then moving from right to left, at every value ofxwe simply add the

corresponding heightstheyvaluesof the two sine waves. When adding the

heights, remember that theyvalues above the axis are positive and those below

the axis are negative (Figure 6.4.1).

1.5

1.0

0.5

0

0.5

1.0

1.5

0 90 180 270 360

Phase ()

Amplitude(m) w1

w2

ws

Figure 6.4.1 Two sinusoidal waves (w1 and w2) with different amplitudes and frequencies travelfrom left to right. The waves superimpose to give the resultant wave w

s.

This procedure can be carried out for any two waves. However, two special

cases emerge when superimposing waves of the same frequency and amplitude

(Figure 6.4.2). If we superimpose two such waves that are in phase, we see

a resulting maximum disturbance in the medium; to be exact, the resulting wave

will have double the amplitude of either of the original waves. This is called

constructiveinterference. If we superimpose two waves that are exactly

180 out of phase, we see a resulting zero disturbance in the medium. The waves

cancel each other out completely, the resulting amplitude is zero and so no

oscillation of the medium is observed. This is called destructive interference.

w1

w2

ws

w1

w2

ws

Constructive interference

Destructive interference

Figure 6.4.2 Two identical sinusoidal waves(w1 and w2) travel from left to

right. They superimpose to give

the resultant wave ws.

Constructive interference

occurs when the phase

difference is 0 (0 radians),

and destructive interference

occurs at 180 ( radians).


8/20


1

Adding two waves together using a graphical method is relatively

straightforward, but adding three or more waves together in this way becomes

extremely time-consuming. A mathematical technique called Fourier analysis and

synthesis allows multiple waves to be added quickly and easily. For example,

electronic music and voice recognition software use Fourier analysis and synthesis

to add and subtract sound waves to create and recognise a wide variety of sounds

(See Physics Feature Beautiful mathematics and electronic music on page 104).When waves reflect from a boundary between two media, the phase of the

reflected wave depends on the nature of that boundary. There are two types:

fixed boundaries or free boundaries (Figure 6.4.3).

A fixed boundary has particles that are unable to oscillate, an example of

which would be a rope tied securely to a wall. If you wiggle the free end of the

rope, a transverse wave will travel down the rope towards the fixed boundary at

the wall. The wave will then be reflected from that boundary. The reflected wave

will be exactly out of phase with the original wave. This is because the rope is

tied at the wall and must always have a displacementy= 0 at that point. While

they overlap, the original wave and its reflection can be thought of as two

interfering waves. Any overlapping waves must superimpose to give zero

displacement at the wall. This can only occur when the original and reflectedwaves are exactly out of phase (phase difference of 180).

In a free boundary the particles in the adjacent media are free to move, so

waves transmitted through or reflected from free boundaries have the same phase

as the original wave.

Reflection from a fixed boundary Reflection from a free boundary

a b

Figure 6.4.3 (a) Waves are reflected from a fixed boundary exactly out of phase; (b) a freeboundary reflects the wave in phase.

Activity 6.2



DESTRUCTIVECAN BE USEFUL

In some factories where loud,

repetitive noise is a problem,

workers can wear special

headphones that sample the

surrounding noise and then

replay into the workers ears a

copy of this noise with exactly

the same amplitude but exactly

180 out of phase with it. The

result is destructive interference,

which means no noise reaches

the workers ears. This is called

anti-phase noise reduction.

However, since this effectdoesnt work very well with non-

repetitive noise such as human

speech, the workers are still able

to hear co-workers talking.


9/20


104

PHYSICS FEATURE

BEAUTIFUL MATHEMATICS AND

ELECTRONIC MUSIC

The French mathematician Jean Baptiste Joseph,

Baron de Fourier (17681830) devised a

beautiful mathematical technique for synthesising a

waveform of any shape imaginable. His theory states

that any wave with a spatial frequency of fcan be

synthesisedby a sum of harmonic waves with

frequencies f, 2f, 3f, 4fand so forth. Any wave can

be thought of as a result of the addition of

overlapping sine and cosine waves.

Consider the example shown in Figure 6.4.4. The

waveform in Figure 6.4.4a is the result of combining

the six sine waves in Figure 6.4.4b. These six sinewaves with different frequencies are called the

harmonics. The frequency of the resultant wave has

the same frequency as the first harmonic (f1). The

harmonics can be illustrated using a spectrum graph

like Figure 6.4.3c. This plots the amplitude of the

harmonic versus the frequency.

Electronically synthesised music utilises the

mathematics of Fourier. An audio engineer

programming an electronic synthesiser keyboard, for

example, would use a signal generator to produce the

harmonic sine waves. By manipulating the amplitudes,frequencies and phases of these sine waves, the

desired sound can be selected. Similarly, a natural

sound can be copied and electronically reproduced.

The waveform of the natural sound is analysed to

determine its harmonics, which can then be easily

reproduced using a signal generator and synthesised

when required.

a

b

f1

f2

f3

f4

f5f6

Harmonics

f1 f2 f3 f4 f5 f6

Frequency

Amplitude

c

Figure 6.4.4 (a) The synthesised waveform; (b) the six componentharmonics of (a); (c) a spectrum graph of the harmonics

CHECKPOINT 6.41 What phase difference is required for two waves to destructively interfere?


10/20


1

6.5 Diagrams used to describe wavesIn addition to the equations and graphs we have been using to describe wave

behaviour, it is common to use two additional diagramswave fronts and

raysto illustrate wave behaviour in media and at boundaries between media.

Waves originate from an oscillating source. We imagine for simplicity that thesource is tiny, called a point source. In Figure 6.5.1, transverse waves move out in

two dimensions from the oscillation caused by a tiny vibrating source. If we draw

a line joining the peak of each of these transverse waves, we have constructed a

wave front. A wave front is therefore an imaginary line that joins points of

equal phase. The concentric circular lines (ripples) that you see on the disturbed

surface of a pond are wave fronts.

For waves that propagate in three dimensions, the wave front would be a

spherical surface joining points of equal phase. The distance between two

adjacent wave fronts is one wavelength. Wave fronts that are closer to a source

appear more curved. As the wave travels a large distance from the source, the

wave fronts appear as parallel lines (called plane waves). A wave of a fixed

frequency travelling through a uniform medium will have wave fronts of equalspacing. The greater the frequency, the closer the spacing of the wave fronts.

Superposition is illustrated by overlapping wave fronts (Figure 6.5.2). Where

the wave fronts overlap, we have two waves combining with the same phase. At

this point there would be constructive interference.

Figure 6.5.2 Overlapping ripples from two disturbances on a water surface. The ripples are wavefronts, and superposition of the two waves occurs where two wave fronts overlap.

An imaginary line drawn perpendicular to a wave front in the direction

of propagation is called a ray (Figure 6.5.3). The ray is simply a line that points

in the direction that the wave front is moving. Rays are commonly used to show

the path of light through an optical system. Unlike wave fronts, rays do not giveany information about the wavelength or frequency of the wave.

CHECKPOINT 6.51 Define the terms wave frontand ray.

2 How does a wave front diagram give information about the wave frequency or wavelength?

Activity 6.3



Waves are emitted in all directions

from the light source.

An imaginary line drawn that joins points

of equal phase is called a wave front.

Figure 6.5.1 Constructing wave fronts fortransverse waves

Figure 6.5.3 A ray is drawn perpendicularthe wave front and shows the

direction of wave propagatio

wave fronts

ray


11/20


106

6.6 Wave reflection and refractionAt the beginning of the chapter, we discussed the energy of a wave and what

happens at the interface between two media (a boundary). When a wave

encounters a boundary three things happen (Figure 6.6.1):

1 Part of the wave energy bounces off the interface and travels back into theoriginal mediaknown as reflection.

2 Part of the wave energy continues into the new mediaknown as

transmission or refraction.

3 Part of the wave energy is transferred to particles in the media as heat

known as absorption.

incident

refracted

reflected

Figure 6.6.1 Parallel light wave fronts incident on a surface (such as a piece of glass). Some ofthe light is reflected from the surface and some is refracted.

REFLECTINGHISTORY

The law of reflection was first

described by the Greek

mathematician Euclid in the

book Catoptrics, dated

approximately 200 BC. Catoptrics

is an ancient Greek term that

means reflection. The firstwritten description of a reflective

surface, a womans looking glass,

appears in Exodus 38 : 8, dated

approximately 1200 BC.

Figure 6.6.2 Anearlydepictionofa reflective

surfaceinart.Thisstone relief

is from the sarcophagusof

QueenKawitandshowsher

holdinga mirror, dated

approximately2061BC.


12/20


1

ReflectionThe behaviour of reflected waves is described by the law of reflection.

This law states that the angle ofincidence equals the angle of reflection.

The angle of incidence (i) is the angle made by the incoming (incident) wave

front and the boundary. The angle of reflection (r) is the angle made by the

outgoing (reflected) wave front and the boundary (Figure 6.6.3). Therefore:

i=r

If a wave is normally incident on a boundary, then i=r= 0 and the wave

reflects back on itself.

A B

A B

A B

A B

mirror surface

mirror surface

mirror surface

mirror surface

Incident wave front

just reaching mirror

Reflected wave front

just leaving mirror

i

i

r

ir

r

a c

b d

Figure 6.6.3 The incoming (incident) wave front makes an angle of i with the reflective surface.The reflected wave front makes an angle of r with the mirror. The law of reflection

says i=r.

Wave front diagrams can quickly become cluttered, so it is usual to represent

the same concept concisely using rays (Figure 6.6.4). A large number of wave

fronts are replaced by an incident and reflected ray. The angles of incidence and

reflection are measured relative to the normal, which is a line drawn

perpendicular to the boundary.

incident ray reflected ray

normal

N

i r

Figure 6.6.4 Reflection of a wave using a ray diagram. The incident and reflected rays make anangle of i and r respectively, relative to the normal (N ).

Describe and apply the law of

reflection and explain the

effect of reflection from a pla

surface.


13/20


108

RefractionImagine that a surf lifesaver is running up the hard sand near the water and is

then continuing on into the soft sand. As the medium changes from hard sand

to soft sand, the surf lifesaver slows down as it is harder to run in soft sand.

In the same way the speed of a wave changes as it moves from one

medium into another. If the wave encounters the boundary at an angle

(i 0), the wave fronts bend as they cross the boundary. This bending ofwaves across boundaries is called refraction. (See Figures 6.6.5 and 6.6.6.)

medium 1

a b

medium 2 medium 1 medium 2

i

i

r

r

vi

vi

vr

vr

i = 0

i

Figure 6.6.6 The wave slows down as it enters the second medium and so the wave fronts becomemore closely spaced. (a) The wave front is normally incident on the boundary (i= 0).

(b) The wave front encounters the boundary at an angle (i 0).

The bending is also evident when the waves path is represented by rays, as

shown in Figure 6.6.7. The incident ray travelling through medium 1 makes

an angle i (angle of incidence) with the normal, and the refracted ray through

medium 2 makes an angle ofr (angle of refraction) with the normal. If the

wave slows down on entering the new medium, the ray bends towards the normal

(i

>r

). If the wave speeds up the opposite occurs: the ray bends away from the

normal (i


14/20


1

The degree to which a wave is refracted depends on the properties of the

media. The physical state, density, crystal structure and temperature of a

substance will affect the speed of the wave through that substance. The speed

of light waves is changed by the refractive index (n) of a substance, while the

acoustic impedance (Z) of a substance changes the speed of sound waves.

TRY THIS!MARCHING TO ILLUSTRATE

REFLECTION AND

REFRACTION

Link arms with some friends to

form a wave front. March in time

at the same speed. Reflect

yourselves from a flat surface,

such as a wall. As each person

reaches the wall, march backwards

at the same speed. Try this first

with the wave front parallel to the

wall and then at an angle. Then

reflect yourself from a curved

surface, like a curved gutter or

garden bed edge. You will see the

wave front shape change. To refract,

the marching speed needs to change as you change medium.Try marching from concrete onto grass. As the medium

changes, halve your speed. The wave front will bend if you

approach the boundary at an angle.

wall grass

concrete

Figure 6.6.8 (a) Students are reflected from the wall by marching backwards. (b) Studentsare refracted across the boundary by changing marching speed.

CHECKPOINT 6.61 Describe the law of reflection.

2 Define the concept of refraction.

a b


15/20

6 PRACTICALEXPERIENCES

110

CHAPTER 6This is a starting point to get you thinking about the mandatory practical

experiences outlined in the syllabus. For detailed instructions and advice, use

in2 Physics @ Preliminary Activity Manual.

ACTIVITY 6.1: MODELLING THE INVERSE SQUARE LAWUse a light probe attached to a data logger or hand-held meter to measure light

intensity at different distances from a source.

Equipment list: a bright light source (lamp), light-sensitive probe or meter,

data logger, computer, tape measure.

metre ruler

photocell

light

source

light

sensorto computer

Figure 6.7.1 Experimental set-up for measuring light intensity at different distances

Discussion questions

1 Describe the relationship between light intensity and distance using the

data collected in this investigation. How does it compare with the inverse

square law?

2 Identifya possible source of experimental error in this investigation. What

strategies could you use to reduce the impact of the experimental error?

ACTIVITY 6.2: SUPERPOSITION OF WAVESUse a cathode ray oscilloscope (CRO) or computer program to observe the

superposition of pulses and waves.

Equipment list: cathode ray oscilloscope, 2 signal generators, graph paper,

computer.

256 Hz

256 Hz

signal

generator

signal

generator

cathode ray oscilloscope (or computer)

Figure 6.7.2 An oscilloscope connected to two signal generators

Plan, choose equipment or

resources for and perform a

first-hand investigation, and

gather information to model the

inverse square law for light

intensity and distance from a

source.

Perform a first-hand

investigation, gather, process

and present information using

a CRO or computer to

demonstrate the principle of

superposition for two waves

travelling in the same medium.


16/20


1


1 Explain the importance of phase difference to the superposition of two

waves with the same frequency and amplitude.

2 Describe the characteristics of the resultant wave when two waves of

different frequencies are superimposed.

ACTIVITY 6.3: WAVE FRONTS AND RAYSUse a light box and a variety of reflective surfaces to observe the reflection of light.

Draw accurate ray and wave front diagrams to show light reflection from plane,

concave and convex surfaces.

Equipment list: transformer, light box, plane mirror, concave mirror, convex

mirror, pencil, ruler, blank paper, protractor.

light box

plane mirror

convave and convex mirrors

Figure 6.7.3 A light box and reflective surfaces


1 Explain how the shape of the reflective surface changes the shape of the

reflected wave front. Refer specifically to the law of reflection.

2 Describe the parts and function of the light box and explain how it

approximates a source a large distance away.

Perform first-hand

investigations and gather

information to observe the pa

of light rays and construct

diagrams indicating both the

direction of travel of the light

rays and a wave front.

Present information using ray

diagrams to show the path of

waves reflected from:

plane surfaces

concave surfaces

convex surfaces.


17/20

6 How wavesbehaveH waveseb ah v

112

Chaptersummary Energy is conserved in all systems.

Ewave=Etransmitted+Ereflected+Eabsorbed The energy of a wave is proportional to the amplitude

squared.

Intensity is defined as the rate of energy transfer

through a given area. It is measured in watts per square

metre (W m2). The intensity of a wave decreases with the square of the

distance from the source I12

d.

Superposition is a property that distinguishes waves

from particles.

The net disturbance at any point in the medium is the

sum of separate waves present.

The superimposed (or net) wave depends on the

amplitude, wavelength, frequency and phase of the

original waves.

Phase is the point in the cycle that an oscillating

particle is up to at a given time. Phase is a dimensionless quantity given as an angle in

degrees or radians.

Waves are in phase if the phase difference is 0 or

0 radians.

Waves are out of phase if the phase difference is

180 or radians.

The superposition of two waves in phase results in

constructive interference.

The superposition of two waves out of phase results in

destructive interference.

A wave front is an imaginary line joining points ofequal phase.

Wave fronts close to a source appear curved; at large

distances, they are parallel (called plane waves).

The distance between two adjacent wave fronts is

one wavelength.

A ray is an imaginary line drawn perpendicular

(at 90) to a wave front. The ray points in the direction

of propagation.

The law of reflection states that the angle of incidence

equals the angle of reflection (i=r).

A wave changes speed as it moves from one medium to

another. This is called refraction. Refraction causes wave fronts and rays to bend as they

cross the boundary from one medium to another.

The degree to which a wave is refracted depends on the

properties of the media.

PHYSICALLY SPEAKINGCreate a visual summary for the concepts in this chapter using a mind map.

1 Copy the table containing words, diagrams and equations.

2 Cut along the dotted lines so that you have 21 separate boxes.

3 Group related boxes together.

4 Stick the groups of boxes onto a sheet of blank paper.

5 Connect boxes with labelled links to form a mind map.

Amplitude Phase Wavelength

Constructive interference Ray I1

2d

Destructive interference Reflection i=r

Distance Refraction

Energy Superposition

Frequency Wave

Intensity Wave front

Reviewquestions


18/20


1

REVIEWING 1 An aquarium has a light on top of the tank, as shown in Figure 6.7.4.

Draw and label the diagram to illustrate what happens to the energy of

the light waves as they propagate into the tank.

light

air pump

fish tank

Figure 6.7.4 An aquarium

2 The amplitude of a wave is doubled. Are the following statements trueor false?

a The wave frequency also doubles.

b The wave period also halves.

c The wave energy also quadruples.

d The wave speed also doubles.

3 Complete the table to show the relationship between intensity and distance.

DISTANCE d 2d 3d 4d 5d1

4d

1

2d

1

2d

INTENSITY I

4 Complete the table to show the relationship between degrees and radians.

DEGREES 30 90 180 270

RADIANS 0

4

32

5 Draw the rays corresponding to the wave front diagrams.

a b


19/20

6 How wavesbehaveH waveseb ah v

114

6 Draw the wave fronts corresponding to the ray diagrams.a b

7 Draw the wave fronts and rays as the wave is reflected from the boundary.

incident ray

mirror35

8 Draw the wave fronts and rays as the wave slows down on entering thenew medium.

medium 1 medium 2

normal

9 Samuel draws a ray diagram of a light beam reflecting from a planesurface. Use Samuels diagram to determine the angle of incidence and

the angle of reflection.

normal

mirror65


20/20


SOLVING PROBLEMS10 A pulse is produced in a string of initial amplitude 35 cm. After the pulse

has travelled 1 m, its amplitude is 7 cm.

a Calculate the percentage of the original energy carried by the pulse

1 m from the source.

b Calculate the percentage of the original energy that has been lost.Can you account for the missing energy?

11 Helen purchases two light bulbs with power ratings of 40 W and 80 W.How far must she stand from the 80 W bulb so that it appears to have

the same intensity as the 40 W bulb?

12 Star A is twice as far away as Star B, but they generate the same light

intensity. Which star appears brighter and by what factor?

13 Stars C and D are both at a distance of 15 parsecs from Earth, butstar C is nine times brighter than D in the night sky. At what distance

would star C have to be in order to appear to be the same brightness as D?

14 A scuba divers underwater microphone detects a whale call 50 m awaywith an intensity of 0.47 mW m2. Another scuba diver is 1 km away at

another dive site. What will be the intensity at that distance? Ignoreabsorption losses.

15 Use graph paper to accurately reproduce these waves. Use the graphicalmethod to superimpose the waves and find the net disturbance.

a b

c d

Present graphical information

solve problems and analyse

information involving

superposition of waves.1.5

1.0

0.5

0

0.5

1.0

1.5

1.0

0.5

0

0.5

1.0

1.5

1.0

0.5

0

0.5

1.0

1.5

1.0

0.5

0

0.5

1.0

how waves behave

Documents