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Waves

EnergyPowerForce

mobile telephonemicrowave ovensatellitesradioTVspace explorationdigital electronicsanaloguelaserlensfax

refractionreflectionaccelerationvibrationoscillationbeatspolarisationinterferenceinductiontravellinginductionmotion

soundlightmicrowavesradioTVIRUVradiationgammaseismicemplightP-waveS-wavespectrumparticlemechanicalX-rayswatertsunamisonicultrasoundrainbow

Wavescresttroughpulsewavelengthtransverselongitudinaltorsionalhertzpitchamplitudefrequencycompressionrarefactionvelocityrefractive indexdestructiveconstructivecolourdensitytensioncoherentresistancematter

beachdrinkgoodbyeMexicanHawaii Five-OBillabonghairwave machinetravelpipeline

heat wavemagnetismgravityMoonplasmafireShark Islandstrengthsets

mobile telephonemicrowave ovensatellites radio TV space exploration

soundlightmicrowavesradioTVIRUVradiationgammaseismicemplightP-waveS-wavespectrumparticlemechanicalX-rayswatertsunamisonicultrasoundrainbow

EnergyPowerForce

cresttroughpulsewavelengthtransverselongitudinaltorsionalhertzpitchamplitudefrequencycompressionrarefactionvelocityrefractive indexdestructiveconstructivecolourdensitytensioncoherentresistancematter

heat wavemagnetismgravityMoonplasmafireShark Islandstrengthsets

refractionreflectionaccelerationvibrationoscillationbeatspolarisationinterferenceinductiontravellinginductionmotion

beachdrinkgoodbyeMexicanHawaii Five-OBillabonghairwave machinetravelpipeline

Waves

laser lensfax

digital electronics analogue

Waves carry energy

microwaves cook food

x-rays can damage DNA molecules in living cells

earthquake waves can knock down buildings

ultrasound waves can warm human flesh

sound waves can make small objects move

water waves can move even massive ships

Light is a wave and light is a form of energy

plants use light energy to carry out photosynthesis

light energy is converted to electrical energy by a solar cell

light energy produces chemical changes on a photographic film

light energy changes silver chloride to silver and chlorine gas

light energy activates activates a semiconductor device called a charge

coupled device (CCD) to produce electrical signals upon which the

operation of video and digital cameras depends

What are waves?

WavesWave motion is the result of a periodic disturbance of a medium, or of space, by some form of vibration (or oscillation) which transmits energy away from the oscillating source of the wave.

Waves are Everywhere

• sound waves• water waves• light• radio waves• microwaves• seismic waves• x-rays• uv rays

Waves in every dimension

• The energy of a waves may spread out as a disturbance in

– one dimension

– two dimensions

– three dimensions

One dimensional waves

• One dimensional waves include

– waves in a stretched rope or string, such as a guitar

– waves in a slinky™

The Nature of the Medium and the Wave

• Waves in a slinky™– Movement of the medium occurs in more than one dimension

– The energy propagates only along a line - one dimensional


• Energy moves in one dimension in the case of– a wave travelling along a string on a string instrument (guitar)– a sound wave confined to a long, narrow tube (didgeridoo)– a sound wave in a musical instrument like a flute

• Demonstration– Lwave.mov or Lwave.avi

• Waves can spread in out in a two dimensional manner

– waves on the surface of water

– the skin on a drum

– human eardrum

– Some loudspeakers


• Waves can spread in out in a three dimensional manner

– Light from a lamp or candle

– Sound from any sound source in air

– Microwaves from a mobile telephone

– Television signals from a TV transmitter

– Light from the Sun


All waves have in common a source of energy, which involves vibration of some sort – the rate

of the vibration, measured in hertz (Hz) (on hertz is one cycle or vibration per second) is called the frequency

a means by which the energy can propagate outwards away from the source as a vibration – the rate at which the wave travels away from the source is called the speed or velocity of the wave and is measured in metres per second (ms–1) in the SI system of units

the transformation of energy from one form to another a transfer of energy from one place to another

Properties of waves

Properties of WavesTransverse Waves

displacementmedium

crest

trough

Properties of Wavesamplitude

wavelengthfrequency

speed

Quantities and Units

The speed or velocity of the wave and is measured in metres per

second (ms–1)

The wavelength of a wave is measured in metres (m)

Measuring properties of waves

Quantities and Units

The rate of the vibration of a wave is called the frequency and it is

measured in hertz (Hz) one hertz is one cycle or vibration per second

Measuring properties of waves

The Wave EquationThe wave equation relates three properties of waves

Frequency (f) Velocity (v) Wavelength ()

The Wave Equation

v f

Write down the frequency of your favourite radio stationWrite down the frequency of your favourite radio station

Radio waves travel at 300 000 km/sRadio waves travel at 300 000 km/s

Calculate the wavelength of these radio wavesCalculate the wavelength of these radio waves

If the station is FM (is there anything else?), then the number you’ve If the station is FM (is there anything else?), then the number you’ve written is most probably the frequency in megahertz (MHz)written is most probably the frequency in megahertz (MHz)One megahertz is one million (10One megahertz is one million (1066) hertz) hertzE.g. 105.7 MHz = 105.7 x 10E.g. 105.7 MHz = 105.7 x 1066 = 1.057 x 10 = 1.057 x 1088

In a calculation, the speed, 300 000 km/s, must be converted to m/s.In a calculation, the speed, 300 000 km/s, must be converted to m/s.The speed of radio waves, and all other forms of electromagnetic The speed of radio waves, and all other forms of electromagnetic waves in air and in a vacuum is 3 x 10waves in air and in a vacuum is 3 x 1088 m/s. m/s.

There are two major categories of waves

• Mechanical Wavesrequire a physical substance or medium in which to travele.g sound waves, water waves

• Electromagnetic Wavesdo not require a physical medium in which to travele.g. light, radio and TV waves, x-rays

Electromagnetic Waves


(m)

Transverse and Longitudinal Waves

• TRANSVERSE WAVESThe particles vibrate perpendicular to the direction in which the wave is travelling.Surface water waves are transverse waves.

• LONGITUDINAL WAVESThe particles vibrate parallel to the direction in which the wave is travelling.Sound waves are longitudinal waves.

ribbit

Types of Waves

• Mechanical waves– Require a medium through which to propagate

• Electromagnetic waves– Do not require a medium through which to propagate– May propagate through a medium

Language used to describe waves• Medium • Displacement• Amplitude• Period• Compression• Rarefaction• Crest• Trough• Transverse wave• Longitudinal wave• Frequency, wavelength, velocity

Particle Motion in Mechanical Waves• Transverse waves

– Particle motion perpendicular to propagation direction

• Longitudinal waves– Particle motion parallel to propagation direction

Particle Motion in Mechanical Waves• Transverse waves

– Particle motion is perpendicular to the propagation direction

Surface water waves

motion of handmotion of handenergy sourceenergy source

particleparticlemotionmotion propagation directionpropagation direction

Sound waves produced by vibrating objectsWhat are Sound Waves?

The energy used to set the tuning fork prongs vibrating causes air particles to vibrate

Sound energy propagates in 3-D as alternating higher and lower pressure variations

ActivitiesActivitiesListen to the sound when a Listen to the sound when a vibrating tuning fork is vibrating tuning fork is touched on a solid wooden touched on a solid wooden surfacesurface

Touch a vibrating tuning fork Touch a vibrating tuning fork against your nose or ear against your nose or ear lobe.lobe.

Listen to the sound produced Listen to the sound produced as the tuning fork is rotated as the tuning fork is rotated close to your ear about its close to your ear about its long axis.long axis.

Dip the vibrating tuning fork Dip the vibrating tuning fork into water.into water.

Pressure variations propagate through a medium away from the source of the vibrations

Sound waves are the result of vibrations or oscillations of particles in a mediumSound waves are the result of vibrations or oscillations of particles in a medium

What are Sound Waves?

The vibrating prongs of the tuning The vibrating prongs of the tuning fork cause the molecules in the fork cause the molecules in the surrounding air to vibrate - sound surrounding air to vibrate - sound propagating as a longitudinal wave propagating as a longitudinal wave motion in 3-D away from the source.motion in 3-D away from the source.

Movie: LWTuningFork.avi

Density is a property of matter. The symbol for density is Density is a property of matter. The symbol for density is ..Density is defined as the mass of a substance per unit of volume.Density is defined as the mass of a substance per unit of volume.

DensityDensity

Density

Water has a density of 1 gcm–3

Mercury has a density of 13.5 gcm–3

Gold has a density of 19.3 gcm–3 that’s 19.3 kg/litre!

The density of solids and liquids is not affected significantly by pressure changes applied to the substance. Gases can be readily compressed, and so changes in pressure, or temperature, have a significant effect on the density of gases.

Increasing pressure on a gas increases the density.Increasing the temperature of a gas decreases the density.

M (g)

V (cm3 )

Sound waves travel faster in warm air than cold (denser) airSound waves travel faster in warm air than cold (denser) airSound waves travel faster in gases with a lower molecular massSound waves travel faster in gases with a lower molecular massGenerally Generally vsolids > vliquids > vgases

The Effect of Density on the Speed Sound Waves

The speed of sound in air is given by the expressionThe speed of sound in air is given by the expressionvT = 331.45 + 0.59T m/sWhere T is the number of degrees above 0°C

Under conditions of a temperature inversion (temperature increasing with increasing height), the sound waves will be refracted downwards, and therefore may be heard over larger distances. This frequently occurs in winter and at sundown.

This table shows the speed of longitudinal and transverse waves in different mediaThis table shows the speed of longitudinal and transverse waves in different media


This table shows that there is no simple correlation between density and wave velocity. The speed of propagation depends on a number of interrelated factors including the stiffness of the medium and the mass/density properties.

MATERIAL Density (gcm–1) VL (m/s) VT (m/s)

copper 8.90 6420 3040

steel 7.86 (iron) 5940 3220

beryllium 1.93 12890 8880

aluminium 2.58 6420 3040

glass 5968 3764

water 1.00 1496

ethanol 0.79 1207

air 0.00139 331.45

helium 0.000178 965

fat 0.95 1450

muscle 1.07 1580

skull bone 1.91 4080

Sound waves travel faster in media that are more elasticSound waves travel faster in media that are more elastic

The speed of any wave depends upon the properties of the medium through which the wave is travelling. Typically there are two essential types of properties which effect wave speed - inertial properties and elastic properties.

The density of a medium is an example of an inertial property .

The greater the inertia (i.e., mass density) of individual particles of the medium, the less responsive they will be to the interactions between neighbouring particles and the slower the wave. If all other factors are equal (and seldom is it that simple), a sound wave will travel faster in a less dense material than a more dense material. Thus, a sound wave travels nearly three times faster in helium than travels in air; this is mostly due to the lower mass of helium particles compared to air particles.

Reference:http://www.physicsclassroom.com/Class/sound/u11l2c.htmlSong: Helium


A tube fitted with pressure gauges, through which a sound travelled would A tube fitted with pressure gauges, through which a sound travelled would record variations in pressure.record variations in pressure.

Relating Crests and Troughs toCompressions and Rarefactions

Compressions (C) are regions Compressions (C) are regions of higher pressure and of higher pressure and rarefactions (R) are regions of rarefactions (R) are regions of lower pressure.lower pressure.

Notice that this graph Notice that this graph shows the pressure at all shows the pressure at all points along the tube at points along the tube at one instant of timeone instant of time

CCCC RRRR

CompressionCompression

Longitudinal waves can thus be represented as a transverse waveLongitudinal waves can thus be represented as a transverse wave


A single pressure gauge recording the pressure at a fixed point in the tube A single pressure gauge recording the pressure at a fixed point in the tube over a period of time would show regular pressure variations.over a period of time would show regular pressure variations.


As the wave propagates from As the wave propagates from left to right along the tube, the left to right along the tube, the pressure alternates from low to pressure alternates from low to high with a frequency equal to high with a frequency equal to that of the sound wave.that of the sound wave.

Notice that this graph Notice that this graph shows the pressure shows the pressure variations at a fixed point variations at a fixed point as the wave moves along as the wave moves along the tube.the tube.

CCCC RRRR

Sound waves range in frequency from 20 Hz to 20 kHz (approximately)Sound waves range in frequency from 20 Hz to 20 kHz (approximately)

Frequency and Pitch of Sound Waves

Sound waves of variable frequency can be produced by a signal generator Sound waves of variable frequency can be produced by a signal generator driving a loudspeaker.driving a loudspeaker.

Frequency is a quantity that can be measured objectively.Frequency is a quantity that can be measured objectively.

Pitch is the subjective quality of a sound, determined by its frequency.Pitch is the subjective quality of a sound, determined by its frequency.

A low frequency sound has a low pitch and a high frequency sound has a A low frequency sound has a low pitch and a high frequency sound has a high pitch.high pitch.

Sound waves with a frequency too high for the human ear Sound waves with a frequency too high for the human ear to hear are called ultrasound. Other animals, including to hear are called ultrasound. Other animals, including dogs, some bats, birds and insects can hear ultrasound.dogs, some bats, birds and insects can hear ultrasound.

Frequency and Pitch of Sound Waves

Sound waves with a frequency too low for the human Sound waves with a frequency too low for the human ear to hear are called infrasound. Animals such as ear to hear are called infrasound. Animals such as dolphins and elephants can hear infrasound.dolphins and elephants can hear infrasound.

ultrasoundultrasound

infrasoundinfrasound

The amplitude of a sound wave at any given frequency is The amplitude of a sound wave at any given frequency is greater if the energy of the wave is greater.greater if the energy of the wave is greater.

Amplitude and Volume of Sound Waves

The volume (or loudness) of a sound of a particular pitch The volume (or loudness) of a sound of a particular pitch increases with the amplitude of the waves.increases with the amplitude of the waves.

Loudness is a subjective quantity.Loudness is a subjective quantity.

Two sounds with exactly the same energy are perceived to have different Two sounds with exactly the same energy are perceived to have different volumes if the frequencies differ, due to the varying sensitivity of the human volumes if the frequencies differ, due to the varying sensitivity of the human ear to sound over the audible spectrum.ear to sound over the audible spectrum.

softersofter louderlouder

It can be deduced that the sound shown by the wave on the right is louder because the amplitude is greater.

When a sound wave meets a boundary between two media, some of the When a sound wave meets a boundary between two media, some of the energy of the wave will be reflected at the boundary.energy of the wave will be reflected at the boundary.

Reflection of Sound - Echoes

Knowing the speed of sound in a particular medium, the distance to a Knowing the speed of sound in a particular medium, the distance to a reflecting surface can be determined.reflecting surface can be determined.

This principle is applied in SONAR used by ships to locate the position of This principle is applied in SONAR used by ships to locate the position of objects under water.objects under water.

Bats use a sophisticated sonar system to navigate and to catch prey.Bats use a sophisticated sonar system to navigate and to catch prey.

View movie: View movie: sonar.mov or sonar.avi

View movie: View movie: EchoReverb.mov or EchoReverb.avi

Investigation

Use a CRO and microphone to investigate

frequency (including the measurement of the unknown frequency of a sound) amplitude complex sound waves from different sources

Use a data logger with microphone input to investigate

echoes absorption and reflection of sound from different surfaces

complex waves (for a Fourier analysis, use a Vernier™ LabPro™ with computer interface)

A cathode ray oscilloscope (CRO) has a screen that shows the variation of a A cathode ray oscilloscope (CRO) has a screen that shows the variation of a voltage input to the CRO with time.voltage input to the CRO with time.

The Cathode Ray Oscilloscope

The input to the cathode ray The input to the cathode ray oscilloscope may be from a oscilloscope may be from a microphone, a device that microphone, a device that converts variations in sound converts variations in sound pressure into corresponding pressure into corresponding voltage changes.voltage changes.

voltagevoltage

timetime

A cathode ray oscilloscope can be used to investigate and measure A cathode ray oscilloscope can be used to investigate and measure properties of sound waves including:properties of sound waves including:

Analysing Sounds with a Cathode Ray Oscilloscope

• FrequencyFrequency• PeriodPeriod• AmplitudeAmplitude

The CRO can also be used to investigate complex sound waves with The CRO can also be used to investigate complex sound waves with components of many different frequencies.components of many different frequencies.

A cathode ray oscilloscope can be used to investigate and measure A cathode ray oscilloscope can be used to investigate and measure properties of sound waves including:properties of sound waves including:


• PeriodPeriod

For this wave it takes 10 ms For this wave it takes 10 ms for 9.5 cycles of the wave.for 9.5 cycles of the wave.T = .01 s/9.5 cycles = 0.00105T = .01 s/9.5 cycles = 0.00105

• FrequencyFrequency

f = 1/T = 1/0.00105 = 950 Hzf = 1/T = 1/0.00105 = 950 Hz

• AmplitudeAmplitude

The CRO can also be used to investigate complex sound waves with The CRO can also be used to investigate complex sound waves with components of many different frequencies.components of many different frequencies.

The oscilloscope record below shows a note produced by a human voice singing. Note that The oscilloscope record below shows a note produced by a human voice singing. Note that the wave is more complex than that produced by a simple whistle.the wave is more complex than that produced by a simple whistle.


•Frequency Frequency (predominant)

f = 1 cycle / 4 ms = 250 Hzf = 1 cycle / 4 ms = 250 Hz

•PeriodPeriod

T = 1/f = 1/250 = 0.004 sT = 1/f = 1/250 = 0.004 s

• Amplitude Amplitude

Observe that the wave is a complex one - due to the presence of frequencies other than the predominant one. These are called harmonics.

An electronic data logger with a microphone input can be used to investigate An electronic data logger with a microphone input can be used to investigate sound waves.sound waves.

Analysing Sounds Using Electronic Data Logging

Data loggers are very flexible instruments to which Data loggers are very flexible instruments to which different sensors capable of measuring a large variety different sensors capable of measuring a large variety of physical quantities can be attached.of physical quantities can be attached.

Data loggers may display data on a graphics calculator or a computer.Data loggers may display data on a graphics calculator or a computer.

The speed of sound can be determined using a data logger to monitor the echo of a sound The speed of sound can be determined using a data logger to monitor the echo of a sound produced at the open end of a tube closed at the other end.produced at the open end of a tube closed at the other end.

Time (s)

0.00 0.00400 0.00800 0.0120 0.0160 0.0200 0.0240

So

un

d L

eve

l (

re

lativ

e)

-1.30

-1.20

-1.10

-1.00

-0.900

-0.800

-0.700

-0.600

-0.500

-0.400

-0.300

-0.200

-0.100

-1.08e-19

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.00

1.10

1.20

1.30

A free sound recording and analysis program called Audacity can be used to A free sound recording and analysis program called Audacity can be used to capture and analyse sounds.capture and analyse sounds.


The software can be downloaded at: http://www.hitsquad.com/smm/programs/Audacity_mac/

http://www.hitsquad.com/smm/programs/Audacity_mac/

The waveform below was captured using Audacity. The sound was created The waveform below was captured using Audacity. The sound was created using a simple wooden flute.using a simple wooden flute.


Available at: http://www.hitsquad.com/smm/programs/Audacity_mac/

http://www.hitsquad.com/smm/programs/Audacity_mac/

The period and frequency of the sound wave can be deduced from this graph.The period and frequency of the sound wave can be deduced from this graph.


6 oscillations

Count off a whole number of cycles - say 6 oscillations

9.2 msPeriod

T = 9.2/6

= 1.5 ms

Frequency

F = 1/T

= 1/(1.5x10–3)

= 666 Hz

These 6 oscillations take 9.2 millisecondsThe frequency is the reciprocal of the period

The The absorption coefficientabsorption coefficient of a material is the of a material is the fraction of sound energy absorbed when the sound strikes the surface of the material.

It therefore takes values between 0 and 1, and is usually frequency dependent. Absorption coefficients of some materials are given in the following table.

Absorption and Reflection of Sound by Different Media

Source: Source: http://www.sfu.ca/sonic-studio/handbook/Absorption_Coefficient.html

First-hand investigation: Investigate the transmission/reflection/absorption of sound by different materials.First-hand investigation: Investigate the transmission/reflection/absorption of sound by different materials.

The transmission and absorption of sound can be investigated using a sound The transmission and absorption of sound can be investigated using a sound level meter placed at the end of a PVC pipe and a constant sound source at level meter placed at the end of a PVC pipe and a constant sound source at the other end.the other end.

Energy Transfer and the Absorption of Sound

speakerspeaker

PVC pipePVC pipe

Test material in Test material in pipepipe

Sound level meterSound level meter

Two or more waves passing interact with each other to produce a combined Two or more waves passing interact with each other to produce a combined effect when they are coincident in the medium.effect when they are coincident in the medium.

The Superposition of Waves

Component amplitudes are added algebraically to produce the resultantComponent amplitudes are added algebraically to produce the resultantReference for animations: Reference for animations: http://www.ceie.sunysb.edu/projectjava/WaveInt/home.htmlSee spreadsheet: See spreadsheet: Superposition

LabPro based investigation of sound sources.LabPro based investigation of sound sources.

The Superposition of WavesFirst-hand Investigation

The Vernier LabPro™ data logger can be used to investigate the addition of sound waves.The Vernier LabPro™ data logger can be used to investigate the addition of sound waves.

The superposition of the sounds of two tuning forks is shown above.The superposition of the sounds of two tuning forks is shown above.

Add the following waves using the Add the following waves using the superposition principlesuperposition principle

Graphical Superposition of Sound WavesExercise

ResultantResultant

ComponentsComponents


radio TV microwaves infrared visible light ultraviolet x-rays gamma rays


radioTV

microwavesinfrared

visible light ultraviolet x-rays gamma rays

Several types of electromagnetic waves are used for communication

Electromagnetic wave JAVA animationElectromagnetic wave JAVA animation

http://www.phy.ntnu.edu.tw/java/emWave/emWave.html

http://home.a-city.de/walter.fendt/physengl/emwave.htm

Electromagnetic waves travel as a pair of interacting electrical and magnetic waves


The planes of the electrical and magnetic waves are perpendicular to the propagation direction

The interacting electrical and magnetic waves travel in planes perpendicular to each other

Electromagnetic waves are the only type of wave capable of travelling through a vacuum

All electromagnetic waves travel at the same speed in a vacuum - 3 x 108 ms–1

[more accurately, speed of light = 2.9979 x 108 ms–1]


Electromagnetic waves travel more slowly in denser transparent media - 2 x108 ms–1 in water

The speed of electromagnetic waves in air is slightly less than their speed in a vacuum

Light travels at 1.24 x 108 ms–1 in diamonds, giving them unique optical properties that contribute to their value as gemstones.

In 2001, experiments were carried out, using extremely low temperature matter, in which light was slowed to a standstill and then allowed to speed back up again to its normal speed.

Future high-speed computers, called quantum computers, may use light to carry out calculations.

Electromagnetic waves interact with matter - they may be


• Reflected

• Slowed down

• Absorbed

• Refracted

The absorption of electromagnetic rays by matter depends on


• The composition of the matter

• The wavelength of the em wave

Absorption

• The distance travelled through the matter

The intensity of an electromagnetic wave is inversely proportional to the square of the distance from the source

Electromagnetic Waves and the Inverse Square Law

The intensity of an electromagnetic wave is inversely proportional to the square of the distance from the source

Electromagnetic Waves and the Inverse Square Law


Communication using Electromagnetic Waves - Amplitude Modulation

The signal is an electrical signal derived from the sound source - a much lower frequency than the carrier wave.

The carrier signal is the radio frequency to which the radio is tuned to receive the signal

Superposition of the signal and the carrier produces an amplitude modulate (AM) wave, which is transmitted to the receiver.

Communication using Electromagnetic Waves - Frequency Modulation

Signal wave

The carrier signal wave is modulated by the signal in such a way that the frequency of the wave undergoes small changes corresponding to amplitude

and frequency characteristics of the signal.

Frequency modulated carrier

Communication using Electromagnetic WavesLimitations

Type of

Radiation

Communication Use Limitations of this Technology

gamma-rays Not used Too high a frequency for electronic

detection and processing. Too

penetrating. Dangerous.

x-rays Not used

ultraviolet Some frequencies used in optical fibre

communications technology

It is difficult to generate ultraviolet light

using solid state electronics

visible Used in optical fibre communication

technology – voice, music, data, video

information

Cannot be used in air because of

interference created by ambient light,

scattering and absorption by the

atmosphere. Is only line of sight in air.

Attenuation of the signal occurs in

optical fibres due to absorption by

impurities in the glass.


Type of

Radiation


near-infrared Used in optical fibre communication


information

Line of sight only in air. Attenuation of

the signal occurs in optical fibres due to

absorption by impurities in the glass.

infrared Used in optical fibre communication


information

Used by hand-held remote control

devices

Attenuation of the signal occurs in

optical fibres due to absorption by

impurities in the glass.

Is only line of sight unless reflected from

objects in a room

microwaves Cellular phone networks, wireless

computer networks – voice, music, data,

video information

Line of sight


Type of

Radiation


TV waves TV – transmission of audio, video

information

Soon text and other data will also be

transmitted using digital TV

Close to line of sight only. Reflection

from objects resulting in two signals can

be a problem (this causes ghosting on TV

sets)

radio waves Radio – voice and music, some amateur

enthusiasts transmit pictures as well.

Some radio wavelengths are reflected by

atmospheric layers and therefore exceed

line of site limitations of shorter

wavelengths.

Cannot carry as much information as

higher frequency waves

Subject to interference in the atmosphere

by electrical storms

Electromagnetic waves may be reflected from a plane surface

Reflection of Electromagnetic Waves

Waves reflected from a plane surface obey two simple rules …

• The angle of incidence equals the angle of reflection from a plane surface

• The incident ray, the reflected wave and the normal to the reflecting surface all lie in the same plane.

This image shows how light waves are reflected from a plane mirror surface

The angle of incidence equals the angle of reflection

Reflection of Electromagnetic Waves

Ray

Box Mirror

ir

Reflection of light rays from a plane vertical mirror.How tall must a mirror be so that the man can see all of his own reflection in the mirror?

mirror

Light

Reflection of Electromagnetic WavesThe Transfer of Information

Microwaves

Radio waves

Plane surfaces

Reflection of Electromagnetic WavesRay diagrams and Applications

Convex reflectors

Concave reflectors

The ionosphere is a layer of the atmosphere containing charged atoms and molecules. This layer reflects radio waves with frequencies less than 30 MHz, allowing them to be transmitted over the horizon.

When electromagnetic waves encounter a boundary at which there is a change of medium, the waves may change speed and undergo a change in the direction of propagation, called refraction.

Refraction of Electromagnetic Waves

The bending of the wavefront occurs due to a change in the speed of the wave.

There is a corresponding change in the wavelength of the wave, since the speed of the wave must equal the product of its frequency and wavelength. The frequency cannot change.

Refraction of light waves is responsible for the formation of a rainbow - as well as enabling our eyes to produce a focussed image.

Reflection from a plane surface

Reflection and Refraction of Electromagnetic Waves

Investigation of light waves

Reflection from a curved surface

Refraction at a boundary between media

Ray propagation and wavefronts
























Ray propagation and wavefrontsWaves can be thought of as travelling as a series of wavefronts. The crests of the waves could represent the wavefront.

propagation

wavefronts

Waves may speed up or slow down if they encounter a change in the medium in which they are travelling

Refraction of Waves

This change may be the result of encountering a

• different medium

• change in the properties of the mediumv v

deeperfaster

shallowerslower

faster slower

faster

air Perspex¯

air

water

Rarely, two different media may affect waves in the same way, so the wave velocity does not change

Refraction is a change in the direction of propagation of a wave as a result of a velocity change

Refraction of Waves

• Refraction of light

• Refraction of water wavesdeeperfaster

shallowerslower

DispersionIf a beam of white light enters a glass prism, what emerges from the other side is a spread out beam of many colored light. The various colors are refracted through different angles by the glass, and are ``dispersed'', or spread out.

Because the speed of light is used to define the metre, the speed of light is an exact quantity.

Vlight in vacuum = 299792458 ms–1 [exact]

Vlight in air = 298895771 ms–1 [this is variable]

For most practical purposes, a vacuum and air can be considered to be the same for light, as the speed is very slightly lower in air.

The speed of light

Definition of the metreThe metre is the length of the path travelled by light in

vacuum during a time interval of 1/299 792 458 of a second

A mnemonic not to be taken lightly

2 9 9 7 9 2 4 5 8As Einstein's equations validly predicted, we hold speed constant

Th

e s

peed

of

lig

ht

Definition of the metreThe metre is the length of the path travelled by light in

vacuum during a time interval of 1/299 792 458 of a second

Q: What would happen if the speed of light were only 100 km/h? A: As we approach the speed of light, the aging process slows down. So, if

the speed of light were 100 km/h, we would have even more people speeding, especially older people trying to stay young. As a matter of fact, physics would demand that we go faster than the speed of light. The safest thing is to drive at a steady 100 km/h to keep time and the highway patrol off our necks. Aeroplanes would become obsolete in this slow light world, because you would be going so fast, relatively speaking, that you'd be back before you even left. This would make business trips unnecessary and lead to economic collapse. So, to answer the question, life, if the speed of light were 100 km/h, would be youthful, fast, and dark.

On the speed of light - from the Internet

Defining the metre this way means that the speed of light is now an exact quantity

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second

Refractive index is a quantitative measure of the refractive properties of a material relative to a vacuum. It is directly related to the velocity of light in the medium.

Refractive Index

The symbol used to represent refractive index is “n”

Refractive index for light in a material is defined as

c is the speed of light in a vacuum and v is the speed of light in the mediumNote that RI is a ratio and therefore has no units. Its value is always greater than 1. Why?

n c

v

Medium Refractive Index

vacuum 1.0 (definition)

air 1.003

water 1.33

glass 1.5

diamond 2.42

Refractive index can be related to the angles of incidence and refraction because these are directly related to the change in speed of light travelling from one medium to another.

Refractive Index - Snell’s Law

Refractive index for light in a material is expressed as

i

r

n c

v

sin(i)

sin(r)

n v1

v2

sin(i)

sin(r )

Reflected ray

Refracted ray

Use Snell’s law to determine the refractive index of the transparent acrylic plastic prism below, and hence calculate the speed of light in acrylic plastic.

Refractive Index - Snell’s Law

Refractive index for light in a material is expressed as

i

r

n c

v

sin(i)

sin(r)

n v1

v2

sin(i)

sin(r )

Reflected ray

Refracted ray

Use four pins to trace the path of a ray of light through a rectangular glass prism.

A first-hand investigation of refractive index of glass

The path followed by the light is not a straight line …

… and a “bird’s eye” view of the apparatus

The pins behind the glass are positioned so that, as seen through the prism, they line up with the pins in front of the prism.

Observe that the tops of the pins (visible above the prism) behind the prism do not line up with the bottoms of the same pins as seen through the prism. The light from each part follows a different path, and refraction of the light as it passes through the prism makes the pins appear to be further to the left than what they really are.

A first-hand investigation of refractive index of glass

And hence the refractive index can be determined from

Compare your result with those of others in the class and comment on your observations.

Find out the refractive index of glass. Compare your research with that of others.What do you conclude from the comparison?

n c

v

sin(i)

sin(r)

ii

rr

A ray of light travelling from a material with a higher refractive index to one of lower refractive index is refracted away from the normal - the angle of refraction is greater than the angle of incidence.

Refraction and Total Internal Reflection

Total internal reflection occurs when the refracted ray is parallel to the surface of the interface between the media. All of the light is reflected - none actually travelling along the surface

The minimum angle of incidence for which all the light is reflected back into the medium is called the critical angle.

Place a small piece of paper between two glass prisms as

shown below

Observing Total Internal Reflection

Then look in from the end at the paper between the pieces of glass

What do you notice?


Total internal reflection occurs within each prism. Light entering from one end of the prism does not pass through the glass from the inside to the paper and so cannot reflect off the paper. The light never passes through the internal surface of the glass onto the paper, the paper is not visible when looking in from the ends of the prisms.

path of light raypath of light ray

path of light raypath of light ray

Light entering from one end of the prism reflects off the internal surface of the prism as it passes through the glass.


Viewed from other angles, a variety of interesting effects can be observed

Place a triangular prism on a flat surface, with a small piece of paper under the centre of the prism.


photo

photo

Place an object behind the prism, and then looking from the front, from different angles relative to the flat surface, observe the piece of paper and the object behind the prism. At certain angles a reflection of the object appears on the lower prism surface and the paper disappears.

eyeeye

The minimum angle of incidence for which all the light is reflected back into the medium is called the critical angle.

Refraction and Total Internal Reflection

The critical angle is represented by the symbol ic

It can be calculate from sin(ic) 1

n

What is the critical angle for glass with a refractive index of 1.5?

What is the critical angle for diamonds having a refractive index of 2.42?

42°

24°

Optical fibres use the principle of internal reflection to reflect light along the fibre with almost no loss of energy.

Total Internal Reflection and Optical Fibres

The light can be used to transmit digitally encoded information at a very high rate.

Most information communicated digitally passes through an optical fibre at some point in its transmission.

Light internally reflected

Telephony

Communication and the Digital Storage of Data

Computer data

Sound

Images - still and moving

Digital data may be stored• in computer RAM (silicon semiconductor memory)• magnetically on floppy disks or hard drives• optically on CDs and DVDs• can you think of any others?

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Sound Waves


Date post:	11-Jan-2016
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