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AQA AS Specification

Lessons Topics

1 & 2 Progressive Waves

Oscillation of the particles of the medium; amplitude, frequency, wavelength,

speed, phase, (path differencecovered in optics section).

c = f

3 & 4 Longitudinal and transverse wavesCharacteristics and examples, including sound and electromagnetic waves.

Polarisation as evidence for the nature of transverse waves; applications e.g.

Polaroid sunglasses, aerial alignment for transmitter and receiver.

5 to 8 Superposition of waves, stationary waves

The formation of stationary waves by two waves of the same frequency

travelling in opposite directions; no mathematical treatment required.Simple graphical representation of stationary waves, nodes and antinodes on

strings.

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Waves

A wave is a means of transferring energy

and momentum from one point to

another without there being any transfer

of matter between the two points.

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Describing Waves

1. Mechanical or Electromagnetic

Mechanical waves are made up of particles vibrating.

e.g. sound air molecules; water water mo lecules

All these waves require a substance for transmission

and so none of them can travel through a vacuum.

Electromagneticwaves are made up of oscillatingelectric and magnetic fields.

e.g. l ight and radio

These waves do not require a substance fortransmission and so all of them can travel through avacuum.

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Describing Waves

2. Progressive or Stationary

Progressivewaves are waves where there is a nettransfer of energy and momentum from one point toanother.

e.g. sound produced by a person speaking; l igh t from alamp

Stationarywaves are waves where there is a NO nettransfer of energy and momentum from one point to

another.e.g. the wave on a gu itar str ing

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Describing Waves

3. Longitudinal or Transverse

Longitudinalwaves are waves

where the direction of vibration of

the particles is parallel to thedirection in which the wave

travels.

e.g. sound

wave direction

vibrations

LONGITUDINAL WAVE

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Describing Waves

Transversewaves are waveswhere the direction of vibration of

the particles or fields is

perpendicular to the direction in

which the wave travels.

e.g. water and all electrom agnetic

waves

Test fo r a transverse wave:Only TRANVERSE waves undergo

polarisation.

wave direction

vibrations

TRANSVERSE WAVE

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Polarisation

The oscillations within a transverse wave and the

direction of travel of the wave define a plane. If the

wave only occupies one plane the wave is said to

be plane polarised.

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Polarisation

Light from a lamp is unpolarised. However,

with a polarising filter it can be plane

polarised.

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Polarisation

If two crossed filters are used then no light

will be transmitted.

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Aerial alignment

Radio waves (and microwaves) aretransmitted as plane polarised waves.In the case of satellite television, twoseparate channels can be transmittedon the same frequency but withhorizontal and vertical planes ofpolarisation.

In order to receive thesetransmissions the aerial has to bealigned with the plane occupied by theelectric field component of theelectromagnetic wave.

The picture shows an aerial aligned toreceive horizontally polarised waves.

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Measuring waves

Displacement,x

This is the distance of an oscillating particle from its undisturbedor equilibrium position.

Amplitude, a

This is the maximum displacement of an oscillating particle from

its equilibrium position. It is equal to the height of a peak or thedepth of a trough.

amplitude a

undisturbed

or equilibrium

position

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Measuring waves

Phase, This is the point that a particle is at within anoscillation.

Examples: top of peak, bottom of trough

Phase is sometimes expressed in terms of anangle up to 360. If the top of a peak is 0then

the bottom of a trough will be 180.

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Measuring waves

Phase difference,This is the fraction of a cycle between two particleswithin one or two waves.

Examp le: the top of a peak has a phase dif ference ofhal f of one cycle compared w ith the bo ttom of a

trough.

Phase difference is often expressed as an angledifference. So in the above case the phase difference is180. Also with phase difference, angles are usually

measured in radians.Where: 360= 2 radian; 180= rad; 90= /2 rad

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Measuring waves

Wavelength,This is the distance between two consecutiveparticles at the same phase.

Example: top-of-a-peak to the next top -of -a-peak

unitmetre, m

wavelength

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Measuring wavesPeriod, T

This is equal to the time taken for one complete

oscillation in of a particle in a wave.

unitsecond, s

Frequency, f

This is equal to the number of complete oscillations in

one second performed by a particle in a wave.

unithertz, HzNOTE: f = 1 / T

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The wave equation

For all waves:

speed = frequency x wavelength

c = f

where speed is in ms

-1

provided frequency is in hertzand wavelength in metres

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Complete

Wave speed Frequency Wavelength Period

600 m s-1 100 Hz 6 m 0.01 s

10 m s-1 2 kHz 0.5 cm 0.5 ms

340 ms-1 170 Hz 2 m 5.88 ms

3 x 108ms-1 200 kHz 1500 m 5 x 10-6s

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Answers

Wave speed Frequency Wavelength Period

600 m s-1 100 Hz 6 m 0.01 s

10 m s-1 2 kHz 0.5 cm 0.5 ms

340 ms-1 170 Hz 2 m 5.88 ms

3 x 108ms-1 200 kHz 1500 m 5 x 10-6s

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Superposition of waves

This is the process thatoccurs when two waves ofthe same type meet.

The principle ofsuperposition

When two waves meet,the total displacement at apoint is equal to the sum

of the individualdisplacements at thatpoint

reinforcement

cancellation

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Stationary waves

A stationary wave can be formed by thesuperposition of two progressive waves

of the same frequency travelling in

opposite directions.

This is usually achieved by superposing

a reflected wave with its incident wave.

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Formation of a stationary wave

Consider two waves, Aand B, each ofamplitude a, frequency fand period Ttravelling

in opposite directions.

(1) At time, t = 0

Wave B Amplitude = 2a

Wave A

RESULTANT WAVEFORM

REINFORCEMENT

N A N A N A N A N A N A N

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(2) One quarter of a cycle later, at time, t = T/4both waves have moved by a quarter of a

wavelength in opposite directions.

Wave B

Wave A

RESULTANT WAVEFORM

CANCELLATION

Amplitude = 0

N A N A N A N A N A N A

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(3) After another quarter of a cycle, at time,t = T/2both waves have now moved by a

half of a wavelength in opposite directions.

Wave B

Wave A

Amplitude = 2a

RESULTANT WAVEFORM

REINFORCEMENT

N A N A N A N A N A N A N

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(4) One quarter of acycle later, at time,t = 3T/4both waves will

undergo cancellationagain.

(5) One quarter of acycle later, at time, t = Tthe two waves willundergo superpositionin the same way as attime, t = 0

N A N A N A N A N A N

(6) Placing all fourresultant waveforms on topof each other gives:

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Nodes (N) and Antinodes (A)

NODES are points within a stationary wave thathave the MINIMUM (usually zero) amplitude.

These have been marked by an N in the

prev ious waveforms.

ANTINODESare points within a stationary

wave that have the MAXIMUM amplitude.

These have been marked by an A in the

previous waveforms and have an ampl i tude

equal to 2a

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Comparison of stationary and progressive waves

Property Stationary Wave Progressive Wave

Energy &Momentum No net transfer from one pointto another Both move with speed:c = f x

Amplitude Varies from zero at NODES to a

maximum at ANTINODES

Is the same for all particles

within a wave

Frequency All particles oscillate at the

same frequency except those at

nodes

All particles oscillate at the

same frequency

Wavelength This is equal to TWICE the

distance between adjacent

nodes

This is equal to the distance

between particles at the

same phase

Phase

differencebetween two

particles

Between nodes all particles are

at the same phase. Any othertwo particles have phase

difference equal to m where

m is the number of nodes

between the particles

Any two particles have

phase difference equal to2d / where d is the

distance between the two

particles

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Examination question

The diagram below shows a microphone being used todetect the nodes of the stationary sound wave formedbetween the loudspeaker and reflecting surface. Thesound wave has a frequency of 2.2 kHz.

to

oscilloscope

microphonereflecting

surface

loudspeaker

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(a) Explain how a stationary is formed between theloudspeaker and reflecting surface. [3]

(b) When the microphone is moved left to right by 45 cm

it covers six inter-nodal distances. Calculate thewavelength and speed of the progressive sound wavesbeing used to form the stationary wave. [4]

(c) The nodes nearest to the reflecting surface havenearer zero amplitude compared with those nearer the

loudspeaker. Why? [3]

to

oscilloscope

microphonereflecting

surface

loudspeaker

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(a)

The reflected sound wave undergoes

superposition with the incident sound waveproduced by the loudspeaker. [1 mark]

Nodes are formed when the peak of one wave

superposes with the trough of the other,cancellation occurs. [1 mark]

Antinodes are formed when the peak of one

wave superposes with the peak of the other,reinforcement occurs. [1 mark]

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(b)

Wavelength equals twice the distance between

nodes.Internodal distance = 45 cm / 6 = 7.5 cm

Therefore sound wavelength = 15 cm [2 marks]

c = f x

= 2.2 kHz x 15 cm

= 2 200 Hz x 0.15 m

speed of sound waves = 330 ms-1 [2 marks]

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(c)

The amplitude of a sound wavedecreases with distance due to its energyspreading out. [1 mark]

The size of a peak just before reflectionand that of a trough just after reflectionwill be similar and so almost perfectcancellation will occur and theconsequent node produced will have anear zero amplitude. [1 mark]

The size of a peak just after productionby the loudspeaker will, however, bemuch larger than that of a trough afterreflection and travel back to the speaker.Therefore incomplete cancellation willoccur and the consequent node producedwill still have a significant amplitude.

[1 mark]

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Stationary waves on strings

Fundamental mode, foThis is the lowest frequency that can produce astationary wave.

The length of the loop, L is equal to half of a wavelength.

and so: = 2L

also: fo= c / = c / 2L

L= length of a loop

node nodeantinode

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First Overtone, 2foThis is the second lowest frequency that can produce a

stationary wave.The length of two loops, L is equal to one wavelength.

and so: = L

also: 2 fo= c / L

L= length of two loops =

N A N A N

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QuestionA string of length 60 cm has fundamental frequency of20 Hz. Calculate:(a) the wavelength of the fundamental mode

(b) the speed of the progressive waves making up thestationary wave

(c) the number of loops formed if with the same stringthe length of the string was increased to 1.2m and thefrequency to 30Hz

(a) In the fundamental mode there is one loop of length

equal to .Therefore wavelength = 2 x 60 cm

= 1.2 m

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(b) c = f x

= 20 Hz x 1.2 m

Speed of the progressive waves = 24 ms-1

(c) If the frequency is increased to 30Hz the wavelengthwill now be given by:

= c / f

= 24 / 30= 0.8 m

but each loop length =

= 0.4 m

there will therefore be: 1.2 / 0.4 loops

Number of loops = 3

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Internet Links Wave lab- shows simple transverse & longitudinal

waves with reflection causing a stationary wave - by

eChalk Wave Effects- PhET - Make waves with a dripping

faucet, audio speaker, or laser! Add a second source

or a pair of slits to create an interference pattern. Also

shows diffraction.

Virtual Ripple Tank- falstad

Fifty-Fifty Game on Wave Types - by KT - Microsoft

WORD

Simple transverse wave- netfirms Simple longitudinal wave- netfirms

Simple wave comparision- amplitude, wavelength -

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Fifty-Fifty Game on Wave Types - by KT - Microsoft

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Wave on a String- PhET - Watch a string vibrate in

slow motion. Wiggle the end of the string and make

waves, or adjust the frequency and amplitude of anoscillator. Adjust the damping and tension. The end

can be fixed, loose, or open.

Vend diagram quiz comparing light and sound waves-

eChalk

Superposition of two pulses- NTNU

Superpositon of two oppositely movingprogressive waves- NTNU

Superposition of two pulses or waves-

7stones

Fourier - Making Waves-PhET - Learn how to

make waves of all different shapes by adding up

sines or cosines. Make waves in space and time

and measure their wavelengths and periods. See

how changing the amplitudes of different harmonicschanges the waves. Compare different

mathematical expressions for your waves.

Beats - Sound Pulses- Explore Science

Beats- netfirms

Beats- Fendt

Resonance in a string- netfirms

Stationary wave modes of vibration- netfirms

Standing Longitudinal Wave- Fendt

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Core Notes from Breithaupt pages 174 to 1851. Draw diagrams and explain what is

meant by (a) transverse and (b)

longitudinal waves. Give twoexamples of each type.

2. (a) What is meant by polarisation? (b)What is the difference between planepolarised and unpolarised light? (c)How can unpolarised light be changedinto plane polarised light? (d) Whattype of waves can display polarisationeffects?

3. What is a stationary wave? How is itdifferent from a progressive wave?(see page 180)

4. Define in the context of wave motion:(a) amplitude; (b) frequency; (c)wavelength; & (d) phase. You may

wish to illustrate your answers withdiagrams.

5. Give the equation for wave speed interms of other wave quantities.

6. What is the principle of superposition? Explain,using diagrams, how the processes ofreinforcement and cancellation can occur (p180).

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Notes on Describing Waves & Polarisation

from Breithaupt pages 174, 175 & 180

1. Draw diagrams and explain what is meant by (a)transverse and (b) longitudinal waves. Give twoexamples of each type.

2. (a) What is meant by polarisation? (b) What is thedifference between plane polarised and unpolarised

light? (c) How can unpolarised light be changed intoplane polarised light? (d) What type of waves candisplay polarisation effects?

3. What is a stationary wave? How is it different from aprogressive wave? (see page 180)

4. What are (a) mechanical & (b) electromagnetic waves.In what ways are they different?

5. Try the Summary Questions on page 175.

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Notes on Measuring Waves

from Breithaupt pages 176 & 177

1. Define in the context of wave motion: (a) amplitude; (b)frequency; (c) wavelength; & (d) phase. You may wishto illustrate your answers with diagrams.

2. Give the equation for wave speed in terms of otherwave quantities.

3. Calculate (a) the speed of a wave of frequency 60 Hzand wavelength 200 m. (b) the wavelength of a waveof speed 3 x 108ms-1and frequency 150 kHz; (c) thefrequency of a wave of wavelength 68 cm and speed340 ms-1

4. What is meant by phase difference? Show howangular measurement in radians is used.

5. Try the Summary Questions on page 177.

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Notes on Superposition & Stationary Waves

from Breithaupt pages 180 to 185

1. What is the principle of superposition?

Explain, using diagrams, how the

processes of reinforcement and

cancellation can occur (p180).