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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 -
7stones
Fifty-Fifty Game on Wave Types - by KT - Microsoft
WORD
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).