Chapter 6 – Wave behaviour (16 lessons including test)
Lesson
6.1 Beautiful
colours,
wonderful
sounds
Content
Introduction to range of effect produced by the superposition of waves
and how they contribute to the beauty of the world around us.
See EMANIM !
Activities
Homework
Activity 10D
‘Loudspeaker and baffle’
Slinky
Wave machine
Ripple tank
Ripple tank software
Read student book on
superposition phenomena.
Revise GCSE work on waves.
Activity 260S
‘Introduction to phasors’
Activity 20P ‘Path
difference and phase
differences’,
Activity 40E ‘Beats:
Mixing waves in time’
Qs 10W ‘Phase difference
and superposition’
Qs 20W ‘Superposition of
waves: a drawing exercise’
Exam questions on phasors

Know the meaning of the terms wavelength, frequency,
period, amplitude, wave speed, transverse, longitudinal.
 Recall and use the equation v = fλ to perform wave
calculations.
Lesson 1: Introduce wave characteristics and properties, recapping
GCSE using the slinky, wave machine, ripple tank, ripple tank
software, CD-ROM images to illustrate: transfer of energy by waves,
transverse and longitudinal waves, wavelength, frequency, period,
amplitude, wave speed equation with sample calculations, examples
of different types of waves, plane and circular waves. Demonstrate
Activity 10D (loudspeaker and baffle) as introduction to phase and
superposition.

Know the meaning of the terms phase, phasor, radian
measure, superposition.
 Draw phasor arrows for a wave.
 Draw diagrams to show the superposition of waves by either
(1) adding amplitudes directly or (2) adding phasors and
taking vertical projection.
 Determine the phase difference (in degrees or radians)
between a pair of waves from amplitude-time traces.
Lesson 2: Introduce phasor concept, illustrating with Activity 260S.
Discuss phase-angle relationship, introducing radian measure.
Discuss superposition and phase difference, using p132. Make sure
that that both the following methods for obtaining the superposition
amplitude are covered: (1) adding amplitudes directly (see Qs 10W)
and (2) adding phasors and taking vertical projection. Note that
superposition of waves in antiphase will only lead to a zero amplitude
resultant if the initial amplitudes of the two waves are the same.
Illustrate the above with experiment Activity 20P, stressing that sound
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A. M. James, Matthew Arnold School, Oxford
1
Lesson
Content
waves are actually longitudinal waves, and that the scope trace is an
artifact of the microphone detection. Measure period of wave and path
difference required to give superposition in order to work out speed of
sound. Now use the A+B add function on the two channel scope to
illustrate the result of adding various amplitude-phase combinations of
the two waves, as per p132. Students should be able to work out the
phase differences between pairs of waves from wave traces, and
complete phasor diagrams for them (see exam questions). Note that
the phenomenon of beats is not explicitly required by the specification,
but a simple question cropped up in the June 2005 paper, so it may be
worth devoting a little time to some simple examples.
Activities
UP June 08 Q7; June 07
Q3; Jan. 07 Q4; Jan. 07
Q7
Homework
Activity 10E 'Computer
animation: Superposition
and standing waves'
Activity 30E 'Hearing
superposition'
Activity 40E 'Beats:
Mixing waves in time'
Activity 90E ‘Interference
patterns in a ripple tank’
Qs 40S ‘Superposition of
sound waves’
Qs 30S ‘Lloyd’s mirror for
microwaves’


Know the meaning of the term coherent.
Know that to observe interference effects requires two
coherent sources producing waves with the same wavelength.
 Explain sound interference experiments in terms of wave
superposition, using either path difference or phasor
explanations.
 Calculate positions on maxima and minima in sound
interference experiments, using geometric constructions.
 Predict and observe the effect on the nodal spacing of
changing the separation of the sources.
Lesson 3: Demonstrate Activity 30E ‘Hearing superposition’ using
both ear and microphone to illustrate the variation in intensity.
Brainstorm possible reasons for observations, linking with Activity
10D. Explain Activity 30E in terms of superposition, with both path
difference and phasor treatments. Use ripple tank (Activity 90E) and/or
ripple tank software demo to demonstrate the pattern of constructive
and destructive interference. The effect on the nodal spacing of
changing the source separation can be shown using the ripple tank
and/or ripple tank software, dragging the sources together. Qs 40S
test application of geometrical principles to this situation.
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
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Explain microwave superposition experiments.
Explain the operation of a radar gun in terms of wave
A. M. James, Matthew Arnold School, Oxford
2
Lesson
Content
superposition.
 Use data on the frequency at which the intensity of the
combined signal fluctuates in a radar gun system to determine
the speed of a car.
 Explain the observation of a spectrum of colours in either oil
films or soap bubbles in terms of wave superposition effects.
Lesson 4: Demonstrate Activity 60P ‘Superposition of microwaves’
and/or 70P ‘Partial reflection of microwaves’. Activity 120D from
Chapter 12 is an alternative to Activity 70P. Activity 70P is the basis of
the ‘radar gun’ used in police speed traps. It has come up in exam
questions, see June 2002, so it is worth spending some time on it.
Define the term coherence in relation to this discussion.
Discuss formation of oil film colours as another example of a
superposition effect very closely related to Activity 70P, and
brainstorm other examples, for example: sieve, net curtains, TV
images, newspaper photographs.
Activities
Homework
Activity 60P
‘Superposition of
microwaves’
Activity 70P ‘Partial
reflection of microwaves’
(see also Ch.12 Activity
120D)
Qs 60S ‘Partial reflection of
sound waves’
Qs 70S ‘Superposition and
speed measurement’ (deals
with radar gun explicitly, but
note that working in worked
solution on teacher’s CD
ROM is wrong, although
answer is correct)
June 2002 exam questions on
radar gun
Qs 80X ‘Superposition
outside the laboratory’
UP Jan. 08 Q10


Know the meaning of the term standing wave.
Explain, with the aid of diagrams, how standing waves are
formed from the superposition of two travelling waves.
 Know that the nodal spacing in a standing wave system is
equal to half the wavelength, and that this may be used to
determine the wavelength of a wave.
 Explain why there must be nodes at the ends of a string in
which standing waves are set up.
Lesson 5: Introduce standing waves by demonstrating the relationship
between length and frequency using the ocarina and/or sonometer.
This will be explained in due course.
Now demonstrate or do as circus the following experiments: (1)
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Activity 100E 'Standing
waves on a rubber cord'
Activity 120P 'Standing
Reading 10T ‘The Nautilus
loudspeaker’
Reading 20T ‘Acoustics of
3
Lesson
Content
Activity 100E (rubber cord); (2) Activity 110P (sound waves); (3)
sonometer with vibration generator. Explain formation of standing
waves using the Wave Superposition software to show how two waves
travelling in opposite directions give rise to a superposition effect. See
http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipewaves.html
and
http://phet.colorado.edu/simulations/sims.php?sim=Wave_on_a_String
Key findings: (a) certain points on the wave axis always have zero
amplitude; (b) these nodal points are spaced by half a wavelength; (c)
for vibrations on a string, there are nodes at the ends.
It is worthwhile demonstrating the effect of changing the frequency on
the nodal pattern with the Wave Superposition program, confirming
the changes in the node spacing using the rubber cord experiment.
Also, change length of rubber cord, and note change in frequency of
the harmonics that results.
Also, demonstrate marshmallows in microwave oven experiment to
illustrate formation of standing waves and determination of speed of
electromagnetic waves by measuring the nodal spacing from the
cooking pattern. Students should be able to interpret diagrams such
as that on p134, and do exam questions such as q11 in the pilot
paper.




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Activities
waves in tubes: Kundt's
experiment',
Activity 110P ‘Standing
waves with sound waves’
Activity 130P ‘Standng
waves with microwaves’
Sonometer
Animations from
University of
Southampton ‘Sound
Waves’ CD ROM
Homework
rooms’
Draw the standing wave patterns for the first several
harmonics of a standing wave set up on a stringed musical
instrument.
Use the equation v = fλ and the length of the string to
determine the frequencies/wavelengths of the first several
harmonics of a stringed instrument.
Draw the standing wave patterns (displacement nodes) for the
first several harmonics of a standing wave set up in a wind
instrument closed at both ends.
Use the equation v = fλ and the length of the string to
determine the frequencies/wavelengths of the first several
harmonics of a wind instrument closed at both ends.
A. M. James, Matthew Arnold School, Oxford
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Lesson
Content
 Draw the standing wave patterns (displacement nodes) for the
first several harmonics of a standing wave set up in a wind
instrument open at one end.
 Use the equation v = fλ and the length of the string to
determine the frequencies/wavelengths of the first several
harmonics of a wind instrument open at one end.
 Know that displacement nodes correspond to pressure
antinodes in a vibrating column of air.
 Predict and explain the effect on the pitch of the note
produced of shortening the string or the column of air in a
musical instrument.
 Explain why a flute has a higher pitch than an oboe, although
both instruments are approximately the same length.
 Explain the observation of standing waves in musical
instruments in terms of wave superposition effects.
Lesson 6-7: Superposition effects in musical instruments. Begin by
asking what determines the pitch/frequency of sounds produced by
musical instruments. This will normally generate a range of valid
responses about tube and string lengths, which can be used to
develop the arguments. You can demonstrate the ocarina and/or
sonometer here. Discuss the formation of standing waves in stringed
instruments, noting that plucking a string gives rise to all the
harmonics, with the fundamental dominating, unless the string is
“stopped” at the middle: you could demonstrate this effect with the
sonometer, and also show the Southampton CD ROM animations. Go
through the calculation of fundamental and overtone frequencies.
Students should be able to complete diagrams showing the nodal
patterns for the different harmonics.
Now go through an analogous treatment for wind instruments with
tubes closed at both ends, so that there are nodes at each end as with
the stringed instrument. Page 130 has useful diagrams, although the
CD ROM images show transverse displacement representations of the
pressure. You may prefer to have students complete the new sheet
“Standing waves in pipes”, which is a more accessible alternative to
the book and CD. Discuss the displacement of air along the wave axis,
remembering that sound waves are longitudinal waves. Students
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A. M. James, Matthew Arnold School, Oxford
Activities
Homework
Activity 120P ‘Kundt’s
experiment’
Animations from
University of
Southampton ‘Sound
Waves’ CD ROM
Activity 150D ‘More
complicated standing
waves’
Qs 80X 'Superposition
outside the laboratory'
Qs 100S ‘Standing waves in
pipes’
Qs p132
UP June 08 Q8; Jan. 08
Q7; Jan. 07 Q9June 07
Q8
5
Lesson
Content
should be able to complete a diagram showing the nodal pattern for
different harmonics, and calculate their frequencies (new sheet). You
could demonstrate Kundt’s tube to show the formation of a nodal
pattern, although note that this is not like a musical instrument in that a
speaker whose frequency is selected provides the sound wave in
Kundt’s tube.
Now extend the treatment to pipes open at both ends, and then those
closed at one end, noting that an open end corresponds to an
antinode in air displacement (pressure node). Students should be able
to complete diagrams showing the nodal patterns for different
harmonics, and calculate their frequencies (see new sheet).
A good rule to remember is that for all except pipes open at one end,
the fundamental vibration corresponds to the tube length being half a
wavelength (see new sheet).
Another good rule to remember is that for all except pipes open at one
end, the harmonic frequencies go f, 2f, 3f, 4f…., while pipes open at
one end have harmonic frequencies f, 3f, 5f, 7f….. (see new sheet).
Note that, in general, the longer the air column or string that is
vibrating, the longer the standing wavelengths, and hence the lower
the
frequency,
explaining
the
observations
with
the
ocarina/sonometer.
Use also the OHT with a series of examples of standing waves to
match up with written descriptions to test out understanding.
6.2 What is
light?
Historical development of ideas about the nature of light, looking at
ideas of Romer, Huygens and Newton.




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Activities
Homework
Explain how Romer was able to determine the speed of light
from observations of Jupiter’s moons.
Compare and contrast Newton’s and Huygens’ models of
light.
Show how Huygens wavelet construction can be used to
explain plane waves, reflection and refraction.
Use a software modelling activity to show that the path light
takes through materials corresponds to the minimum travel
time.
A. M. James, Matthew Arnold School, Oxford
6
Lesson
Content
Lesson 8: Discuss Romer’s measurement of the speed of light.
Possible also to use fibre optic kit to determine speed of light through
glass. Compare Newton’s and Huygens’ model of light. Discuss
Huygens’ wavelet construction and its application to expanding
spherical wavefronts and plane waves, demonstrating using Ripple
tank software (multiple sources) and DM50S. Demonstrate reflection
and refraction using ripple tank, then discuss Huygens’ wavelet model
of reflection and refraction. Use Activity 170P or 180S to demonstrate
principle of least time to show that the shortest-time path is consistent
with Snell’s Law.
6.3 Wave
behaviour
understood
in detail
Young’s promotion of wave theory in the 19th century, Fraunhofer’s
development of the grating, measurements of the wavelength of light.
Activities
DM 40S 'Overlapping
ripples'
DM 50S 'Ripple tank
images'
Ripple tank software
Ripple tank
Activity 170P 'A focusing
mirror with string’
Activity 180S ‘Designing
parabolic mirrors’
Homework
Reading 30T 'Historical
attempts to measure the
speed of light'
Qs 110S ‘Measuring the
speed of light’
Qs p139
Reading 70T ‘More about
Snell’s Law’
Activity 210E
‘Interference patterns in
a soap film’
Qs p144
Qs 130X ‘Calculating
wavelength in two slit

Explain interference effects qualitatively in terms of wave
superposition.
 Observe and record the interference pattern obtained in a
Young’s slits experiment.
 Explain, with the aid of a diagram, the formation of bright and
dark fringes in a Young’s slit experiment.
 Understand the derivation of the equation n = d sin .
 Use the equation n = d sin  to carry out calculations on
interference experiments, including the determination of laser
wavelengths.
 Use the equation n = d sin  to predict the effect of altering
the slit spacing.
 Explain light interference in terms of wave superposition
effects.
Lesson 9: Interference. Recap sound and water wave interference.
Introduce with Activity 210E demonstration. Demonstrate Young’s slits
experiment using laser source and various slit spacings, recording the
fringe spacing (Activity 230E). Explain light interference, using the
handout “Two slit light interference” and p141. It is important to stress
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Lesson
Content
that each slit acts like a point source of circular waves, with
constructive interference arising only at those angles corresponding to
path differences of whole number of waves. Go through derivation of
n = d sin , and sample calculation of laser wavelength from Young’s
slits results. Use also ripple tank and/or ripple tank software to show
how fringe spacing changes with changes in wavelength and slit
spacing.
Activities
Activity 230E 'Measuring
wavelength with Young's
slits'
Homework
interference’
Qs 140X ‘Colours in thin films’
Qs 150S ‘Questions on the
two slit experiment’
Qs 170S ‘Explaining two slit
interference’
Qs 180S ‘Two source
interference: some
calculations’
Qs 190S ‘Superposition of
radio waves’
Reading 50T ‘Fading and
interference’

Observe and record the diffraction pattern obtained when
laser light is passed through a diffraction grating.
 Explain, with the aid of a diagram, the formation of the
diffraction pattern.
 Understand the derivation of the equation n = d sin .
 Use the equation n = d sin  to carry out calculations on
diffraction grating experiments, including the determination of
laser wavelengths.
 Use the equation n = d sin  to predict the effect of altering
the grating spacing.
 Explain diffraction in terms of wave superposition effects.
 Explain how a diffraction grating produces a spectrum when
illuminated with white light.
 Explain diffraction in terms of wave superposition effects.
Lesson 10-11: The diffraction grating. Demonstrate the difference
between light reflected from mirror and that reflected from the surface
of a CD. See also butterfly wing on p123. These phenomena can be
explained by diffraction. Demonstrate diffraction of laser light with
grating, recording the positions of the diffraction spots for the three
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Lesson
Content
different gratings. Explain origin of diffraction pattern as per p143,
using the handout “Diffraction grating calculations”. Note that the
different spots correspond to the orders n = 0, n = 1,… etc. In other
words, the index of the order corresponds to the number of
wavelengths path difference between waves coming through adjacent
slits. Now use measurements made with the three gratings to
determine the laser wavelength. Different students could be given
different measurements from the pool of results to analyse. Note that d
in the equation is much smaller than in two-slit interference, hence the
diffraction pattern is more spread out. It is worthwhile pointing out the
link with diffraction in ripple tank experiments: each slit acts as a point
source, and the diffracted waves superpose to give the observed
effects.
Discuss, using n = d sin , why red light will be diffracted more than
blue. Discuss the appearance of the surface of a CD, explaining how it
can act as a reflection grating to produce diffraction effects, with
different colours within the white light being diffracted at different
angles in accordance with n = d sin . It is worthwhile showing a
diagram of how the reflection grating produces diffraction effects.
Explain butterfly wing effects similarly. Can also use hand
spectroscopes to look at white light or monochromatic sources, noting
both the dispersion effects and the multiple orders. The “diffraction
spectacles” are a fun tool to use.




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Activities
Activity 240E 'Measuring
the wavelength of laser
light'
DM 60S ‘Diffraction and
interference for pleasure’
Homework
Qs p144
Qs 200S ‘Grating calculations’
Qs 210S ‘Using diffraction
gratings’
UP G492 Specimen Q9;
June 08 Q2; June 08 Q8;
June 07 Q11
Observe diffraction by a single slit or aperture using light
and/or water waves, including the effect of varying the slit
width and the wavelength.
Explain the diffraction effects observed in terms of the
equation  = d sin .
Recall and use the beam spreading relationship /d = W/L =
sin  to explain the observations made on varying slit width
and wavelength.
Recall and use the beam spreading relationship /d = W/L =
sin  to perform calculations on telescope and radar
resolution.
A. M. James, Matthew Arnold School, Oxford
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Lesson
Content
 Explain diffraction in terms of wave superposition effects.
Lesson 12: Diffraction by a single aperture. See applet at
www.phys.hawaii.edu/%7Eteb/optics/java/slitdiffr/.
Demonstrate diffraction using the adjustable single slit, white light
source and colour filter and/or laser, using Activity 220E. Also
demonstrate diffraction through a single aperture using ripple tank, to
show the effect of narrowing the slit and reducing the wavelength on
the width of the diffracted beam. It is also possible to see diffraction
through a narrow gap between two fingers. As an everyday example in
the school laboratory, discuss the narrow beams produced by infra red
remote controls, contrasting with the much wider coverage provided
by longer wavelength wireless transmitter. Discuss theory behind
beam spreading relationship /d = W 1/2/L = sin , relating to
observations made with ripple tank and single slit light diffraction (note
that d here is aperture size, not slit spacing). Make the point that
resolution is improved by using large diameter dishes, illustrating with
a calculation. You could mention synthetic aperture radar techniques
and very long baseline interferometry radio telescopes as ways of
artificially creating a giant mirror. When explaining single aperture
diffraction using “Diffraction at a single aperture” oht, develop the
argument as follows: (1) recap diffraction grating in terms of path
difference being whole number of wavelength only at specific angle;
(2) discuss phasor interpretation of diffraction grating; (3) discuss
single aperture diffraction: splitting of wavefront into series of paths,
which have constant difference, and therefore phasors add to zero in a
circle. This is only true for angle  such that  = d sin .
optional
Activities
Homework
Activity 220E ‘Diffraction
by a slit’: use the
mounted adjustable slit
with a carbon filament
lamp, filters and the laser
Qs p148 (not phasor
examples)

Investigate how the wavelength of light can be measured with
more precision and accuracy using successively more refined
techniques
Lesson 13: Measuring the wavelength of light better.
Do Activity 251E, 252E, 253E as demonstrations to show how light
wavelength can be gradually better measured.
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A. M. James, Matthew Arnold School, Oxford
Activities 251E, 252E,
253E ‘Measuring the
wavelength of light better
10
Lesson
Content
6.4 Looking
Forward
Use of phasor representations, link from EM waves to quantum
behaviour
Activities
and better’
Homework
Activity 260S 'Introducing
phasors',
Activity 270S 'Amplitude
and frequency of
oscillations with phasors',
Activity 280S 'Two
phasors at once',
Activity 300S 'Phasors
across space'
Activity 320S 'Young's
slits by phasors',
Activity 330S 'Phasors to
account for two slits'
Activity 350S 'Diffraction
by phasors'
Qs 220S ‘Phasors to
oscillations’
Qs 230S ‘Wave to phasor’
Activity 340S 'Summing
two phasors over time'
Activity 310S 'Beats:
Seen and heard'
Activity 320S 'Young's
slits by phasors'
Activity 330S 'Phasors to
account for two slits'
Qs p148

Use software modelling activities to investigate wave
superposition phenomena using phasors.
Lesson 14: Re-introduce phasors using selection from software
Activities 260S, 270S, 280S, 300S. Now use software Activities 320S
and 330S to explain Young’s slits in terms of phasors. Finish with
Activity 350S to explain diffraction in terms of phasors. This is a good
activity to show the dramatic effect on beam spreading caused by
narrowing down a slit until it is comparable to the wavelength of the
light.

Explore superposition effects using software models to add
phasors
Lesson 15: Explore superposition effects using the following: Activity
340S 'Summing two phasors over time', Activity 310S 'Beats: Seen
and heard', Activity 320S
'Young's slits by phasors', Activity
330S 'Phasors to account for two slits'
Chapter 6 test
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A. M. James, Matthew Arnold School, Oxford
Qs 80X ‘Superposition
outside the laboratory’
Qs p150
11