8.2 The World
Communicates
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Contents
Resources
for Students
Waves
in general
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Part
of the Australia
Telescope Compact Array. Photo courtesy Mike
Gal Click on image for a larger version.
Most astronomical sources emit much
less energy at radio frequencies than at optical frequencies,
so radio telescopes need to be large to 'catch' useful
amounts of energy. But there is another reason.
The smallest angle that a telescope
can resolve is about 1.22*wavelength/diameter (the
Rayleigh criterion). Visible light has wavelengths
of about half a micron, while radio telescopes typically
use wavelengths of centimetres. So a radio telescope
must have a diameter tens of thousands of times bigger
to achieve the same resolution--to make an image with
the same detail.
It
is mechanically difficult to make steerable dishes
much bigger than the 64
m dish at Parkes. However, using an array of dishes
can greatly increase the resolution. The Australia
Telescope compact array can be used with telescopes
across Austalia to achieve baseline nearly as wide
as the whole continent. See the Australia
Telescope outreach facility.
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Resources
for Teachers
Suggestions for
examples and strategies for teaching the syllabus headlines
'1.
Current technologies associated with information transfer
use waves of one form or another.' (The following examples
do not include the EM technologies listed later.)
- Radio
(in the broader sense) is most obvious. See below on point
4.
- TV & video.
light waves -> lenses -> electrical coding of images,
broadcast by EM waves.
- photography &
film. Lenses invite treatement of geometrical optics;
f-number and exposure times -> intensity and energy;
non-reflective coatings -> thin film interference
- Writing & print
use light for reception.
Eye: EM -> chemical energy -> electrical energy
-> voltage-current waves in the nerve fibres (which
are co-ax cables)
Ray optics. Look at someone's eye in profile to see the
curvature of cornea, which is the main refracting element
in eye (it's difficult to make a good underwater eye from
biological materials). The crystalline lens is important,
especially in accommodation
Spectacles and contact lenses
A couple of interesting points: The human eye is close
to or diffraction limited in very bright conditions, and
limited by photon noise at low light intensities.
A laser printer uses light at the input end of print communication,
too.
- Speech & music
use sound and several types of wave (see the appendix
for speech). Vibration of vocal folds or turbulence at
constriction -> standing wave in vocal tract, travelling
wave to ear, mechanical wave in middle ear, fluid &
mechanical wave in cochlear, digital signal to brain.
Traditional musical instruments use standing waves in
air, strings, membranes and some 3D objects. It uses the
same transmission and reception chain.
More recent instruments also use vibrating circuits and
periodic read-out of buffers.
'2.
Sound waves can be used to illustrate many of the properties
of waves that are utilised in communication technologies.'
'3.
Recent technological developments have allowed greater use
of waves in the electromagnetic spectrum that (sic) do not
require a medium for propagation.'
The
electromagnetic
spectrum : wavelengths, frequencies, temperatures, entropy
and information.
- Radio waves
are used for broadcast radio, television, CB radio, (also
for GPS, radar, Omega, but these are not primarily for
communication)
- Microwaves
are used for telephone (including internet, mobile phones)
- Infrared.
Optic fibres using 1.4 microns and solid state lasers.
Remote controls for video etc. (Military and some snakes
use it for detection).
- Visible spectrum.
See elsewhere, but fibre optics used for telephone, data
transmission of many types
- As far as I know,
ultraviolet is not much used for communication.
Some insects use it for detection. Could UV lasers be
used for communication in the future?
- X-rays, gamma
rays. Not used for human communication?
'4.
Many communication technologies use applications of reflection
and refraction of electromagnetic waves.'
- lenses: refraction
- microwave dishes
(pay TV, telephone etc) are parabolic reflectors
- some very large
reflectors (radio telescopes) are used in attempted SETI
communication interfaces and mirrors, plane reflectors
are used in lasers
- optical cables:
reflection and refraction in step-index fibres, refraction
in graded-index fibres long range reception of (HF) AM
radio at night: 'reflection' from ionosphere (cf TV and
FM, where lamda ~ metre, therefore line of sight). It
is of course the wavelength, not the type of modulation
that is important.
'5.
Other properties of electromagnetic waves have potential
for future communication technologies and data storage technologies.'
- This may be true,
but it is difficult to teach directly! Current technologies
already use the electric field, magnetic field, amplitude,
frequency, phase, speed, wavelength, polarisation, quantisation,
superposition (linear and non-linear), non-superposition,
reflection, refraction, interference, diffraction.....
My bet would be that new technologies will use these in
new ways rather than finding too many new properties.
Vacuum field not yet used (directly), quantum superposition
not yet used commercially.
A good but very difficult project: try to think of a property
of EM waves that has not already been used for communication.
Using sound for
a variety of wave examples. 'Sound waves can be used to
illustrate many of the properties of waves that are utilised
in communication technologies.'
Superposition
in air
- i) Simple superposition.
Use two simple sources. e.g. two oscillators and two amplifiers
and speakers. Microphone and CRO. (With 2 mics close to
the sources one can use X-Y setting to get Lissajous figures.)
(Recorders blown softly in high range, the sung vowel
'ee' & whistling often appear to be approximately
sine waves on an oscilloscope.)
- ii) Interference
and diffraction. In the lab, I would suggest working at
> 1 kHz. The sound is annoying, but background noise
is less, small signals can be used, you don't blow up
speakers, and you can work on a smaller scale, so you'll
have fewer problems with reflections. The complications
of reflections and diffraction from nearby objects is
instructive in itself.
Radiation
and travelling waves using sound
- Try radiation experiment
outdoors, or out windows. For a point source, use a small
(<< lamda) hole in a large (>> lamda) baffle.
Or use a speaker in a sealed enclosure (not a reflex).
For high frequencies, you can seal most of the grille
with gaffer tape, leaving just a small hole (say 10 x
10 mm) at the bottom for your "point" source. Remember
that the floor/ground is a reflector. Diffraction and
interference using baffles with slits are also possible.
- I = P/4pi*r^2 is
tricky to organize because of reflections. One possible
solution is to do the experiment close to table-top/floor/ground
and get I = P/2pi*r^2, assuming a hard surface with high
reflection coefficient.
Using single channel CRO you can scan for r dependence.
Use 2 microphones and 2 channel CRO to see phase relations
(and the inevitable reflection effects). Note that the
sound intensity goes ~ as 1/r^2, so the CRO signal (proportional
to sound pressure) goes as 1/r.
If you have a spectrum
analysis package for your sound card (or a digital CRO with
this feature), then each team could use a different frequency,
not harmonically related, and the teacher could use industrial
grade hearing protection and aspirin.
'Model
the effect of different materials on the reflection and
absorption of sound'
This is not easy in
a high school lab.
i) The American
Standards version (using a reflectance tube) can be adapted
for experimental investigations. PVC water or sewage pipe
is fine for this purpose, and good fitting caps are available
cheaply from a plumbers' suppliers. The material to be tested
should be cut to fit neatly inside the pipe. A slot in the
pipe allows you to scan one or preferably two microphones
along the pipe. (Ideally seal the slit around the mics.)
Mics are connected to CRO. Speaker shouldn't touch pipe
to avoid mechanical effects.
Relating these to
the reflection and transmission coefficients is relatively
simple algebra. The material has a reflection coefficient
that is less than one, so the wave in the tube is the
sum of a wave to the right and a smaller wave to the left.
This can also be written as the superposition (sum) of
a standing wave and a wave to the right. At the node of
the standing wave, the amplitude (the minimum amplitude
measured in the tube) equals the amplitude of the travelling
wave, i.e. the difference between the incident and reflected.
At the antinode of the standing wave, the amplitude is
the sum of the incident and reflected.
Another tube cap, with a hole cut slightly smaller than
the ID of the tube, could be used for a rough-and- ready
measurement of transmission with a microphone just outside.
This requires baffles and is less exact, but you could
use the same gear. Perhaps point it out through a window
to minimise reflections onto your external mic, and then
the wall is part of your baffle. Most sound absorbant
materials (like acoustic wool, carpet, fibreglass batts)
absorb much more in the kHz range than at low frequencies.
'Modelling the effects of different materials'. Perhaps
this just means that one calculates what different reflection
and transmission coefficients would do to experiments
like those above. The effects in practical geometries,
such as a room, involve many reflections and are thus
rather involved to model directly. Some acousticians are
now doing that with huge ray-tracing calculations, but
it is rather time consuming for a high school project.
Alternatively, one could go straight to the reverberation
time and Sabine's formula for it. Perhaps we should wait
for clarification on what is meant here
ii) Free field measurements
are complicated indoors by the difficulty of obtaining a
free field. You can set up a nearly plane wave reflecting
at a wall by having the source >> lamda away, but
don't make it too far away or else reflections from other
surfaces are important. Stay either very near or very far
from the floor. Then the reflecting material can be fixed
to the wall.
Speed
of sound in air
i) The time
of flight is more direct. Two channel CRO, two mics
and compare phase. (This can be done at the same time as
the p ~ 1/r experiment. Careful about reflections.
You can use one mic and use the reflection: using impulse
source. This is more easily done with a sound card or storage
CRO, but can be done on a single trace CRO using careful
triggering. Set the trigger to normal and adjust the
trigger level so that it triggers on the first sound and
not on echos. Watch out for multiple reflections (and/or
set the CRO trace to catch only the first). The further
your reflector, the slower the trace and so the easier it
is to see the reflection on a non-storage oscilloscope.
i) Time of flight
in a waveguide. Here is a very low tech measurement,
accurate to a few percent. Use a long hose (say 20 m,
larger ID reduces the attenuation due to wall losses.
Garden hose is a bit too narrow: I use plastic irrigation
hose 19 mm diameter). Tap an open end with the flat of
the hand at one end and listen to the sound of the tap
and of the reflection. Listen carefully to the two sounds
(slap thump - in the echo the high frequency components
are more attenuated than the low). Pretend that these
are the first two beats in a simple rhythm (most people
have a reasonably accurate sense of rhythm) Count multiples
of the interval for 10 or 20 periods. Remember to count
from zero and that it's a round trip. Close the far end
of the pipe with a cork so you don't hear the first reflection.
This is will easily give a value within several percent
of the standard value.
ii) Standing waves
in a cylindrical tube are less direct but give
greater precision. Because of end effects on open tubes,
the change in length of tube required for one extra half
wavelength is a good way to get l. (i.e. go up one harmonic,
then adjust the length to get the same frequency). The
length of the end effect is only weakly dependent on frequency
(to a good approximation, an unbaffled tube's effective
end is 0.6 times the radius beyond its real end).
A slide whistle (swannee whistle) is a cylindrical
resonator with a moveable stop and an inbuilt control
oscillator. Blow a note with the plug nearly all the way
in. Then find a position with the slide further out and
that gives the same note. This is one (or just possibly
two) halfwavelengths. Most people have a sense of pitch
accurate to better than 1% in frequency. Slide whistles
cost only a few $ but the sound of a classroom of students
using them.....
A trombone has a long cylindrical, continuously
adjustable section and can do the same thing. Because
the slide is easily damaged, there are lots of unplayable
trombones around that will still serve for this experiment.
The school band or local junk shop may have one. A mute
may be worth the price.
iv) For approximate
results, one can use a narrow cylindrical tube and neglect
end effects. A cylindrical dijeridu is readily
made from 1-2 m of plastic conduit or plumbing pipe (smooth
the end to be blown). A flute is approximately cylindrical.
These can be used as the 'contextual' introduction to
the exercise. (Our site on the acoustics
of music has introductory material on a range of topics.)
Speed
of sound in other media. Time of flight methods are usually
complicated by reflections.
A stroke rod is a long (> 1 m) cylinder of a metal
(Al is good) in which standing waves are excited by holding
at a node (start at the centre) and rubbing at a non-node
with a cloth containing weight-lifters rosin. The harmonic
series is possible. Measure the frequency using a CRO or a
musical ear. This musical instrument is acoustically like
the bore of a flute, but uses a longitudinal wave in Al instead
of air for the standing wave. (The SSO has a set of these
instruments, but commercial Al rod is almost as good for our
purposes.)
Waves
in slinky springs, water waves, ropes, strings. Displacement-time
graphs
To reduce friction,
suspend a slinky spring from a rod or from the ceiling by
many threads of equal length threads (the longer the better
for transverse waves in a nearly linear medium). This is
a good way to allow a wave under low tension - and therefore
speed: slow enough to see in detail. This method also shows
reflection at a free end (or at least a big change in impedance)
more easily than most media. The tension is controled by
a thread at the end (~ free end for transverse wave), or
by holding it firmly in a hand (~ fixed end). Slinkies can
do transverse and longitudinal waves.
For water waves,
if you have ripple tanks you will probably have gadgets
that came with them, including vibrating bars for making
beams of plane waves, and an instruction manual. In most
cases, reflections are complicating (but interesting) factors.
Remember that water waves have non-linear superposition
when amplitude is not << depth - much loved by surfers,
but a complication for superposition.
For ropes,
rubber ropes (we use the flexible hose that your chemistry
lab may use for the Bunsen burners) have some advantages.
One is that the length can be used to control the tension
for reproducibility. Remember that ropes become non-linear
media when the displacement changes the tension (another
advantage for rubber hose). Comparing stretched ropes (observable
motion at low tension and large mass) with musical string
instruments (which do the same thing too fast to see but
fast enough to hear) is a useful teaching exercise.
Musical string instruments give convenient examples of standing
waves in stretched strings. These are very good for v =
f*lamda (and for the effect of tension and string mass per
unit length on v). The electric guitar has a few ~ velocity
transducers (pick-ups) built-in, and is a familiar context
for many students. A violin or bass bow is useful for exciting
quasi continuous standing waves. Harmonics are easier with
a bow. (Get fibreglass ones for long life.) (For more on
harmonics, see our page strings).
A stroboscope,
running at a frequency of n/m times that of the vibration
(n and m integers) can be used to 'freeze' the motion of
a periodic vibration e.g. a string in a combination of modes
or a drum head in a single mode*. If n = 1, one image per
cycle is seen. For neurological reasons it is unwise
to look at a strobe flashing at frequencies between 2 and
10 Hz.
* With the approximate exceptions of timpani and tabla,
drum head mode frequencies are not at rational fractions.
However, the second lowest mode often lasts lower than the
others.
"present and analyse
displacement-time graphs for longitudinal and transverse
wave motion"
Direct experimental measurements are tricky, although one
can sketch qualitative observations of travelling and standing
waves in a slinky or a rubber hose. The envelope of standing
waves in guitar strings can be seen and sketched. Velocity
sensors (electric guitar pickups) and pressure sensors (microphones)
are much easier for measurements. Observing that the velocity
has no DC component (the string doesn't fly away and there
is no wind), students can integrate the signal graphically,
or you can integrate it on an RC circuit to display displacement
(from pressure to displacement is two integrations).
Experiments
with mobile phones
Turn on, wrap in Al foil and phone its number. Unwrap gradually.
Demonstrates that the good conductor reflects EM waves.
More importantly, it will also stop the phone ringing during
class.
Light rays and
geometrical optics
Laser diodes are a cheap way of getting a beam with low
divergence (buy directly from an electronics or hobby store
for several $ including power supply: just add a battery.
Or else buy assembled in laser pointers). Can use to demonstrate
ray representation of fibre optics. They're also fun toys
for a while and may seem more interesting than light boxes
(lamp source and cylindrical lens, gives a vertical plane
of light). For plotting on paper, light boxes are immediately
usable. A laser can also make a vertical plane of light
by passing it through a cylindrical lens (axis horizontal).
A suitable lens is a short section of plexiglass rod. If
you have light boxes, you probably also have a kit that
goes with them: hemi-cylinders for Snell's law, 2D lenses
for making optical instruments, cylindrical mirrors et hopefully
cetera. (By the way, cylinders of perspex make good model
raindrops to show how rainbows form.)
Some
notes about a guided investigation
This was one of the FAQ's from Teachers: How to avoid the
recipe lab exercise, but still guide an investigation? Here
are some suggestions about trying to make an investigation
less recipe based. I shall use Snell's law (not widely considered
exciting) as an example. For me, the aim of teaching Snell's
law is less important than teaching the method of careful
observation, improvement of measurement technique, generalisation
and testing.
Some demonstrations
to arouse interest, e.g. dismantle camera, use telescope/
microscope, set fire to paper using lens.
Some initial contextual question(s): Where do you find lenses?
How does a lens work? Where would we be without them? Who
invented them? Who invented ?
Does light travel in straight lines? When?
When it doesn't, what happens? Explore and generalise qualitatively.
Some questions: why does the water look shallower? why does
the surface of the water look silvery and strange to swimmers
looking up?
What are the consequences for vision? For natural phenomena?
For optical instruments? (higher performance; mirages, distorted
sun, green flash; spectacles, cameras, telescopes)
Paper work. What sort of relations might be involved? If
you draw a diagram of wave fronts incident on a surface,
what would light bending at an interface look like?
How can you obtain some relevant quantitative data using
the gear we have here?
What makes the arrangement complicated? Are there ways you
can reduce/eliminate the complications or number of things
to measure?
What will be the measurement errors? In particular, what
is the largest measurement error (protractor? ruler? beam
centre estimation?) and is there any way of making it smaller?
Are there some errors that can't be reduced and thus impose
a limit to the precision of your experiment? If so, can
you reduce the other errors to this level?
Can you get a quantitative rule out of this? If different
teams find different rules, what are the cases where they
disagree? Can you test them to see which is supported experimentally?
(If they don't disagree, can they be proved to be identical?
Suppose that you don't get Snell's law, or that you get
a silly value for n, what then? Could the text books be
wrong? Could we have made an error in interpretation, or
a systematic error? How badly does Snell's law fit our data?
How does the difference compare with the error?
Application: back to some of the examples, draw qualitative
diagrams to explain operation. How does a lens or a mirage
work? Do a quantitative ray diagram?
Some
useful gear
that is either or both cheap and readily available.
A
few web resources:
- Physics
in a suitcase - "Portable lecture demonstration kits
in light and optics". Some are suitable for investigative
lab work.
- "VLAB"
Download some simulations, including reflection &
refraction, 'optics bench' with components, interference,
superposition, wave motion, waveguides.
- Spectrum_analyzers
A range of spectrum analysers
- Goldwave
Another spectrum analyser
- Light
and Matter A downloadable text book.
- The American Physical
Society's
educational links
- Acoustics
of music Our site on musical acoustics has quite a
bit about standing waves and the operation of musical
instruments. It has serious research results, but also
has a lot of introductory material aimed at high school
level.
- Some notes about
the physics
of speech.
More sites are linked
to the UNSW School of Physics' new HSC site: HSC
resources, which will be updated from time to time.
It has notes from us, lists of some of the sources of our
gear, and of course a bunch of links. You are invited to
suggest things that we might add to it, to send material
for it, or URLs that you think should be added.
See
also this
link for simple experiments.
Joe
Wolfe / J.Wolfe@unsw.edu.au/
61-2-9385 4954 (UT + 10, +11 Oct-Mar)
HSC
Physics Teachers Course
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