Class practical

This activity provides a good introduction to exponential decay.

Apparatus and Materials

• Infra-red transmitter

• Infra-red receiver

• Jelly fibre approx 22cm long

• DC voltmeter, 2 V full scale deflection
• DC power supply, 4.5 V or 5 V
• Knife (plastic type will be safer)
• Graph paper, laminated if possible

Health & Safety and Technical Notes

Read our standard health & safety guidance

For construction details see apparatus entries.

Procedure

1. Place the jelly fibre on the graph paper.
2. Place the transmitter and receiver at opposite ends, making sure that the diode and receiver are in good contact with the jelly and that they are aligned.

3. Adjust the pre-set potentiometer so that, with a length of about 22 cm of 'fibre', the output voltage is about 0.1 V.
4. Cut about 1 cm from the fibre.
5. Without readjusting the potentiometer, move the transmitter and receiver so that they are again in good contact with the jelly. Record the output voltage.
6. Repeat and collect a set of readings showing how output voltage, V , varies with length, x , of fibre.
7. Display the results on (a) a linear graph of V against x and (b) a graph of ln( V ) against x .
8. Discuss whether the graphs show exponential attenuation (they should!).
9. Use the graphs to obtain a value for the attenuation coefficient.

Teaching Notes

• Unlike the more traditional examples of capacitor discharge and radioactive decay, here students can easily obtain their own data and see the decay occurring without needing either to keep track of a rapidly-occurring process or to deal with background noise and random fluctuations.
• The activity models the attenuation of signals along an optical fibre (or, indeed, through any absorptive medium). In a real fibre, many kilometres of fibre are needed to produce appreciable attenuation.
• In this example, absorption is mainly by water molecules, which are good absorbers of infra-red. The purpose of the gelatine is merely to enable the water to stand up.
• To a very good approximation, the attenuation is indeed exponential and is described by
• V = V₀ exp ( -m x ) where m is the attenuation coefficient.
• A graph of V against x shows the characteristic shape associated with exponential decay, including a well-defined half length over which the output voltage halves.
• ln( V ) = ln( V₀ ) -m x
• A graph of ln( V ) against x is a straight line with gradient -m .
• This experiment comes from...

  Salters Horners Advanced Physics©

  ...University of York Science Education Group.

Diagrams are reproduced by permission of the copyright holders, Heinemann.

This experiment was safety-tested in December 2004

Demonstration

Students apply their knowledge and understanding of wave superposition to an everyday application.

Apparatus and Materials

• Wave transmitter and modulator, 3 cm
• Wave receiver, 3 cm
• Amplifier and loudspeaker
• Leads
• Model CD (see technical notes)

Health & Safety and Technical Notes

Modern equipment using a solid state diode transmitter is safe. Older equipment using a klystron transmitter uses hazardous voltages. The connectors on the leads between the transmitter and the power supply MUST be shielded types to minimise the risk of serious electric shock. The ventilation holes in the power supply may also give access to hazardous voltages, so its use MUST be closely supervised.

Read our standard health & safety guidance

To make the model CD you need

• Piece of chipboard or similar, approx 1.5 m x 20 cm (e.g. a shelf).
• Pieces of plywood or similar, e.g. 0.75 cm thick (build up with card to get the correct thickness). Calculate l/4 from the wavelength of the microwave kit you use.
• Aluminium foil or metallic spray paint.

Cut the plywood into pieces approx 8 cm x 4 cm.

Fix the plywood pieces in a line along the centre of the chipboard, so that there are spaces of about 10 cm between them.

Cover the surface of the chipboard and plywood with metal foil, or spray with metallic paint.

Procedure

1. Support the model CD as shown in the diagram. Ideally, mount it on dynamics trolleys so that it can easily be moved to and fro.
2. To get the correct orientation of transmitter and receiver, arrange for a flat part of the CD surface to be in the beam of the transmitter and adjust the transmitter and receiver to get the strongest possible signal.
3. Adjust the height of the CD so that the 3 cm waves will be reflected from the plywood pieces.

4. Slide the CD to and fro so that the plywood pieces move in and out of the beam. Notice the change in intensity of the reflected signal. When a bump is within the beam, the signal is weak, whereas when the beam is reflected from a flat section the signal is strong.

Teaching Notes

• Students can be asked to discuss the way the reflected signal strength changes, and suggest an explanation based on their knowledge of waves and superposition. Alternatively, this demonstration could be used to introduce constructive and destructive superposition.
• Information is encoded digitally onto the surface of a CD so that it can be read as a sequence of 'on/off' pulses.
• The height of the bumps is one-quarter of the wavelength of the radiation. When a bump lies within the beam, some radiation is reflected from the bump and some from the surrounding area. There is a path difference of one-half a wavelength between these two sets of reflected waves. They combine at the receiver in antiphase, and the net result is a very weak signal. With no bump in the beam, the reflected waves are all in phase so the signal is strong.
• In a real CD player, the CD surface is scanned with a laser emitting radiation of wavelength a few hundred nanometres. This model is scaled up by a factor of several hundred million.
• A more realistic version of this model involves a rotating disc. Details are given on:

  Pearson

  Follow links to:

  Salters Horners Advnced Physics

  ...and click on free resources.
• This experiment comes from...

  Salters Horners Advnced Physics©

  ...University of York Science Education Group.
• Diagrams are reproduced by permission of the copyright holders, Heinemann.

This experiment was safety-tested in January 2005

Class practical

The demonstration models the process of sampling an analogue signal at regular intervals in order to encode information digitally. Students become familiar with the phenomenon of aliasing. They learn that the sampling frequency must be at least twice the highest frequency contained in a signal.

Apparatus and Materials

• Frequency cards, one set (download from technical notes)
• Sampler cards, one set (download from technical notes)
• OHP acetate or tracing paper, clean sheets
• OHP pen

Health & Safety and Technical Notes

Read our standard health & safety guidance

The frequency cards may be printed onto OHP acetate sheets.

The sample cards should be printed on card or thick paper and then narrow slots cut out as indicated.

frequency cards

sample cards

Procedure

1. Place sampler card 1 over frequency card C, then place a sheet of clean acetate or tracing paper on top of the sampler card.
2. Make crosses or large dots at all the places where the wave is visible through the sampler card.
3. Remove the sampler and frequency cards and join the dots with a simple wavy line.
4. Reveal card 1 and compare it with the reconstructed wave. The two have the same repeat distance and similar amplitude.
5. Now repeat the procedure with sampler card 4 and frequency card A, being careful not to reveal card 4 to the observer until after you have carried out the sampling and reconstruction. This time, the reconstructed wave is far from a faithful reproduction of the original - the repeat distance is much greater - which is a surprising result.
6. Repeat with other combinations of sampler and frequency cards.

Teaching Notes

• This works well as a demonstration to the whole class using an OHP. Alternatively, students could perform the demonstration themselves in small groups - but the element of surprise is then absent.
• The frequency cards model a signal which varies sinusoidally with time.
• Provided a signal is sampled at regular intervals with a sampling frequency at least twice the signal frequency, then the original signal frequency can be faithfully reconstructed. If the sampling frequency is less than twice the signal frequency, the reconstructed signal is not faithful to the original as it has a different frequency. The introduction of spurious frequencies into a signal, as a result of inappropriate sampling, is known as aliasing.
• In telecommunications, care must be taken to ensure that the sampling frequency is at least twice the highest frequency contained in a signal.
• This experiment comes from Salters Horners Advanced Physics©, University of York Science Education Group.

Salters Horners

• Diagrams are reproduced by permission of the copyright holders, Heinemann.

This experiment was safety-checked in December 2004

Demonstration

To show that a laser beam can easily be modulated to carry information.

Apparatus and Materials

• Laser (e.g. He Ne or diode type)
• Strobe wheel
• Photodiode light detector circuit
• Audio frequency (AF) generator with amplification stage, or audio amplifier
• Loudspeaker
• Second version
• Small mirror mounted on any stiff surface e.g. a sheet of metal

Health & Safety and Technical Notes

Check that the laser is labelled 'Class 2' and warn students not to stare into the beam.

Read our standard health & safety guidance

Alignment of the beam on the photodiode is very important; if the beam is too strong the photodiode will saturate and not work well. You may need to adjust the beam so it falls just on the edge of the photodiode. You may also need to turn the lights off in the room: fluorescent tubes will cause the detector to hum at 100 Hz.

A photodiode detector circuit may be found in most electronics texts. A diagram of a very simple one is shown. It uses a 9 V battery, a 100 kΩ resistor and 0.1 μF capacitor.

Procedure

1. Align the laser so that the beam falls on the photodiode. The photodiode can be connected to the amplification stage of the AF generator and the output of the generator goes to a speaker. Note the AF generator is used only as an amplifier - an ordinary audio amplifier would also do.
2. Place the hand strobe wheel so it intercepts the laser beam. Spinning the wheel interrupts the beam many times a second, causing the audio output to click or hum.
3. If the beam is first reflected off a small mirror mounted on a surface, then a click will be heard when the surface is tapped, e.g. with a pencil.

Teaching Notes

• The photodiode is crudely converting the presence or absence of light into a click on the speaker. Interrupting or modulating (i.e. changing the intensity) the laser beam, therefore, changes the resistance of the diode. This demonstrates how digital data can be carried by a laser beam.
• The reflection experiment shows how laser detectors can be used to pick up conversations inside a room, by analyzing the vibrations of the glass windows.

Demonstration

This experiment shows that electromagnetic radiation in the infrared region is emitted from warm objects such as the human body.

Apparatus and Materials

• Mirror galvanometer, with sensitivity of about 20 mm per μA
• X-band microwave detector with its horn

Health & Safety and Technical Notes

Do not use any source of power on the diode detector. Do not use a Gunn diode source.

Read our standard health & safety guidance

Do not use a transmitter. Do not apply any source of power.

Note: even under good conditions the galvanometer, with a sensitivity in μV, will have a deflection of only about 5% fsd.

David Sumner says: "I used a diode detector, Unilab 045.674, which comes complete with a horn. This detector has enormous bandwidth. Any similar X-band receiver can be used."

Procedure

1. Set up the apparatus
2. Cover the horn window with metal foil. Zero the galvanometer and carefully switch it to the most sensitive range.
3. Remove the foil and point the horn at the body, at a distance of a few centimetres. There will be a noticeable deflection.

Teaching Notes

• Students may be surprised to discover that they emit infra-red radiation. Thermal imaging systems used by the military and by emergency workers (e.g. seeking people trapped in burning or collapsed buildings) detect this infra-red radiation.
• You can show that the detector is responding to infra-red radiation by placing a simple aluminium reflector, painted black, between the radiation source (human body) and detector. The detector will show no effect. Infra-red photons are absorbed by the black coating; any microwaves noise will be reflected without any loss.
• The experiment can also be used when discussing radio telescopes. While gathering radio waves emitted from astronomical objects, radio telescopes also detect ‘noise’ in the form of infra-red radiation from Earth’s horizon, the atmosphere and the antenna itself.
• The operation of a radio telescope involves identifying noise power and improving the signal-to-noise ratio. Radio astronomers think of the various contributions to noise in terms of system noise ‘temperature’. Nobel prize-winners Wilson and Penzias were studying just such effects when they identified cosmic microwave background radiation, corresponding to a black body radiator at a temperature of 3 K.
• Electromagnetic radiation will be detected from the head, body, limbs, etc. and also from a plastic bucket of hot water. This will mainly be infra-red radiation but may also include some from the microwave region (depending on the detector used). Radiation will not be detected from a metal container, since reflective surfaces are poor radiators of infra-red radiation.
• The long wavelength portion of the electromagnetic spectrum gathered by a radio telescope is referred to as the Rayleigh-Jeans region. In this region, as wavelength increases, the solid angle of the beam that an antenna collects also increases, meaning it sees a greater surface emitting noise consisting of infra-red radiation. But as wavelength increases, the surface brightness decreases. These two effects counteract each other, so the noise power per bandwidth interval is uniform across the...

  Rayleigh-Jeans region

• Electromagnetic radiation gathered will warm the telescope’s detector, producing ‘Johnson noise’, random motions of electrons in a metal conductor. Johnson noise power, P , in watts, given by P = 4 kT Δ f , where k is Boltzmann's constant in joules per kelvin, T is the conductor temperature in kelvins, and Δ f is the bandwidth in hertz.
• Some astronomical detectors are cooled by liquid helium to reduce Johnson noise.

This experiment was originally submitted by David Sumner, a Science Technician at Glebelands School in Surrey. It now incorporates improvements suggested by microwave engineer Jiri Polivka, of Santa Barbara, California.