Topic 12.5
Stationary and
progressive waves
Stationary waves
Aims
In this experiment you will identify the length of stationary waves in a current-carrying
vibrating wire in a magnetic field. You will pay particular attention to how you can increase
the precision of the measurement.
Safety
Check electrical leads. Ensure that the wire is held firmly between the blocks.
Equipment, materials and method
1 For this experiment you will require a low-voltage ac power supply, a length of wire,
connecting leads, a metre ruler, two magnets in a holder, a prism, a board with a pulley, a
G-clamp, two wooden or plastic blocks, a micrometer and a 2.0 N weight.
2 Set up the apparatus as shown in the diagram below. The magnets should be adjusted so
that they are approximately halfway between the clamped end of the wire and the prism.
The prism should touch the wire firmly.
3 Switch on the power supply to about 6 V. Move the prism slowly along the wire until you
observe an increase in the amplitude of vibration. Find the position where the amplitude is
maximum. Record the length L.
4 Repeat the experiment several times, moving the prism first from one direction and then
from the other in order to find an average value of L.
5 Measure the average diameter of the wire, d, taking two perpendicular measurements at
several places.
6 Note the frequency of the ac supply.
Questions
1 Why should the diameter of the wire be measured at different places both vertically and
horizontally?
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Topic 12.5
Stationary and
progressive waves
2 Calculate:
(a) the wavelength of the stationary waves on the wire
(b) the speed of progressive waves on the wire at this tension.
Results
Use your results and the formula below to calculate a value for the mass per unit length  of
the wire. Hence determine the density of the wire.
The mass per unit length of the wire, , is given by
=
T
c2
where T is the tension in the wire (= 2.0 N) and c is the speed of the progressive waves on the
wire at this value of tension.
Discussion
Calculate the range of values for the length and for the diameter and hence work out the
percentage uncertainty in each measurement of the length. What is the main reason for this
uncertainty?
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Topic 12.5
Stationary and
progressive waves
Technicians Notes
Equipment and materials
For this experiment each student or pair of students will require the following equipment:
 a length of wire (SWG 32 is suitable)
 a low-voltage ac power supply to give 6 V
 connecting leads
 a metre ruler
 two magnets in a holder (Those used for small demonstration motors are suitable; there
must be a magnetic field around the wire. If you need to construct a new set, make sure
the magnets face each other across the yoke.)
 a prism (perspex ideally), or a knife edge in a block of wood if available
 a board with a pulley
 a G-clamp
 two wooden or plastic blocks
 a micrometer
 a 2.0 N weight to suspend on the free end of the wire
Safety
Check the electrical wiring.
Ensure that the G-clamp is tight and firmly holds the blocks and wire in position. It is best to
make an S-shape between the blocks. Then it is harder for the wire to be pulled through.
If the prism is glass, ensure that students do not handle it if it is dropped.
Ensure heavy apparatus is in a safe position on the bench.
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Topic 12.5
Stationary and
progressive waves
Teaching Notes
Aims
 To observe resonance / standing waves in a wire oscillating in a magnetic field.
 To measure the length of the wire, taking into consideration the uncertainty and taking
reasonable precautions to minimise this uncertainty.
 To measure the diameter of a wire, taking into account the variations in its manufacture.
Safety
Check electrical wiring. Ensure that the G-clamp is tight and firmly holds the blocks and wire
in position. If the prism is glass, ensure that students do not handle it if it is dropped. Ensure
heavy apparatus is in a safe position on the bench.
3 This experiment will take about 15 minutes.
4 The prism must be moved slowly along the wire. The magnets should be adjusted so that
they are approximately halfway between the clamped end of the wire and the prism.
5 The vibrations may not be observable away from the natural frequency.
6 Ensure that students do not ‘fix’ their readings to be the same. There should be a wide
variation in the length. Approaching the point of maximum amplitude from different
directions should give similar, but different, values. One way of ensuring this is to remove
the ruler whilst determining the position and replace it to make the measurement.
7 Suggested extension: students could be provided with a signal generator and investigate
harmonics.
Answers to questions
1 The wire’s diameter will vary along its length due to manufacturing techniques. It should
be measured in two perpendicular directions at several positions along the wire.
2 (a) The wavelength is twice the measured length of the wire.
(c) Use ‘speed = frequency  wavelength’.
Discussion
The main reason for the error in the length is the judgement by eye of where the amplitude is
maximum. The main reason for the error in the diameter would be random variations due to
the manufacturing process.
Practical assessment opportunities
3 PSA – Selecting and using equipment: 0–3 marks
(Following instructions and group work; organisation and safety assessed at end of
course.)
ISA preparation:
practical task – practice in making precise and reliable measurements, carrying out
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Topic 12.5
Stationary and
progressive waves
calculations and estimating errors
written task – carrying
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