Student Worksheet
Activity 26: Investigating stationary waves on a string
Objective
(a) To observe standing waves at a number of different
frequencies
(b) To appreciate that the standing wave is a superposition
phenomenon, caused by travelling waves moving through
one another
(c) To find a relationship between frequency of vibration
and wavelength
Safety
• Sufferers from epilepsy and migraine attacks should
beware of stroboscopic light, especially at low
frequencies, as used here. Place a black screen or
curtain so that only the vibrating cord is illuminated
by the flashing light and not its surroundings.
• Make sure the cord is securely clamped at both ends
and that you do not stand too close.
Procedure
1. Stretch a length of rubber cord between wooden blocks
in two clamps on retort stands which are G-clamped
about 2 m apart to the edge of the bench. Attach a
vibration generator, driven by a signal generator, close
to one end of the cord via a wire hook, as shown in
Figure 26.
2. Set the signal generator to 10 Hz.
3. Increase the frequency slowly until the cord oscillates
in a steady pattern. The lowest-frequency pattern, the
fundamental mode, occurs when there is maximum
amplitude, an antinode, in the middle of the cord and
little or no movement at the ends. The first observed
steady pattern may have two or three antinodes.
4. Increase the frequency further until another stationary
wave occurs. Note that the distance between
successive nodes or antinodes is a half a wavelength.
5. Record the frequency of the signal generator and the
number of antinodes for each standing wave produced.
6. Observe the steady patterns using a stroboscopic light
flashing at the same frequency as the vibration
generation. Change the stroboscope frequency
gradually to observe the nature of the stationary wave.
Observe that in any given loop, all parts of the rubber
cord move in phase, although with different amplitudes.
Maximum amplitude occurs at the antinode. In adjacent
loops, the oscillations of the cord are in antiphase, that
is, they are π radians out of phase.
7. Increase the tension in the cord by loosening one
clamp and pulling the cord through the blocks. Thus the
length of the vibrating cord is kept the same.
8. Repeat steps 2 to 5.
Equipment/materials
• Two retort stands, bosses and clamps
• Two G-clamps
• Four small wooden blocks to clamp rubber cord
• Rubber cord, 1 to 4 mm2 square cross section,
1 to 2 m long
• Vibration generator
• Signal generator with low-impedance sine-wave
output, range 10–100 Hz
• Short length of stiff wire
• Ruler
• Stroboscope
Analysis of results
• Find a relationship between the wavelength of the
standing wave and the frequency of vibration.
• Find the speed of the travelling wave on the cord.
• Find out how the speed of the wave changes when
the cord is stretched.
From the examiner
To produce a stationary wave pattern by superposing
incident and reflected waves, only certain frequencies are
possible. The time taken for the wave to travel along the
length of the cord has to be an integral number of periods
of the oscillator producing the wave.
Questions
1. At which points on the cord are transmitted and reflected waves always in phase? At which points on the cord are
transmitted and reflected waves always in antiphase?
2. The fundamental frequency of the sound produced by a stretched string depends on its length, tension and mass per
unit length. In which direction does the frequency change when each of these quantities is increased, without changing
the other two? Explain your answers.
3. Standing waves are observed and used in a wide range of phenomena, for example, in a guitar. Suggest some other
examples.
Practical activities have been checked for health and safety advice by CLEAPSS. All users will need to review the
risk assessment information and may need to adapt it to local circumstances.
© Pearson Education Ltd 2008
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Figure 26
Practical activities have been checked for health and safety advice by CLEAPSS. All users will need to review the
risk assessment information and may need to adapt it to local circumstances.
© Pearson Education Ltd 2008
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Teacher Worksheet
Activity 26: Investigating stationary waves on a string
Objective
(a) To observe standing waves at a number of different
frequencies
(b) To appreciate that the standing wave is a superposition
phenomenon, caused by travelling waves moving through
one another
(c) To find a relationship between frequency of vibration
and wavelength
From the examiner
To produce a stationary wave pattern by superposing
incident and reflected waves, only certain frequencies are
possible. The time taken for the wave to travel along the
length of the cord has to be an integral number of periods
of the oscillator producing the wave.
Procedure
1. Changing the tension in the cord, either by pulling the
clamps apart or by moving the cord through one of the
clamps, enables fine tuning to be done if you want the
standing wave to occur at an arithmetically convenient
frequency (thereby enabling simple numbers to be
used).
2. For a discussion of the wave transmitted down the
cord, being reflected and interfering with the
approaching wave, it is best to work at the lowest
frequencies, that is, with only one or two antinodes if
possible. The cord can be held lightly at a node without
the wave being altered.
3. A useful discussion could be generated by considering
why the maximum amplitude decreases as the
frequency is increased and the cord is divided into
more half-wavelength sections.
4. Step 5 can be looked on as a challenge to find the
maximum number of nodes that can be counted along
the cord before the vibration of the cord just becomes a
continuous blur.
5. Very large oscillations can be generated in the cord at
low frequencies if the cord is not under much tension. It
is possible to watch these oscillations build up as an
example of resonance, with more energy being stored
in the system at each cycle.
6. This is a resonance phenomenon. As such the driver
and the driven are π/2 out of phase at resonance. The
phase difference occurs within the vibration generator
between the current in the coil – the driver – and the
motion of the plunger which is connected rigidly to the
cord – the driven.
Safety
• Sufferers from epilepsy and migraine attacks should
beware of stroboscopic light, especially at low
frequencies, as used here. Place a black screen or
curtain so that only the vibrating cord is illuminated
by the flashing light and not its surroundings.
• Make sure the cord is securely clamped at both ends
and that students do not stand too close.
Answers
Question 1
Transmitted and reflected waves are in phase at
antinodes, as we have constructive interference. They
are in antiphase at nodes, where there is always exactly
destructive interference.
Question 2
A longer cord means a longer wavelength, hence a lower
frequency, as the speed of the wave is unchanged.
As tension increases, so the speed increases, and so the
frequency increases as wavelength is unchanged.
As mass per unit length increases, the inertia becomes
greater so the speed decreases. The wavelength is
unchanged so the frequency goes down.
Question 3
It is a good class exercise to see how many examples
the group can generate.
Practical activities have been checked for health and safety advice by CLEAPSS. All users will need to review the
risk assessment information and may need to adapt it to local circumstances.
© Pearson Education Ltd 2008
This document may have been altered from the original
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Technician Worksheet
Activity 26: Investigating stationary waves on a string
Objective
(a) To observe standing waves at a number of different
frequencies
(b) To appreciate that the standing wave is a
superposition phenomenon, caused by travelling waves
moving through one another
(c) To find a relationship between frequency of vibration
and wavelength
Safety
• Sufferers from epilepsy and migraine attacks should
beware of stroboscopic light, especially at low
frequencies, as used here. Place a black screen or
curtain so that only the vibrating cord is illuminated by
the flashing light and not its surroundings.
• Make sure the cord is securely clamped at both ends
and that students do not stand too close.
Requirements per student*/group of students
Notes
Two retort stands, bosses and clamps
G-clamp the two retort stands to the edge of the bench at a
distance apart equal to the lightly-stretched length of the
rubber cord.
Two G-clamps
Four small wooden blocks, for example, hardboard sheet
50 mm square
To hold the rubber cord firmly in the clamps
Rubber cord, 1 to 4 mm2 square cross section,1 to 2 m long
The cord should be fixed horizontally above the bench under
slight tension at the height of the hook in the wire attached
to the vibration generator.
Vibration generator
The generator should be placed under the cord 2 to 5 cm
from the clamped end of the cord.
Signal generator with low-impedance sine-wave output
To drive the generator from about 10 Hz to about 100 Hz
Short length of stiff wire
One end is attached to the vibration generator, and the other
should have the end bent over to allow the rubber to be
pushed in and held.
Ruler
1.0 m ruler
Stroboscope
With a range of 10 to 100 Hz
Notes
Practical activities have been checked for health and safety advice by CLEAPSS. All users will need to review the
risk assessment information and may need to adapt it to local circumstances.
© Pearson Education Ltd 2008
This document may have been altered from the original
26/30