1. 17 Superposition and
standing waves
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2. Introduction
When two or more waves meet, the result is found by
the principle of superposition.
At any instant, the resultant displacement is simply the
sum of the displacements of the individual waves.
Constructive and destructive interference are obvious
examples of this idea.
It also explains the formation of standing waves.
Melde’s experiment to show
standing waves
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3. Melde’s experiment
The vibrator sends waves along the string.
They reflect at the other end.
The outgoing and reflected waves then interfere.
At certain frequencies, a standing wave (or stationary
wave) pattern of loops is formed.
At certain point – nodes – the
two waves interfere
destructively.
There is no vibration. There
are nodes at the ends of the
string
node
antinode
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4. Half-way between the nodes are antinodes. The string
vibrates with a large amplitude.
When the vibration has its maximum amplitude, the two
waves are interfering constructively
Changing the frequency slightly causes the standing
waves to disappear.
Changing the length, tension or thickness of the string
causes the standing waves to appear at different
frequencies.
The wavelength of the wave is twice the distance from
one node to the next.
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5. Conditions for a standing wave
Two identical but oppositely travelling waves interfere
with each other to form a standing wave.
Often, one wave is a reflection of the other.
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Incident wave in blue, reflected wave in red
Using the principle of superposition
Diagram on slide 6 show two waves which make a standing
wave. They are shown at two instants in time.

6. 6
Two waves in
phase
Out of phase
(phase difference = ½ λ)
The waves are progressive
waves travelling in opposite
directions
Above them are the
resultant waves – worked
out by adding the
displacements of the two
progressive waves.
Air columns
When the frequency of a loudspeaker is changed, a
point is reached where the noise becomes much louder.
Sound waves are reflected by the closed end of the
column, forming a standing wave in the air column inside
the cylinder.

7. 7
λ/4 3λ/4
There is a node at the foot
of the air column and an
anti-node at the top
The lowest frequency at
which this occurs, the
length of the air column is
one quarter of the
wavelength of sound.
A standing wave is formed again at three times this
frequency, with three-quarters of the wave fitting in
the column.

8. Questions
1. A string of length 1.2 m is stretched and vibrated so
that a standing wave consisting of 2 loops is formed.
Sketch this, and calculate the wavelength of the
waves on the string.
2. Microwaves are directed at a sheet of steel. A
detector is used to investigate the intensity of the
waves between the source and the plate. A pattern
of high and low intensity regions is found; the
separation of adjacent high intensity regions is 1.5
cm. what is the wavelength of the microwaves?
3. Explain why nodes occur in standing waves.
4. In a vibrating air column experiment, the air column
is 20 cm long. The lowest frequency which produces a
standing wave is 400 Hz. Calculate the wavelength
and speed of the sound wave.
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