Download Standing waves in the microwave range

Standing waves in the microwave range
TEP
Related topics
Microwaves, electromagnetic waves, reflection, inverse square law
Principle
If electromagnetic waves are reflected to and fro between two reflectors, a standing wave
results. The wavelength λ of the standing wave can be used to determined the frequency f
of the waves.
Note
Prior to performing this experiment, it would be helpful, though not mandatory, to perform
the experiments P2460301 "Reflection, transmission, and refraction of microwaves" and
P2460401 "Propagation of microwaves (inverse square law)".
Equipment
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1
1
1
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Microwave set 11742-93
Microwave transmitter
Microwave probe
Microwave control unit
Metal plate
Additional equipment
Multi-range meter, analogue
Connecting cord, 32 A, 750 mm, red
Connecting cord, 32 A, 750 mm, blue
Barrel base PHYWE
Support rod, stainless steel 18/8, l = 250 mm, d = 10 mm
Right angle clamp PHYWE
Plate holder, opening width 0-10 mm
Adhesive tape
07028-01
07362-01
07362-04
02006-55
02031-00
02040-55
02062-00
Fig. 1: Experiment set-up
Tasks
Measure the wavelength of a standing wave and determine its frequency based on this
value. Determine the state of oscillation directly at the reflector by way of extrapolation.
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TEP
Standing waves in the microwave range
Background knowledge
If a wave is reflected between two locations, a standing wave results between these
locations. A standing wave has fixed antinodes and nodes.
The standing wave forms as a result of the superposition of two waves of the same
frequency and amplitude propagating in opposite directions. The frequency of the standing
wave is identical to the frequency of the waves, but its (maximum) amplitude is twice the
original amplitude.
Since all electromagnetic waves propagate at the speed of light (c = 3·108 m/s), the
wavelength λ for the standing wave can be used to determine its frequency:
f=
c
λ
(1)
Set-up and procedure
Set the experiment up as shown in Fig. 2.
Fig. 2: Experiment set-up
Connect the microwave transmitter and probe to their associated sockets of the control unit
(see Fig. 3). Connect the multi-range meter to the voltmeter output of the control unit and
select the 3 V measuring range (direct voltage). The loudspeaker and internal or external
modulation are not required for this experiment.
Fig. 3: Connectors and settings of the control unit
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Standing waves in the microwave range
TEP
Mount the probe and reflector plate (use a clamp holder) on the support rod in the barrel
base by way of the boss head (see Fig. 4). Ensure that the dot-shaped mark of the probe
points upwards. There is no need for fastening an additional reflector on the transmitter,
since the transmitter housing is reflective itself. If necessary, fasten the meter rule to the
experiment surface by way of some adhesive tape.
Fig. 4: Fastening of the reflector plate and probe
Position the transmitter and reflector plate at opposite ends of the scale on the meter rule
(e.g. the transmitter at 790 mm and the plate at 80 mm). Ensure that the plate is
absolutely perpendicular and in a centred position in the beam path so that the radiation
will be reflected back directly to the transmitter.
Fig. 5: Experiment set-up in detail
Place the probe in the beam path so that the probe is perpendicular to the direction of
propagation of the radiation and the measuring head is located directly above the meter
rule (see Fig. 5). Switch the microwave transmitter on by connecting the control unit to the
mains power supply and set the amplitude controller to maximum. Check the height of the
probe in its holder by varying the height of the boss head in order to maximise the
voltmeter reading. If necessary, reduce the amplitude if the selected measuring range is
exceeded when changing the position by a few centimetres along the meter rule.
With an accuracy of half a centimetre, position the probe as close to the reflector plate as
possible without touching the latter with the probe (use the scale of the meter rule for
orientation).
Then, measure the radiation intensity for various positions of the probe. To do so, move the
probe towards the transmitter in steps of 0.5 cm and note down the reading of the
voltmeter. When reading the position, ensure to look at the meter rule perpendicularly from
above without any parallax. Ensure also that the probe is always aligned perpendicularly
with regard to the meter rule, i.e. that it is not offset (see Fig. 6). Inaccuracies when
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Standing waves in the microwave range
TEP
reading the meter rule are the main source of error during this experiment. This is why the
highest possible level of accuracy is absolutely essential. Record a minimum of 15 to 20
measurement values.
Fig. 6: Reading the meter rule (for example the position s = 440 mm)
Then, switch the internal loudspeaker of the control unit on and set the modulator to
"internal". Move the probe along the meter rule over the entire distance and listen closely
to the volume of the signal. Note down your observation.
Evaluation
Determine the periodicity of the standing wave, and in a next step its frequency, based on
the measurement data. Perform an extrapolation in order to determine the oscillation state
at the location of the reflector plate. For your representation, transform the measured
(absolute) positions into relative positions with regard to the transmitter.
Please note that, for smaller distances s, the intensity profile along the standing wave is
subject to a clear decrease (see also the experiment P2460401 "Propagation of microwaves
(inverse square law)". This is also the reason why the volume of the loudspeaker signal
increases strongly towards the transmitter in the second part of the experiment.
Fig. 7: Standing wave with intensity variation
This loss of intensity despite the reflection is caused by the broadening of the beam. As a
result, part of the microwave radiation is reflected into angles outside of the original beam
path. Figure 7 shows a comparison measurement for positions in the direct vicinity of the
transmitter.
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Standing waves in the microwave range
TEP
In order to determine the periodicity based on the adaptation of a sine function, we
recommend using only the values taken in the vicinity of the reflector, since this is where
the changes are smallest in the sense of the inverse square law.
(Absolute) position Relative position s
in mm
in mm
U in V
100
690
0.125
105
685
2.175
110
680
1.775
115
675
0.05
120
670
1.875
125
665
2.9
130
660
0.05
135
655
1.875
140
650
2.675
145
645
0.05
150
640
2.15
155
635
1.95
160
630
1.05
165
625
0.95
170
620
2.75
175
615
1.25
180
610
0.225
185
605
2.525
Table 1: Example data
Fig. 8: Standing wave with extrapolation
Based on the example data in table 1, the adaptation of a sine function leads to a
periodicity of 15.79 mm for the standing wave (see Fig. 8). Since the distance of the
minima (nodes) or maxima (antinodes) corresponds to half the wavelength, this periodicity
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TEP
Standing waves in the microwave range
leads to a wavelength of 31.58 mm.
Correspondingly, the resulting value for the frequency f is
c
m
1
f = =3⋅108 /31.58⋅10−3 m≈9.499⋅109
λ
s
s
(2)
This means that the microwave transmitter is operated with 9.5 GHz.
If the adaptation (see Fig. 8) is extrapolated up to the location of the metal plate
(here: 710 mm), it becomes obvious that there is a node (zero amplitude). This is exactly
the reflection requirement for the electric field vector: The plate is a location of reflection
so that a standing wave can form.
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