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 P46030 "Reflection, transmission, and refraction of microwaves" and P46040 "Propagation of microwaves (inverse square law)". Equipment Microwave set 74-93 Microwave transmitter Microwave probe Microwave control unit Metal plate Additional equipment Multi-range meter, analogue Connecting cord, 3 A, 750 mm, red Connecting cord, 3 A, 750 mm, blue Barrel base PHYWE Support rod, stainless steel 8/8, l = 50 mm, d = 0 mm Right angle clamp PHYWE Plate holder, opening width 0-0 mm Adhesive tape 0708-0 0736-0 0736-04 0006-55 003-00 0040-55 006-00 Fig. : 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. www.phywe.com P46050
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 08 m/s), the wavelength λ for the standing wave can be used to determine its frequency: f= c λ () Set-up and procedure Set the experiment up as shown in Fig.. Fig. : 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 P46050
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 www.phywe.com P46050 3
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 5 to 0 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 P46040 "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. 4 P46050
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 00 690 0.5 05 685.75 0 680.775 5 675 0.05 0 670.875 5 665.9 30 660 0.05 35 655.875 40 650.675 45 645 0.05 50 640.5 55 635.95 60 630.05 65 65 0.95 70 60.75 75 65.5 80 60 0.5 85 605.55 Table : Example data Fig. 8: Standing wave with extrapolation Based on the example data in table, the adaptation of a sine function leads to a periodicity of 5.79 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 www.phywe.com P46050 5
leads to a wavelength of 3.58 mm. Correspondingly, the resulting value for the frequency f is c m f = =3 08 /3.58 0 3 m 9.499 09 λ s s () 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: 70 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. 6 P46050