Standing wave patterns

Just like light reflects from a mirror, so radio waves will reflect from a smooth surface. Since the wavelengths of radio waves are much longer

than those of visible light, surfaces such as brick that appear rough and do not produce clear reflections at visible wavelengths will appear smooth to radio waves. When a surface is smooth you can predict the effect of the reflected wave by considering a virtual source on the other side of the reflecting surface. Radio waves tend to be narrow band (equivalent to a laser) and, when a direct and reflected wave interact, they form what is known as an ‘interference pattern’. The word ‘inter- ference’ can be confusing here. We are not talking about interference from an unwanted transmitter. Rather we are saying that the direct and reflected waves interfere with each other.

Imagine a receiver that receives a signal from a distant transmitter and a reflection of the signal from a smooth wall. The reflected signal has to travel further than the direct signal. This extra distance travelled means that the reflected signal will be out of phase with the direct signal by the time it reaches the receiver (this will be compounded by the fact that the wave will suffer a phase shift at the reflecting surface). At the receiver the direct and reflected waves will add together. To perform this addition we use a phasor diagram. This is very similar to a vector diagram that you use to add forces, except that each phasor represents a sine wave at a particular frequency with a particular phase shift. It is a fact that, if you add together two sine waves of exactly the same frequency with a phase offset, the result is another sine wave at that frequency with a phase different from that of either of the constituents. You can use a phasor diagram only if all the sine waves involved are of exactly the same frequency (they are then said to be ‘coherent’). With reflected signals, the reflection will always be at exactly the same frequency as the direct signal (unless the reflection is from a moving object). Indeed, phasor diagrams are not limited to adding two sine waves together; as long as the signals are all coherent, you can use such a diagram to add together as many sine waves as you wish. For more on phasor addition, refer to the appendix.

We shall now return to our situation of ‘direct signal plus single reflection’ as illustrated in figure4.1. Suppose that we locate our receiver at a spot where the direct and reflected signals add in phase. We should receive a strong signal. We shall now move the transmitter a fraction of a wavelength away from the reflecting surface towards the transmitter. The

direct signal will travel a shorter distance to the receiver and the reflected signal will travel a longer distance. The two signals will no longer be in phase and the resultant of combining the signals will not be as strong. A point will be reached where the two signals are in anti-phase. At this point the signal received will be a minimum. If the reflected and direct signals are of equal amplitude they will cancel each other out, resulting in zero signal being received. This can happen over relatively short distances. If the direct and reflected waves are travelling in exactly opposite directions at the receiver, a movement of only a quarter of a wavelength will change the situation from zero phase shift (a maximum) to a phase shift of 180 degrees (a minimum).

The direction of motion of the receiver is crucial. If the receiver moves along a line that bisects the angle between the direct and reflected waves then the phase difference will not alter and the signal level received will be constant. It is possible to draw a plan view with lines joining points of equal phase difference. The line joining points where the phase differ- ence is zero will show where a maximum will occur and lines joining points where the phase difference is 180 degrees will show a minimum. Figure4.2shows a plan view of two coherent waves interacting. The solid black lines are the wave fronts representing the peaks of waves travelling in the direction indicated by the solid black arrow. The dashed lines rep- resent the troughs of an electromagnetic wave travelling in the direction

Receiver Reflecting

surface

Figure 4.1 A plan view showing two possible routes for the signal to travel from transmitter to receiver: a direct route and via a single reflection.

indicated by the dashed arrow. The faint lines join the positions where a trough of one wave will occur at the same location as a peak of the other. At these points there will be a null. As these waves travel, the points at which the null occurs stay in the same place and the interaction produces what is known as a ‘standing wave’ pattern.

In between the nulls there is a point where peaks from the two waves coincide. As the waves travel, troughs from the two waves will coincide at the same points as where peaks coincided a moment before. These points suffer a maximum disturbance. This clearly shows why we refer to an interference pattern being established between the direct and reflected waves. Figure4.3gives a three-dimensional view of the standing wave pattern. Rather than showing an instantaneous view of the electric field in a space, it shows the r.m.s. value of the electric field. The field would be varying at the frequency of the two coherent waves that produce the pattern.

One factor that affects the form of the interference pattern is the angle between the reflected and direct waves. We have used the situation where they are travelling in opposite directions. This produces the shortest distance between maxima and minima in the interference pat- tern. If the geometry of the situation is such as to produce small angles between the direct and incident waves, the distances will be much larger. The shortest distance between two successive maxima in an interference

Figure 4.2 Wave fronts indicating the peaks (solid black line) of one wave and the troughs (dashed line) of another. Thin lines join points where there would be a null.

pattern is k=(1 − cos h), where h is the angle between the directions of travel of the direct and reflected waves.

The standing wave patterns illustrated thus far are accurate for cases when the strength of the reflected wave is almost as strong as that of the

Figure 4.3 A three- dimensional view showing r.m.s. values of electric field strength within a standing wave pattern. Although the individual waves travel, the pattern remains stationary.

–25 –20 –15 –10 –5 0 5 10 0 100 200 300 400 500 600 700 800

Phase shift (degrees)

R e la tive s igna l s tre ngth ( d B)

Figure 4.4 The variation in resultant signal strength for reflection coefficients of 0.9 (producing the sharpest troughs), 0.7, 0.5, 0.3 and 0.1 (producing the shallowest troughs).

incident wave. Then, near-total cancellation will occur. If the reflected signal is weaker then the variation between peaks and troughs will not be as great. The ratio of the amplitudes of the reflected and incident waves is known as the reflection coefficient. Figure4.4shows how the variation in signal strength reduces as the reflection coefficient reduces from 0.9 to 0.1.