# Sec 7.9 - Waves 241 times they cancel This leads to a...

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Waves 241 7.9 WIRELESS RADIO WAVES Radio waves are coordinated oscillations of electric and magnetic F elds that can trans- mit energy from one place to another, even through empty space. When we speak of the electric and magnetic F elds together, we refer to them as the electromagnetic (EM) F eld. Radio waves are a type of electromagnetic wave . What is oscillating is not a times they cancel. This leads to a pulsating of the loudness of the sound wave. The rate at which the loudness pulsates equals the difference of the two frequencies—in this case the difference equals 261.63 262.63 = 1 Hz, or 1 beat/sec. So, the period of beats, T B , is 1 sec. An example illustrates how this beating comes about. In Figure 7.27 , the sound wave shown in the lower curve oscillates 20 times in 40 msec, so its frequency is f 1 = 20 ÷ 40 msec = 500 Hz. The wave shown in the middle curve oscillates 21 times in 40 seconds, so its frequency f 2 = 21 ÷ 40 msec = 525 Hz. The difference between the two frequencies is 525 − 500 = 25 Hz. The wave shown at the top is the sum of the two other waves, obtained by adding the displacements of the two at each instant in time. At time t = 40 msec, both original waves are at one of their maximums (crests), so when they are added, a large value is obtained. At t = 20 msec, one of the original waves is at a maximum whereas the other is at a minimum, so when they are added, a zero value is obtained. They add destructively. At t = 60 msec they again add destructively. The period, T B , of the beats (time between destructive interference times) is seen to equal 40 msec. This equals the inverse of the frequency difference: T ff B = 1 21 , where f 2 is the larger of the two frequencies (so we get a positive result). In our example we F nd T B 1 525 Hz 500 Hz = 1 25Hz =40 10 sec=4 –3 0 s e c m This calculated beat period agrees with the period seen in the graph. To summarize, the beat period is the time is takes for two waves of unequal frequency to get out of synch (out of phase) and then back in synch (in phase) with each other. FIGURE 7.27 Illustration of wave beats. The top wave is the sum of the two lower waves. Each wave is graphed on a different vertical axis. Time (msec) Displacement or pressure diference 70 60 50 40 30 20 10 0 T B T B TAF-K10173-08-1107-007.indd 241 TAF-K10173-08-1107-007.indd 241 4/24/09 9:28:30 PM 4/24/09 9:28:30 PM

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242 The Silicon Web: Physics for the Internet Age material object or medium but rather the electric and magnetic f elds themselves. Radio waves are thereFore quite diFFerent From sound waves, which require a material medium such as air to travel. ±or example, a radio wave generated on Earth could cause changes in the actions oF the Rover vehicles on Mars, as in Figure 7.28 . In contrast, a loud sound made in the Earth’s atmosphere cannot be “heard” on Mars, because sound waves cannot travel through empty space. (Despite the exciting sound eFFects we hear in our Favorite sci-f movies.) Another way in which radio waves are diFFerent From sound waves is their Frequency range. Commercial radio stations operate at very high Frequencies—0.5–100 MHz—compared to sound Frequencies, which are in the human
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Sec 7.9 - Waves 241 times they cancel This leads to a...

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