Cases – Chapter 12
1. Microwave ovens allow for some interesting cooking and funny disasters.
a. Baked Alaska is a dessert in which a hot, baked meringue contains cold, frozen ice cream. The reverse is Frozen Florida, a
dessert in which cold, frozen meringue contains boiling hot liqueur. Frozen Florida is prepared by taking a frozen meringue ball
(cooked egg whites) containing liquid liqueur (a water–alcohol mixture that remains liquid at low temperature) out of the
freezer and putting it in a microwave oven briefly. Why does the liqueur get hot while the meringue remains frozen?
b. If you try to cook an egg in a microwave oven, the egg may explode. Compare this result to the process of cooking popcorn
in a microwave oven.
c. Some prepared foods come with browning sheets that contain very thin metallic layers. These sheets become hot in a
microwave oven and help to brown the surface of the food. Why does a thin metallic film become so hot?
d. If you wrap a piece of food in sturdy metal screening with holes about 2 millimeters on a side, the food won’t cook in a
microwave oven. Why can’t the microwaves get through the screen’s holes the way light can?
2. As a DJ at a very small local radio station, you often find yourself involved in technical issues for the station’s two channels,
one of which is AM at 1020 kHz and the other of which is FM at 89.5 MHz. The station is in the process of building a new
transmitting system.
a. To save money, the director wants to use a single antenna for both channels. You warn him that the AM channel needs a
taller antenna than the FM channel. Why is that true?
b. The director had planned to put the antennas next to the station, which is in a valley at the base of a small mountain. You
suggest putting them at the top of the mountain, despite the extra cost of wires. Why is altitude important, particularly for the
FM antenna?
c. The AM channel must be careful not to “overmodulate” the radio wave during very loud passages because it distorts the
sound people hear in their radios. You explain this effect as due to moments when the transmitter actually turns itself
completely off. Why would the transmitter stop transmitting any wave at all?
d. The FM channel must also avoid overmodulation during loud passages because it will get in trouble with the FCC. Other
FM stations in your area will also be angry at your station for spoiling the reception of their transmissions. How can your FM
station affect those other FM stations when they operate at different carrier wave frequencies?
3. Your garage door opener is triggered by a radio transmitter. You press the button in your car to open the door.
a. When you press the button, the transmitter moves charge onto and off a small antenna. Why doesn’t it just put charge on the
antenna and leave the charge there?
b. If you’re close enough to the garage door, it will open. Why must the transmitter and receiver be close together?
c. When you press the button of your transmitter, the radio in your car still sounds normal. Why doesn’t the transmitter
interfere with radio reception in your car?
d. In the early days of garage door openers you could drive around town opening other people’s garages. To make things more
secure, the transmitters now send codes to the receivers using AM modulation. Each transmitter turns itself on and off quickly
in a pattern that’s recognized only by the proper receiver. Graph the charge on a transmitter’s antenna as a function of time
during such an AM transmission.
4. When you talk on a cellular telephone, two radio waves connect you with the telephone network. Your telephone transmits one
of these waves, and a stationary base unit sends the other to you. Base units are located a few kilometers apart and each one
provides service to the telephones in its vicinity—its “cell.” A connection between a telephone and a base unit occupies one of
832 channels currently allocated to cellular communications. Each channel corresponds to radio waves of two frequencies: a
lower frequency wave (in the range 825.03–849.96 MHz) that’s emitted by the telephone and a higher frequency wave (in the
range 870.03–894.96 MHz) that’s emitted by the base unit. The waves of different channels are spaced 0.030 MHz (30 kHz)
apart and those of your telephone and its base unit are 45 MHz apart.
*a. When your telephone and its base unit are connected on Channel 1, your telephone’s wave has a frequency of 825.03 MHz,
and its base unit’s wave has a frequency of 870.03 MHz. What are the wavelengths of those two waves?
*b. What is the proper length for the telephone’s antenna if it’s to have a natural resonance at the frequency of the radio wave
it’s transmitting?
c. Why will there be a problem if 900 people in a conference center all try to use their cellular telephones at once?
d. The base unit usually has several antennas, so that it can interact with a cell phone located anywhere around it through any
wave polarization. However, a minimal base unit could get by with a single antenna oriented vertically. A single antenna
oriented horizontally would leave certain people on the ground unable to interact with this base unit at all. Where would these
people be located, and why wouldn’t they be able to interact with this horizontal antenna?
e. If the base unit were using a single vertical antenna, your telephone’s antenna would also have to be vertical to work well.
Why?
f. If you’re in a valley or a metal building, your telephone may lose contact with the base unit. Why?
g. Your telephone modulates its carrier wave in order to send your voice to the base unit. Why must it be careful not to produce
waves that have frequencies that are more than 15 kHz away from that of its carrier wave?
h. If you talk while traveling, a computer system makes sure that your telephone is always communicating with the nearest
base unit. Why is it important that every telephone and base unit transmit the weakest radio waves that still permit reliable
communication between them?
5. The Global Positioning System or GPS is a system of earth-orbiting satellites that provide position information to anyone with
a GPS radio receiver. Each satellite transmits two microwaves, one at 1.57542 GHz and the other at 1.2276 GHz. These waves
are modulated by carefully timed pulses so that by measuring exactly when it receives those pulses from four or more satellites, a
GPS receiver can determine its position on earth to within a few centimeters.
a. Because each satellite carries a time-standard cesium atomic clock, its pulses are emitted at precisely known times. The GPS
receiver knows exactly when it receives the pulses, so it can tell exactly how far it is from the satellite. How?
b. Because a GPS receiver only receives microwaves from satellites that are above the horizon, there must be at least 17
satellites in orbit at once. Why can’t the receiver detect satellites that are below the horizon?
*c. What are the wavelengths of the two microwaves?
*d. One of the reasons for using microwaves in the GPS is that microwaves can be received by small antennas with welldefined locations. How long should an antenna be to receive the lower frequency GPS microwave?
e. Geologists are using the GPS to study motions of the earth’s crust that are as small as a few millimeters. To do this, they
actually study the electric and magnetic fields of the microwaves. Why would two GPS receivers located a few centimeters
apart detect somewhat different electric and magnetic fields if they studied the microwave from one particular satellite at
precisely the same moment?
6. A cordless microphone uses a 925-MHz carrier wave to carry sound information from a performer to the audio system of a
theater.
a. The tank circuits in the microphone and in the theater’s receivers have carefully been tuned to precisely the same resonant
frequencies. Why is this adjustment important?
b. The frequencies of the waves emitted by the microphone include those slightly above and below 925 MHz. Explain.
c. Because the performer moves and tips the microphone during the performance, the theater uses two receivers at different
locations. This ensures that the radio wave from the microphone is always strong at one of the receivers. How is it possible for
the wave to be weak at one of the receivers?
d. Each receiver has two antennas oriented at right angles to one another. Why does this ensure that the receiver can detect the
radio wave regardless of how the microphone’s antenna is tipped?