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Magazine Problem 59
A police car's radar gun emits microwaves with a frequency of $f_{1}=36.0
\mathrm{GHz}$. The beam reflects from a speeding car, which is moving away at
\(43.0 \mathrm{m} / \mathrm{s}\) with respect to the police car. The frequency
of the reflected microwave as observed by the police is \(f_{2} .\) (a) Which is
larger, \(f_{1}\) or \(f_{2} ?\) (b) Find the frequency difference \(f_{2}-f_{1}\)
[Hint: There are two Doppler shifts. First think of the police as source and
the speeder as observer. The speeding car "retransmits" a reflected wave at
the same frequency at which it observes the incident wave. \(]\)
Problem 60
What must be the relative speed between source and receiver if the wavelength
of an EM wave as measured by the receiver is twice the wavelength as measured
by the source? Are source and observer moving closer together or farther
apart?
Problem 61
How fast would you have to drive in order to see a red light as green? Take
\(\lambda=630\) nm for red and \(\lambda=530 \mathrm{nm}\) for green.
Problem 62
Calculate the frequency of an EM wave with a wavelength the size of (a) the
thickness of a piece of paper \((60 \mu \mathrm{m}),(\mathrm{b})\) a
\(91-\mathrm{m}\) -long soccer field, (c) the diameter of Earth, (d) the
distance from Earth to the Sun.
Problem 63
The intensity of solar radiation that falls on a detector on Earth is $1.00
\mathrm{kW} / \mathrm{m}^{2} .\( The detector is a square that measures \)5.00
\mathrm{m}$ on a side and the normal to its surface makes an angle of
\(30.0^{\circ}\) with respect to the Sun's radiation. How long will it take for
the detector to measure
\(420 \mathrm{kJ}\) of energy?
Problem 65
The antenna on a cordless phone radiates microwaves at a frequency of $2.0
\mathrm{GHz}$. What is the maximum length of the antenna if it is not to
exceed half of a wavelength?
Problem 66
Two identical television signals are sent between two cities that are \(400.0 \mathrm{km}\) apart. One signal is sent through the air, and the other signal is sent through a fiber optic network. The signals are sent at the same time but the one traveling through air arrives \(7.7 \times 10^{-4}\) s before the one traveling through the glass fiber. What is the index of refraction of the glass fiber?
Problem 67
An AM radio station broadcasts at \(570 \mathrm{kHz}\). (a) What is the
wavelength of the radio wave in air? (b) If a radio is tuned to this station
and the inductance in the tuning circuit is \(0.20 \mathrm{mH},\) what is the
capacitance in the tuning circuit? (c) In the vicinity of the radio, the
amplitude of the electric field is \(0.80 \mathrm{V} / \mathrm{m} .\) The radio
uses a coil antenna of radius \(1.6 \mathrm{cm}\) with 50 turns. What is the
maximum emf induced in the antenna, assuming it is oriented for best
reception? Assume that the fields are sinusoidal functions of time.
Problem 68
A 60.0 -m \(\mathrm{W}\) pulsed laser produces a pulse of EM radia tion with
wavelength \(1060 \mathrm{nm}\) (in air) that lasts for 20.0 ps (picoseconds).
(a) In what part of the EM spectrum is this pulse? (b) How long (in
centimeters) is :
single pulse in air? (c) How long is it in water \((n=1.33) \equiv\)
(d) How many wavelengths fit in one pulse? (e) What is the total
electromagnetic energy in one pulse?
Problem 69
The range of wavelengths allotted to the radio broadcast band is from about
\(190 \mathrm{m}\) to \(550 \mathrm{m} .\) If each station needs exclusive use of
a frequency band \(10 \mathrm{kHz}\) wide, how many stations can operate in the
broadcast band?
