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A certain 50.0-Hz AC power line radiates an electromagnetic wave having a maximum electric field strength of 13.0 kV/m. (a) What is the wavelength of this very low frequency electromagnetic wave? (b) What is its maximum magnetic field strength?

(a) 6.00 × 10 6 m size 12{5 "." "00" times "10" rSup { size 8{6} } " m"} {}

(b) 4 . 33 × 10 5 T size 12{4 "." "33" times "10" rSup { size 8{ - 5} } " T"} {}

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During normal beating, the heart creates a maximum 4.00-mV potential across 0.300 m of a person’s chest, creating a 1.00-Hz electromagnetic wave. (a) What is the maximum electric field strength created? (b) What is the corresponding maximum magnetic field strength in the electromagnetic wave? (c) What is the wavelength of the electromagnetic wave?

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(a) The ideal size (most efficient) for a broadcast antenna with one end on the ground is one-fourth the wavelength ( λ / 4 size 12{λ/4} {} ) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 50.0 m high, what frequency does it broadcast most efficiently? Is this in the AM or FM band? (b) Discuss the analogy of the fundamental resonant mode of an air column closed at one end to the resonance of currents on an antenna that is one-fourth their wavelength.

(a) 1.50 × 10 6 Hz, AM band
(b) The resonance of currents on an antenna that is 1/4 their wavelength is analogous to the fundamental resonant mode of an air column closed at one end, since the tube also has a length equal to 1/4 the wavelength of the fundamental oscillation.

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(a) What is the wavelength of 100-MHz radio waves used in an MRI unit? (b) If the frequencies are swept over a ± 1 . 00 size 12{ +- 1 "." "00"%} {} range centered on 100 MHz, what is the range of wavelengths broadcast?

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(a) What is the frequency of the 193-nm ultraviolet radiation used in laser eye surgery? (b) Assuming the accuracy with which this EM radiation can ablate the cornea is directly proportional to wavelength, how much more accurate can this UV be than the shortest visible wavelength of light?

(a) 1 . 55 × 10 15 Hz size 12{1 "." "55" times "10" rSup { size 8{"15"} } " Hz"} {}

(b) The shortest wavelength of visible light is 380 nm, so that

λ visible λ UV = 380 nm 193 nm = 1 . 97 . alignl { stack { size 12{ { {λ rSub { size 8{"visible"} } } over {λ rSub { size 8{"UV"} } } } } {} #= { {"380 nm"} over {"193 nm"} } {} # =1 "." "97" "." {}} } {}

In other words, the UV radiation is 97% more accurate than the shortest wavelength of visible light, or almost twice as accurate!

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TV-reception antennas for VHF are constructed with cross wires supported at their centers, as shown in [link] . The ideal length for the cross wires is one-half the wavelength to be received, with the more expensive antennas having one for each channel. Suppose you measure the lengths of the wires for particular channels and find them to be 1.94 and 0.753 m long, respectively. What are the frequencies for these channels?

The picture of a television reception antenna mounted on the roof of a house. An enlarged image of the antenna is also shown. The antenna has a long horizontal rod having smaller cross wires of decreasing length from left to right. The cross wires are numbered from two to thirteen.
A television reception antenna has cross wires of various lengths to most efficiently receive different wavelengths.
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Conversations with astronauts on lunar walks had an echo that was used to estimate the distance to the Moon. The sound spoken by the person on Earth was transformed into a radio signal sent to the Moon, and transformed back into sound on a speaker inside the astronaut’s space suit. This sound was picked up by the microphone in the space suit (intended for the astronaut’s voice) and sent back to Earth as a radio echo of sorts. If the round-trip time was 2.60 s, what was the approximate distance to the Moon, neglecting any delays in the electronics?

3 . 90 × 10 8 m size 12{3 "." "90" times "10" rSup { size 8{8} } " m"} {}

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Lunar astronauts placed a reflector on the Moon’s surface, off which a laser beam is periodically reflected. The distance to the Moon is calculated from the round-trip time. (a) To what accuracy in meters can the distance to the Moon be determined, if this time can be measured to 0.100 ns? (b) What percent accuracy is this, given the average distance to the Moon is 3 . 84 × 10 8 m size 12{3 "." "84"´"10" rSup { size 8{8} } " m"} {} ?

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Radar is used to determine distances to various objects by measuring the round-trip time for an echo from the object. (a) How far away is the planet Venus if the echo time is 1000 s? (b) What is the echo time for a car 75.0 m from a Highway Police radar unit? (c) How accurately (in nanoseconds) must you be able to measure the echo time to an airplane 12.0 km away to determine its distance within 10.0 m?

(a) 1 . 50 × 10 11 m size 12{1 "." "50" times "10" rSup { size 8{"11"} } " m"} {}

(b) 0 . 500 μ s size 12{0 "." "500 "ms} {}

(c) 66.7 ns

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Integrated Concepts

(a) Calculate the ratio of the highest to lowest frequencies of electromagnetic waves the eye can see, given the wavelength range of visible light is from 380 to 760 nm. (b) Compare this with the ratio of highest to lowest frequencies the ear can hear.

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Integrated Concepts

(a) Calculate the rate in watts at which heat transfer through radiation occurs (almost entirely in the infrared) from 1 . 0 m 2 size 12{1 "." 0" m" rSup { size 8{2} } } {} of the Earth’s surface at night. Assume the emissivity is 0.90, the temperature of the Earth is 15º C size 12{"15"°C} {} , and that of outer space is 2.7 K. (b) Compare the intensity of this radiation with that coming to the Earth from the Sun during the day, which averages about 800 W/m 2 size 12{"800"" W/m" rSup { size 8{2} } } {} , only half of which is absorbed. (c) What is the maximum magnetic field strength in the outgoing radiation, assuming it is a continuous wave?

(a) 3 . 5 × 10 2 W/m 2 size 12{-3 "." 5´"10" rSup { size 8{2} } " W/m" rSup { size 8{2} } } {}

(b) 88%

(c) 1 . 7 μ T size 12{1 "." 7 mT} {}

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Questions & Answers

full meaning of GPS system
Anaele Reply
how to prove that Newton's law of universal gravitation F = GmM ______ R²
Kaka Reply
sir dose it apply to the human system
Olubukola Reply
prove that the centrimental force Fc= M1V² _________ r
Kaka Reply
prove that centripetal force Fc = MV² ______ r
Kaka
how lesers can transmit information
mitul Reply
griffts bridge derivative
Ganesh Reply
below me
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
Timothy Reply
what is a conductor
Timothy
hello
Timothy
below me
why below you
Timothy
no....I said below me ...... nothing below .....ok?
dust particles contains both positive and negative charge particles
Mbutene
corona charge can verify
Stephen
when pressure increases the temperature remain what?
Ibrahim Reply
what is frequency
Mbionyi Reply
define precision briefly
Sujitha Reply
CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.
MITHRA Reply
hope this helps
what's critical angle
Mahmud Reply
The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
dude.....next time Google it
okay whatever
Chidalu
pls who can give the definition of relative density?
Temiloluwa
the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
Chidalu
What is momentum
aliyu Reply
mass ×velocity
Chidalu
it is the product of mass ×velocity of an object
Chidalu
how do I highlight a sentence]p? I select the sentence but get options like copy or web search but no highlight. tks. src
Sean Reply
then you can edit your work anyway you want
Wat is the relationship between Instataneous velocity
Oyinlusi Reply
Instantaneous velocity is defined as the rate of change of position for a time interval which is almost equal to zero
Astronomy

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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