(a) Find the values of e"/e' for seawater for the frequencies 87.5 MHz and 108 MHz. Do you expect electromagnetic waves in the 87.5-108 MHz band to experience signif- icant attenuation as they propagate through seawater? Explain your answer.

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Transmission of electromagnetic energy through the ocean is practically impossible
in certain frequency ranges due to high attenuation. In this problem, we will consider
electromagnetic waves in the typical FM radio band. For this problem, you may as-
sume that seawater (that is, the water in the ocean) is nonmagnetic and has a relative
permittivity, € 81, and a conductivity, o 4 S/m.
(a) Find the values of e"/e' for seawater for the frequencies 87.5 MHz and 108 MHz.
Do you expect electromagnetic waves in the 87.5-108 MHz band to experience signif-
icant attenuation as they propagate through seawater? Explain your answer.
(b) Consider an electromagnetic wave in the FM radio band (that is, with a fre
quency between 87.5 MHz and 108 MHz) propagating through seawater. Calculate
as a function of frequency (in MHz) the approximate propagation distance over which
the amplitude of the electric field associated with this wave is reduced by a factor of
one thousand.
(c) Now let's say that a right-hand circularly polarized electromagnetic wave at a
frequency of 100 MHz is incident on the surface of the ocean. For simplicity, let's say
that the surface of the ocean is the ry-plane with the +z-direction pointing into the
ocean's surface. The wave travels in the +z-direction. Write an expression for the
electric field phasor associated with this wave for z> 0 (that is, under the surface of
the ocean). Assume that the electric field has a magnitude of 1 V/m just below the
ocean's surface.
(d) Find an expression for the average power density that the electromagnetic wave
described in part (c) carries in the ocean. In other words, find an expression for the
average power density carried by the wave as a function of z for z > 0.
(e) Determine the depth below the surface of the ocean at which the power den-
sity carried by the electromagnetic wave in parts (c) and (d) will be attenuated by
40 dB.
Transcribed Image Text:Transmission of electromagnetic energy through the ocean is practically impossible in certain frequency ranges due to high attenuation. In this problem, we will consider electromagnetic waves in the typical FM radio band. For this problem, you may as- sume that seawater (that is, the water in the ocean) is nonmagnetic and has a relative permittivity, € 81, and a conductivity, o 4 S/m. (a) Find the values of e"/e' for seawater for the frequencies 87.5 MHz and 108 MHz. Do you expect electromagnetic waves in the 87.5-108 MHz band to experience signif- icant attenuation as they propagate through seawater? Explain your answer. (b) Consider an electromagnetic wave in the FM radio band (that is, with a fre quency between 87.5 MHz and 108 MHz) propagating through seawater. Calculate as a function of frequency (in MHz) the approximate propagation distance over which the amplitude of the electric field associated with this wave is reduced by a factor of one thousand. (c) Now let's say that a right-hand circularly polarized electromagnetic wave at a frequency of 100 MHz is incident on the surface of the ocean. For simplicity, let's say that the surface of the ocean is the ry-plane with the +z-direction pointing into the ocean's surface. The wave travels in the +z-direction. Write an expression for the electric field phasor associated with this wave for z> 0 (that is, under the surface of the ocean). Assume that the electric field has a magnitude of 1 V/m just below the ocean's surface. (d) Find an expression for the average power density that the electromagnetic wave described in part (c) carries in the ocean. In other words, find an expression for the average power density carried by the wave as a function of z for z > 0. (e) Determine the depth below the surface of the ocean at which the power den- sity carried by the electromagnetic wave in parts (c) and (d) will be attenuated by 40 dB.
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