Answer :
a) The intensity at a quarter of the distance is 1.068 W/[tex]m^2[/tex].
b) The wavelength of the transmitted signal is approximately 2.972 m.
c) tThe distance from the source when the intensity is 0.134 W/[tex]m^2[/tex] is approximately 1183.5 m.
d) The absorption pressure at that distance is approximately 4.47 x [tex]10^{-10}[/tex] Pa.
e) The effective electric field (rms) at that distance is approximately 1.32 x [tex]10^{-4}[/tex] V/m.
To solve the given problems, we need to use the formulas related to electromagnetic waves and their properties.
a) The intensity of a wave is inversely proportional to the square of the distance from the source.
Therefore, if the distance is reduced to a quarter, the intensity will increase by a factor of 4.
Thus, the intensity at a quarter of the distance from the radio station will be 4 times the initial intensity: I = 4 * 0.267 W/[tex]m^2[/tex] = 1.068 W/[tex]m^2[/tex].
b) The wavelength of a wave can be determined using the formula: wavelength = speed of light / frequency.
The speed of light in a vacuum is approximately 3 x 10^8 m/s.
Converting the frequency from MHz to Hz, we have f = 100.8 x 10^6 Hz.
Substituting these values into the formula, we get: wavelength = (3 x 10^8 m/s) / (100.8 x 10^6 Hz) ≈ 2.972 m.
c) To find the distance from the source when the intensity is 0.134 W/[tex]m^2[/tex], we rearrange the formula for intensity and distance: distance = √(power / (4π * intensity)).
Given that the power of the antenna is 5 MW (5 x 10^6 W) and the intensity is 0.134 W/[tex]m^2[/tex], we can calculate the distance: distance = √((5 x 10^6 W) / (4π * 0.134 W/m^2)) ≈ 1183.5 m.
d) The absorption pressure exerted by the wave can be calculated using the formula: pressure = intensity / (speed of light).
Substituting the intensity and the speed of light, we get: pressure = 0.134 W/[tex]m^2[/tex] / (3 x 10^8 m/s) ≈ 4.47 x 10^-10 Pa.
e) The effective electric field (rms) can be determined using the formula: electric field = √(2 * power / (speed of light * area)).
Given that the power is 5 MW, the speed of light is 3 x 10^8 m/s, and assuming the wave is spreading in all directions (isotropic), the area is 4π[tex]r^2[/tex], where r is the distance.
Substituting these values, we have: electric field = √(2 * (5 x 10^6 W) / (3 x 10^8 m/s * (4π * (1183.5 m)^2))) ≈ 1.32 x [tex]10^{-4}[/tex] V/m.
In summary, a) the intensity at a quarter of the distance is 1.068 W/[tex]m^2[/tex], b) the wavelength of the transmitted signal is approximately 2.972 m, c) the distance from the source when the intensity is 0.134 W/[tex]m^2[/tex] is approximately 1183.5 m, d) the absorption pressure at that distance is approximately 4.47 x [tex]10^{-10}[/tex] Pa, and e) the effective electric field (rms) at that distance is approximately 1.32 x [tex]10^{-4}[/tex] V/m.
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