Answer 4_6_6
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The
ASTRA satellite transmits radio waves (speed = 3 ´
108 m/s) at a frequency of 12.5 GHz (1 GHz = 1 ´
109 Hz). (a)
What is the wavelength of the signal? (b)
The transmitting dish is 1.6 m in diameter.
Find the angle of diffraction. (c)
What
is the radius of the circular patch that receives the signal? The height
of the satellite is 3.6 ´
107 m above the earth (Ignore the curvature of the Earth)
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(a) l = c/f = 3 ´ 108 m/s ¸ 12.5 ´ 109 Hz = 0.024 m (= 2.4 cm) (P) |
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(b) sin q = l/a = 0.024 m/1.6 m = 0. 015 (P) |
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q = sin-1 0.015 = 0.86o (P) |
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(c) Radius = 3.6 ´ 107 m ´ tan 0.86 = 3.6 ´ 107 m ´ 0.015 (P) |
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= 540 000 m (=
540 km) (P) |
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