Answer 4_6_6

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)               

 

(a) l = c/f = 3 ´ 108 m/s ¸ 12.5 ´ 109 Hz = 0.024 m (= 2.4 cm) (P)

 

(b) sin q = l/a = 0.024 m/1.6 m = 0. 015 (P)

 

q = sin-1 0.015 = 0.86o (P)

 

(c) Radius = 3.6 ´ 107 m ´ tan 0.86 = 3.6 ´ 107 m ´ 0.015 (P)

 

= 540 000 m  (= 540 km) (P)

 

 

 

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