A radio telescope consists of two antennas separated by a distance of 200 metres

Question

A radio telescope consists of two antennas separated by a distance of 200 metres. Each antenna is tuned to receive the frequency 20 MHz. The signals from each antenna are fed into a common amplifier, but one signal first passes through a phase adjustor which delays the phase by an amount chosen so that the telescope can "look" in different directions. With zero phase delay, plane radio waves incident vertically produce signals which add constructively at the amplifier. What should the phase delay be so that signals coming from an angle 10 degrees from the vertical (in the plane formed by the vertical and the line joining the antennas) add constructively at the amplifier?

Select one:
a. 34.73 m
b. 196.96 m
c. 14.55 radians
d. 3.64 radians
e. 82.5 radians

answer is 14.55 rad, how to do this?

Explanation / Answer

here,

y = v/f where v = the speed of light (3*10^8) and f is the frequency in Hz

y = the distance from the source to the plane of the antennas

y = 3*10^8 / 20*10^6
y = 15 meters

Next, solve for m.

theta = 10 degree

d*sin(theta) = m*y

where d = the distance between the antennas = 200 m

[200 * sin(10)] / 15 = m

m = 2.32

Remember that m must be an integer. (constructive waves)

Finally, the answer must be put into radians.

phase delay of the signals = 2.32* (2*pi) = 14.55 radians

then the phase delay is c. 14.55 radians

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