Home Physics Wave and Sound General A radio station broadcasting at a frequency …
Physics Wave and Sound General MCQ (Single Correct)

A radio station broadcasting at a frequency of 1500 kHz generates a directional beam by using an array of 4 point source antennas driver in phase with each other by the same transmitter. The antennas are arranged along an east west line so that each antenna is 50 m from the next one.

A
In what direction will be radiated signal be greatest?
B
How much signal radiates in east west direction.

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Text Solution

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The antennas radiate symmetrically in all direction and in phase with each other hence radiated waves from the antennas can suffer constructive or destructive interference

The radiated signal will be a maximum in a direction perpendicular to the array since in this direction the waves are all in phase with each other.

If f is the frequency and C is the velocity of radio waves, then their wavelength λ is given by

λ = = or λ = 200 m.

Note that c = speed of light since the waves form part of EM spectrum

Now the spacing between the antennas in EW direction is 50 m = λ /4. Hence, in the EW direction, antennas 1 and 3 are out of phase with each other by λ /2 and so cancel each other by destructive interference. Similarly 2 and 4 cancel each other.

Thus the net signal in EW direction is zero.

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