You find yourself on an island with no way off – You know that there are ships i

Question

You find yourself on an island with no way off – You know that there are ships in the shipping lanes that are far from the island (21 miles or 35 km) so you cannot see them with the unaided eye.

You believe that you might be able to signal the ships but you need to be able to know when the ships are there because you cannot signal all of the time – this requires you to see the ships.

Also the island is volcanic and often emits plumes of smoke and ash – so a signal fire will not work.

During your exploring of the island you have found a bunch of potentially useful equipment. This list includes:

A radio transmitter fixed at 156.8 MHz (which is the international frequency for distress signals).

Two radio towers separated by a distance of 9.56 m and each consisting of a telephone pole topped by a 1.912 m tall conductive metal antenna. Each has a wire running up the telephone pole and attached to the antenna.

You mount your telescope on a telescope tripod in the exact middle between the two radio towers. The tripod has an angle scale attached so you can tell the angle of the telescope with respect to the line connecting the two towers.

The wire connecting the transmitter to the two radio towers has an alligator clip on the end. This wire is clamped to a solid wire running between the two towers. In effect you can connect the transmitter at different relative distances from the two towers, starting at a difference in path of -20m to a path difference of +20m. It is currently set to the exact middle or a path difference of 0m.

When you look into the telescope you notice that there are periodically boats going by. They are too far away to see with your unaided eye but are radially visible in the telescope.

You have determined that the transmitter is not strong enough to reach the boats using only one antenna.

What do you do?

Explanation / Answer

Answer:

Here We need to create distance of line of sight, then create constructive interference at that common point
To know constructive interference, the path difference equal to zero or integral multiple of wavelength.
wavelength = speed of light/radio frequncy = 3 x 10^8/156.8 x 106 = 1.913 m
TO get this transmitter can be fixed at middle point near telescope. So we can make path difference=0.
And when we can see the ship/boats in telescope, we try to send signal through both antenna so that it can create stronger distress signal
as a result of constructive interference

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