Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Radio waves from a star, of wavelength 244 m, reach a radio telescope by two sep

ID: 1512686 • Letter: R

Question

Radio waves from a star, of wavelength 244 m, reach a radio telescope by two separate paths, as shown in the figure below (not drawn to scale). One is a direct path to the receiver, which is situated on the edge of a cliff by the ocean. The second is by reflection off the water. The first minimum of destructive interference occurs when the star is = 22.0° above the horizon. Find the height of the cliff. (Assume no phase change on reflection. The image is not drawn to scale; assume that the height of the radio telescope is negligible compare to the height of the cliff.)

Explanation / Answer

The signal reflected off the water travels further.
For the destructive interference, the signals need to be 50% out of phase, which occurs when the sloping distance is half a wavelength = 244/2=122 m

The vertical component is sin22 = vert/244
vert height = sin22/122m=0.003

Ans- So the height of the cliff is 0.003 m